%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SCT171+5 : 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 : n020.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 08:55:40 AM UTC 2026
% Result : Theorem 1.15s 1.45s
% Output : Proof 1.21s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(tsy_c_Arrow__Order__Mirabelle__rvjphhsdgg_OIIA_res,axiom,
ti(fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),arrow_612047104le_IIA) = arrow_612047104le_IIA,
file('theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__rvjphhsdgg_OIIA_res) ).
fof(tsy_c_Arrow__Order__Mirabelle__rvjphhsdgg_OLin_res,axiom,
ti(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),arrow_638930832le_Lin) = arrow_638930832le_Lin,
file('theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__rvjphhsdgg_OLin_res) ).
fof(tsy_c_Arrow__Order__Mirabelle__rvjphhsdgg_OProf_res,axiom,
ti(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),arrow_1834574746e_Prof) = arrow_1834574746e_Prof,
file('theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__rvjphhsdgg_OProf_res) ).
fof(tsy_c_Arrow__Order__Mirabelle__rvjphhsdgg_Oabove_res,axiom,
ti(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),arrow_1726925404_above) = arrow_1726925404_above,
file('theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__rvjphhsdgg_Oabove_res) ).
fof(tsy_c_Arrow__Order__Mirabelle__rvjphhsdgg_Odictator_res,axiom,
ti(fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,bool)),arrow_1990387629ctator) = arrow_1990387629ctator,
file('theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__rvjphhsdgg_Odictator_res) ).
fof(tsy_c_Arrow__Order__Mirabelle__rvjphhsdgg_Omkbot_res,axiom,
ti(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_844286440_mkbot) = arrow_844286440_mkbot,
file('theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__rvjphhsdgg_Omkbot_res) ).
fof(tsy_c_Arrow__Order__Mirabelle__rvjphhsdgg_Omktop_res,axiom,
ti(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_992993526_mktop) = arrow_992993526_mktop,
file('theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__rvjphhsdgg_Omktop_res) ).
fof(tsy_c_Arrow__Order__Mirabelle__rvjphhsdgg_Ounanimity_res,axiom,
ti(fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),arrow_1932713123nimity) = arrow_1932713123nimity,
file('theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__rvjphhsdgg_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,
ti(fun(fun(arrow_1384031255e_indi,bool),nat),finite_card(arrow_1384031255e_indi)) = finite_card(arrow_1384031255e_indi),
file('theBenchmark.p',tsy_c_Finite__Set_Ocard_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_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_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_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_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_fFalse_res,axiom,
ti(bool,fFalse) = fFalse,
file('theBenchmark.p',tsy_c_fFalse_res) ).
fof(tsy_c_fTrue_res,axiom,
ti(bool,fTrue) = fTrue,
file('theBenchmark.p',tsy_c_fTrue_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_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),f) = f,
file('theBenchmark.p',tsy_v_F_res) ).
fof(tsy_v_Lab_____res,axiom,
ti(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),lab) = lab,
file('theBenchmark.p',tsy_v_Lab_____res) ).
fof(tsy_v_Lba_____res,axiom,
ti(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),lba) = lba,
file('theBenchmark.p',tsy_v_Lba_____res) ).
fof(tsy_v_P_____res,hypothesis,
ti(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),p) = p,
file('theBenchmark.p',tsy_v_P_____res) ).
fof(tsy_v_a_____res,axiom,
ti(arrow_1212486748le_alt,a) = a,
file('theBenchmark.p',tsy_v_a_____res) ).
fof(tsy_v_b_____res,axiom,
ti(arrow_1212486748le_alt,b) = b,
file('theBenchmark.p',tsy_v_b_____res) ).
fof(tsy_v_c_____res,hypothesis,
ti(arrow_1212486748le_alt,c) = c,
file('theBenchmark.p',tsy_v_c_____res) ).
fof(tsy_v_d_____res,hypothesis,
ti(arrow_1212486748le_alt,d) = d,
file('theBenchmark.p',tsy_v_d_____res) ).
fof(tsy_v_e_____res,axiom,
ti(arrow_1212486748le_alt,e) = e,
file('theBenchmark.p',tsy_v_e_____res) ).
fof(tsy_v_h_____res,axiom,
ti(fun(arrow_1384031255e_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_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_612047104le_IIA,f)),
file('theBenchmark.p',fact_0_assms_I3_J) ).
fof(fact_1_u,axiom,
hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_1932713123nimity,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_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),p),arrow_1834574746e_Prof)),
file('theBenchmark.p',fact_3__096P_A_058_AProf_096) ).
fof(fact_4_in__mkbot,axiom,
! [X_2,Y_1,L,Z_1] :
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),X_2),Y_1)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,L),Z_1)))
<=> ( ( ti(arrow_1212486748le_alt,X_2) != ti(arrow_1212486748le_alt,Z_1)
=> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),X_2),Y_1)),L)) )
& ( ti(arrow_1212486748le_alt,X_2) = ti(arrow_1212486748le_alt,Z_1)
=> ti(arrow_1212486748le_alt,X_2) != ti(arrow_1212486748le_alt,Y_1) )
& ti(arrow_1212486748le_alt,Y_1) != ti(arrow_1212486748le_alt,Z_1) ) ),
file('theBenchmark.p',fact_4_in__mkbot) ).
fof(fact_5_in__mktop,axiom,
! [X_2,Y_1,L,Z_1] :
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),X_2),Y_1)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,L),Z_1)))
<=> ( ( ti(arrow_1212486748le_alt,Y_1) != ti(arrow_1212486748le_alt,Z_1)
=> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),X_2),Y_1)),L)) )
& ( ti(arrow_1212486748le_alt,Y_1) = ti(arrow_1212486748le_alt,Z_1)
=> ti(arrow_1212486748le_alt,X_2) != ti(arrow_1212486748le_alt,Y_1) )
& ti(arrow_1212486748le_alt,X_2) != ti(arrow_1212486748le_alt,Z_1) ) ),
file('theBenchmark.p',fact_5_in__mktop) ).
fof(fact_6__C2_C,axiom,
! [P_1,Pa,A_4,B_3,Aa,Ba] :
( ti(arrow_1212486748le_alt,Aa) != ti(arrow_1212486748le_alt,Ba)
=> ( ti(arrow_1212486748le_alt,A_4) != ti(arrow_1212486748le_alt,B_3)
=> ( ti(arrow_1212486748le_alt,Aa) != ti(arrow_1212486748le_alt,B_3)
=> ( ti(arrow_1212486748le_alt,Ba) != ti(arrow_1212486748le_alt,A_4)
=> ( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),Pa),arrow_1834574746e_Prof))
=> ( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),P_1),arrow_1834574746e_Prof))
=> ( ! [I] :
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Ba)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Pa,I)))
<=> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_4),B_3)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),P_1,I))) )
=> ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Ba)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,Pa)))
<=> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_4),B_3)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,P_1))) ) ) ) ) ) ) ) ),
file('theBenchmark.p',fact_6__C2_C) ).
fof(fact_7__C1_C,axiom,
! [P_1,Pa,A_4,B_3,Aa,Ba] :
( ti(arrow_1212486748le_alt,Aa) != ti(arrow_1212486748le_alt,Ba)
=> ( ti(arrow_1212486748le_alt,A_4) != ti(arrow_1212486748le_alt,B_3)
=> ( ti(arrow_1212486748le_alt,Aa) != ti(arrow_1212486748le_alt,B_3)
=> ( ti(arrow_1212486748le_alt,Ba) != ti(arrow_1212486748le_alt,A_4)
=> ( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),Pa),arrow_1834574746e_Prof))
=> ( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),P_1),arrow_1834574746e_Prof))
=> ( ! [I] :
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Ba)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Pa,I)))
<=> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_4),B_3)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),P_1,I))) )
=> ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Ba)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,Pa)))
=> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_4),B_3)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_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_1212486748le_alt,Aa) != ti(arrow_1212486748le_alt,Ba)
=> ( ti(arrow_1212486748le_alt,Ba) != ti(arrow_1212486748le_alt,Ca)
=> ( ti(arrow_1212486748le_alt,Aa) != ti(arrow_1212486748le_alt,Ca)
=> ( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),Pa),arrow_1834574746e_Prof))
=> ( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),P_1),arrow_1834574746e_Prof))
=> ( ! [I] :
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Ba)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Pa,I)))
<=> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Ba),Ca)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),P_1,I))) )
=> ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Ba)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,Pa)))
<=> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Ba),Ca)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,P_1))) ) ) ) ) ) ) ),
file('theBenchmark.p',fact_8__C4_C) ).
fof(fact_9_pairwise__neutrality,axiom,
! [P_1,Pa,A_4,B_3,Aa,Ba] :
( ti(arrow_1212486748le_alt,Aa) != ti(arrow_1212486748le_alt,Ba)
=> ( ti(arrow_1212486748le_alt,A_4) != ti(arrow_1212486748le_alt,B_3)
=> ( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),Pa),arrow_1834574746e_Prof))
=> ( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),P_1),arrow_1834574746e_Prof))
=> ( ! [I] :
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Ba)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Pa,I)))
<=> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_4),B_3)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),P_1,I))) )
=> ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Ba)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,Pa)))
<=> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_4),B_3)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_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_1212486748le_alt,Aa) != ti(arrow_1212486748le_alt,Ba)
=> ( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),Pa),arrow_1834574746e_Prof))
=> ( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),P_1),arrow_1834574746e_Prof))
=> ( ! [I] :
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Ba)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Pa,I)))
<=> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Ba),Aa)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),P_1,I))) )
=> ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Ba)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,Pa)))
<=> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Ba),Aa)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_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] :
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,I)))
<=> ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,I)),n))
=> ( ( hAPP(arrow_1384031255e_indi,nat,h,I) != n
=> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,I)),e))) )
& ( hAPP(arrow_1384031255e_indi,nat,h,I) = n
=> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,I)),c),e))) ) ) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,I)),n))
=> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,I)),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_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,hAPP(nat,arrow_1384031255e_indi,hAPP(fun(arrow_1384031255e_indi,nat),fun(nat,arrow_1384031255e_indi),hAPP(fun(arrow_1384031255e_indi,bool),fun(fun(arrow_1384031255e_indi,nat),fun(nat,arrow_1384031255e_indi)),hilbert_inv_into(arrow_1384031255e_indi,nat),top_top(fun(arrow_1384031255e_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_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),ord_less(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1384031255e_indi),arrow_992993526_mktop),p)),e))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),fequal(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),arrow_1726925404_above),p)),c)),e))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1384031255e_indi),arrow_844286440_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_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,p)))
<=> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),ord_less(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1384031255e_indi),arrow_992993526_mktop),p)),e))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),fequal(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),arrow_1726925404_above),p)),c)),e))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1384031255e_indi),arrow_844286440_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_2,B_1] : 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_2),B_1))) ),
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_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),ord_less(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1384031255e_indi),arrow_992993526_mktop),p)),e))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),fequal(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),arrow_1726925404_above),p)),c)),e))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1384031255e_indi),arrow_844286440_mkbot),p)),e)))),arrow_1834574746e_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_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),e)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),ord_less(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1384031255e_indi),arrow_992993526_mktop),p)),e))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),fequal(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),arrow_1726925404_above),p)),c)),e))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1384031255e_indi),arrow_844286440_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_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),ord_less(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1384031255e_indi),arrow_992993526_mktop),p)),e))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),fequal(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),arrow_1726925404_above),p)),c)),e))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1384031255e_indi),arrow_844286440_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_1384031255e_indi,bool),nat,finite_card(arrow_1384031255e_indi),top_top(fun(arrow_1384031255e_indi,bool))))),
file('theBenchmark.p',fact_19_n_I1_J) ).
fof(fact_20_injh,axiom,
hBOOL(hAPP(fun(arrow_1384031255e_indi,bool),bool,hAPP(fun(arrow_1384031255e_indi,nat),fun(fun(arrow_1384031255e_indi,bool),bool),inj_on(arrow_1384031255e_indi,nat),h),top_top(fun(arrow_1384031255e_indi,bool)))),
file('theBenchmark.p',fact_20_injh) ).
fof(fact_21_Pair__inject,axiom,
! [X_b,X_a,A_3,B_2,A_5,B_4] :
( hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_3),B_2) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_5),B_4)
=> ~ ( ti(X_a,A_3) = ti(X_a,A_5)
=> ti(X_b,B_2) != 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_4,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_4),B_3)
<=> ( ti(X_b,Ba) = ti(X_b,B_3)
& ti(X_a,Aa) = ti(X_a,A_4) ) ),
file('theBenchmark.p',fact_22_Pair__eq) ).
fof(fact_23_IIA__def,axiom,
! [Fa] :
( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_612047104le_IIA,Fa))
<=> ! [X_1] :
( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),X_1),arrow_1834574746e_Prof))
=> ! [Xa] :
( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),Xa),arrow_1834574746e_Prof))
=> ! [A_2,B_1] :
( ! [I] :
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_2),B_1)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),X_1,I)))
<=> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_2),B_1)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Xa,I))) )
=> ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_2),B_1)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Fa,X_1)))
<=> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_2),B_1)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Fa,Xa))) ) ) ) ) ),
file('theBenchmark.p',fact_23_IIA__def) ).
fof(fact_24_unanimity__def,axiom,
! [Fa] :
( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_1932713123nimity,Fa))
<=> ! [X_1] :
( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),X_1),arrow_1834574746e_Prof))
=> ! [A_2,B_1] :
( ! [I] : hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_2),B_1)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),X_1,I)))
=> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_2),B_1)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Fa,X_1))) ) ) ),
file('theBenchmark.p',fact_24_unanimity__def) ).
fof(fact_25_top1I,axiom,
! [X_a,X_2] : hBOOL(hAPP(X_a,bool,top_top(fun(X_a,bool)),X_2)),
file('theBenchmark.p',fact_25_top1I) ).
fof(fact_26_UNIV__I,axiom,
! [X_a,X_2] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),top_top(fun(X_a,bool)))),
file('theBenchmark.p',fact_26_UNIV__I) ).
fof(fact_27_iso__tuple__UNIV__I,axiom,
! [X_a,X_2] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),top_top(fun(X_a,bool)))),
file('theBenchmark.p',fact_27_iso__tuple__UNIV__I) ).
fof(fact_28_prod_Orecs,axiom,
! [X_b,X_c,X_a,F1,Aa,Ba] : hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_rec(X_b,X_c,X_a),F1),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),Aa),Ba)) = hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),F1,Aa),Ba),
file('theBenchmark.p',fact_28_prod_Orecs) ).
fof(fact_29_top__apply,axiom,
! [X_b,X_a] :
( top(X_a)
=> ! [X_2] : hAPP(X_b,X_a,top_top(fun(X_b,X_a)),X_2) = top_top(X_a) ),
file('theBenchmark.p',fact_29_top__apply) ).
fof(fact_30_not__top__less,axiom,
! [X_a] :
( top(X_a)
=> ! [A_3] : ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),top_top(X_a)),A_3)) ),
file('theBenchmark.p',fact_30_not__top__less) ).
fof(fact_31_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_31_linorder__cases) ).
fof(fact_32_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_32_order__less__asym) ).
fof(fact_33_xt1_I10_J,axiom,
! [X_a] :
( order(X_a)
=> ! [Z,Y,X] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),Y))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X)) ) ) ),
file('theBenchmark.p',fact_33_xt1_I10_J) ).
fof(fact_34_order__less__trans,axiom,
! [X_a] :
( preorder(X_a)
=> ! [Z,X,Y] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),Z))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z)) ) ) ),
file('theBenchmark.p',fact_34_order__less__trans) ).
fof(fact_35_xt1_I2_J,axiom,
! [X_a] :
( order(X_a)
=> ! [C,B_2,A_3] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),A_3))
=> ( B_2 = C
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),A_3)) ) ) ),
file('theBenchmark.p',fact_35_xt1_I2_J) ).
fof(fact_36_ord__less__eq__trans,axiom,
! [X_a] :
( ord(X_a)
=> ! [C,A_3,B_2] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2))
=> ( B_2 = C
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),C)) ) ) ),
file('theBenchmark.p',fact_36_ord__less__eq__trans) ).
fof(fact_37_xt1_I1_J,axiom,
! [X_a] :
( order(X_a)
=> ! [C,A_3,B_2] :
( A_3 = B_2
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),B_2))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),A_3)) ) ) ),
file('theBenchmark.p',fact_37_xt1_I1_J) ).
fof(fact_38_ord__eq__less__trans,axiom,
! [X_a] :
( ord(X_a)
=> ! [C,A_3,B_2] :
( A_3 = B_2
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),C))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),C)) ) ) ),
file('theBenchmark.p',fact_38_ord__eq__less__trans) ).
fof(fact_39_xt1_I9_J,axiom,
! [X_a] :
( order(X_a)
=> ! [B_2,A_3] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),A_3))
=> ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2)) ) ),
file('theBenchmark.p',fact_39_xt1_I9_J) ).
fof(fact_40_order__less__asym_H,axiom,
! [X_a] :
( preorder(X_a)
=> ! [A_3,B_2] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2))
=> ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),A_3)) ) ),
file('theBenchmark.p',fact_40_order__less__asym_H) ).
fof(fact_41_order__less__imp__triv,axiom,
! [X_a] :
( preorder(X_a)
=> ! [Pa,X_2,Y_1] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_1))
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_2))
=> hBOOL(Pa) ) ) ),
file('theBenchmark.p',fact_41_order__less__imp__triv) ).
fof(fact_42_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))
=> Y != X ) ),
file('theBenchmark.p',fact_42_order__less__imp__not__eq2) ).
fof(fact_43_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))
=> X != Y ) ),
file('theBenchmark.p',fact_43_order__less__imp__not__eq) ).
fof(fact_44_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_44_order__less__imp__not__less) ).
fof(fact_45_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_45_order__less__not__sym) ).
fof(fact_46_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))
=> X != Y ) ),
file('theBenchmark.p',fact_46_less__imp__neq) ).
fof(fact_47_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_47_linorder__neqE) ).
fof(fact_48_linorder__antisym__conv3,axiom,
! [X_a] :
( linorder(X_a)
=> ! [Y_1,X_2] :
( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_2))
=> ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_1))
<=> ti(X_a,X_2) = ti(X_a,Y_1) ) ) ),
file('theBenchmark.p',fact_48_linorder__antisym__conv3) ).
fof(fact_49_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_49_linorder__less__linear) ).
fof(fact_50_not__less__iff__gr__or__eq,axiom,
! [X_a] :
( linorder(X_a)
=> ! [X_2,Y_1] :
( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_1))
<=> ( ti(X_a,X_2) = ti(X_a,Y_1)
| hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_2)) ) ) ),
file('theBenchmark.p',fact_50_not__less__iff__gr__or__eq) ).
fof(fact_51_linorder__neq__iff,axiom,
! [X_a] :
( linorder(X_a)
=> ! [X_2,Y_1] :
( ti(X_a,X_2) != ti(X_a,Y_1)
<=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_2))
| hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_1)) ) ) ),
file('theBenchmark.p',fact_51_linorder__neq__iff) ).
fof(fact_52_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_52_order__less__irrefl) ).
fof(fact_53_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_53_UNIV__def) ).
fof(fact_54_pred__equals__eq2,axiom,
! [X_a,X_b,S,R_1] :
( ! [X_1,Xa] :
( hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_1),Xa)),R_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),Xa)),S)) )
<=> ti(fun(product_prod(X_a,X_b),bool),R_1) = ti(fun(product_prod(X_a,X_b),bool),S) ),
file('theBenchmark.p',fact_54_pred__equals__eq2) ).
fof(fact_55_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_55_less__top) ).
fof(fact_56_inv__f__eq,axiom,
! [X_a,X_b,X_2,Y_1,F] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool))))
=> ( hAPP(X_a,X_b,F,X_2) = ti(X_b,Y_1)
=> hAPP(X_b,X_a,hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),top_top(fun(X_a,bool))),F),Y_1) = ti(X_a,X_2) ) ),
file('theBenchmark.p',fact_56_inv__f__eq) ).
fof(fact_57_inv__f__f,axiom,
! [X_a,X_b,X_2,F] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool))))
=> hAPP(X_b,X_a,hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),top_top(fun(X_a,bool))),F),hAPP(X_a,X_b,F,X_2)) = ti(X_a,X_2) ),
file('theBenchmark.p',fact_57_inv__f__f) ).
fof(fact_58_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_58_inj__fun) ).
fof(fact_59_inv__into__f__f,axiom,
! [X_a,X_b,X_2,F,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
=> hAPP(X_b,X_a,hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),A_1),F),hAPP(X_a,X_b,F,X_2)) = ti(X_a,X_2) ) ),
file('theBenchmark.p',fact_59_inv__into__f__f) ).
fof(fact_60_inv__into__f__eq,axiom,
! [X_a,X_b,Y_1,X_2,F,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
=> ( hAPP(X_a,X_b,F,X_2) = ti(X_b,Y_1)
=> hAPP(X_b,X_a,hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),A_1),F),Y_1) = ti(X_a,X_2) ) ) ),
file('theBenchmark.p',fact_60_inv__into__f__eq) ).
fof(fact_61_inj__eq,axiom,
! [X_a,X_b,X_2,Y_1,F] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool))))
=> ( hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,F,Y_1)
<=> ti(X_a,X_2) = ti(X_a,Y_1) ) ),
file('theBenchmark.p',fact_61_inj__eq) ).
fof(fact_62_inj__on__def,axiom,
! [X_a,X_b,F,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
<=> ! [X_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))
=> ! [Xa] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),A_1))
=> ( hAPP(X_a,X_b,F,X_1) = hAPP(X_a,X_b,F,Xa)
=> ti(X_a,X_1) = ti(X_a,Xa) ) ) ) ),
file('theBenchmark.p',fact_62_inj__on__def) ).
fof(fact_63_inj__on__contraD,axiom,
! [X_a,X_b,X_2,Y_1,F,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
=> ( ti(X_a,X_2) != ti(X_a,Y_1)
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_1),A_1))
=> hAPP(X_a,X_b,F,X_2) != hAPP(X_a,X_b,F,Y_1) ) ) ) ),
file('theBenchmark.p',fact_63_inj__on__contraD) ).
fof(fact_64_inj__on__iff,axiom,
! [X_a,X_b,Y_1,X_2,F,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_1),A_1))
=> ( hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,F,Y_1)
<=> ti(X_a,X_2) = ti(X_a,Y_1) ) ) ) ),
file('theBenchmark.p',fact_64_inj__on__iff) ).
fof(fact_65_inj__onD,axiom,
! [X_a,X_b,X_2,Y_1,F,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
=> ( hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,F,Y_1)
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_1),A_1))
=> ti(X_a,X_2) = ti(X_a,Y_1) ) ) ) ),
file('theBenchmark.p',fact_65_inj__onD) ).
fof(fact_66_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_66_inj__on__id2) ).
fof(fact_67_injD,axiom,
! [X_a,X_b,X_2,Y_1,F] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool))))
=> ( hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,F,Y_1)
=> ti(X_a,X_2) = ti(X_a,Y_1) ) ),
file('theBenchmark.p',fact_67_injD) ).
fof(fact_68_inj__imp__inv__eq,axiom,
! [X_a,X_b,G,F] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool))))
=> ( ! [X_1] : hAPP(X_a,X_b,F,hAPP(X_b,X_a,G,X_1)) = ti(X_b,X_1)
=> hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),top_top(fun(X_a,bool))),F) = ti(fun(X_b,X_a),G) ) ),
file('theBenchmark.p',fact_68_inj__imp__inv__eq) ).
fof(fact_69_injI,axiom,
! [X_a,X_b,F] :
( ! [X_1,Y_2] :
( hAPP(X_a,X_b,F,X_1) = hAPP(X_a,X_b,F,Y_2)
=> ti(X_a,X_1) = ti(X_a,Y_2) )
=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool)))) ),
file('theBenchmark.p',fact_69_injI) ).
fof(fact_70_assms_I1_J,axiom,
hBOOL(hAPP(fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),f),hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool)),pi(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1834574746e_Prof),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_638930832le_Lin)))),
file('theBenchmark.p',fact_70_assms_I1_J) ).
fof(fact_71__096Lba_A_058_ALin_096,axiom,
hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),lba),arrow_638930832le_Lin)),
file('theBenchmark.p',fact_71__096Lba_A_058_ALin_096) ).
fof(fact_72__096Lab_A_058_ALin_096,axiom,
hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),lab),arrow_638930832le_Lin)),
file('theBenchmark.p',fact_72__096Lab_A_058_ALin_096) ).
fof(fact_73_Lin__irrefl,axiom,
! [Aa,Ba,L] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),L),arrow_638930832le_Lin))
=> ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Ba)),L))
=> ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Ba),Aa)),L)) ) ),
file('theBenchmark.p',fact_73_Lin__irrefl) ).
fof(fact_74_notin__Lin__iff,axiom,
! [X_2,Y_1,L] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),L),arrow_638930832le_Lin))
=> ( ti(arrow_1212486748le_alt,X_2) != ti(arrow_1212486748le_alt,Y_1)
=> ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),X_2),Y_1)),L))
<=> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Y_1),X_2)),L)) ) ) ),
file('theBenchmark.p',fact_74_notin__Lin__iff) ).
fof(fact_75_ext,axiom,
! [X_a,X_b,F,G] :
( ! [X_1] : hAPP(X_a,X_b,F,X_1) = hAPP(X_a,X_b,G,X_1)
=> ti(fun(X_a,X_b),F) = ti(fun(X_a,X_b),G) ),
file('theBenchmark.p',fact_75_ext) ).
fof(fact_76_mem__def,axiom,
! [X_a,X_2,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
<=> hBOOL(hAPP(X_a,bool,A_1,X_2)) ),
file('theBenchmark.p',fact_76_mem__def) ).
fof(fact_77_Collect__def,axiom,
! [X_a,Pa] : hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Pa) = ti(fun(X_a,bool),Pa),
file('theBenchmark.p',fact_77_Collect__def) ).
fof(fact_78_mktop__Lin,axiom,
! [X_2,L] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),L),arrow_638930832le_Lin))
=> hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,L),X_2)),arrow_638930832le_Lin)) ),
file('theBenchmark.p',fact_78_mktop__Lin) ).
fof(fact_79_mkbot__Lin,axiom,
! [X_2,L] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),L),arrow_638930832le_Lin))
=> hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,L),X_2)),arrow_638930832le_Lin)) ),
file('theBenchmark.p',fact_79_mkbot__Lin) ).
fof(fact_80_above__Lin,axiom,
! [L,X_2,Y_1] :
( ti(arrow_1212486748le_alt,X_2) != ti(arrow_1212486748le_alt,Y_1)
=> ( hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),L),arrow_638930832le_Lin))
=> hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,L),X_2),Y_1)),arrow_638930832le_Lin)) ) ),
file('theBenchmark.p',fact_80_above__Lin) ).
fof(fact_81_const__Lin__Prof,axiom,
! [L] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),L),arrow_638930832le_Lin))
=> hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),combk(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),arrow_1384031255e_indi),L)),arrow_1834574746e_Prof)) ),
file('theBenchmark.p',fact_81_const__Lin__Prof) ).
fof(fact_82_in__above,axiom,
! [X_2,Y_1,L,Aa,Ba] :
( ti(arrow_1212486748le_alt,Aa) != ti(arrow_1212486748le_alt,Ba)
=> ( hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),L),arrow_638930832le_Lin))
=> ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),X_2),Y_1)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,L),Aa),Ba)))
<=> ( ( ti(arrow_1212486748le_alt,X_2) != ti(arrow_1212486748le_alt,Ba)
=> ( ( ti(arrow_1212486748le_alt,Y_1) != ti(arrow_1212486748le_alt,Ba)
=> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),X_2),Y_1)),L)) )
& ( ti(arrow_1212486748le_alt,Y_1) = ti(arrow_1212486748le_alt,Ba)
=> ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),X_2),Aa)),L))
| ti(arrow_1212486748le_alt,X_2) = ti(arrow_1212486748le_alt,Aa) ) ) ) )
& ( ti(arrow_1212486748le_alt,X_2) = ti(arrow_1212486748le_alt,Ba)
=> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Y_1)),L)) )
& ti(arrow_1212486748le_alt,X_2) != ti(arrow_1212486748le_alt,Y_1) ) ) ) ),
file('theBenchmark.p',fact_82_in__above) ).
fof(fact_83_dictatorI,axiom,
! [I_1,Fa] :
( hBOOL(hAPP(fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),Fa),hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool)),pi(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1834574746e_Prof),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_638930832le_Lin))))
=> ( ! [X_1] :
( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),X_1),arrow_1834574746e_Prof))
=> ! [A_2,B_1] :
( ti(arrow_1212486748le_alt,A_2) != ti(arrow_1212486748le_alt,B_1)
=> ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_2),B_1)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),X_1,I_1)))
=> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_2),B_1)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Fa,X_1))) ) ) )
=> hBOOL(hAPP(arrow_1384031255e_indi,bool,hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,bool),arrow_1990387629ctator,Fa),I_1)) ) ),
file('theBenchmark.p',fact_83_dictatorI) ).
fof(fact_84_PiE,axiom,
! [X_a,X_b,X_2,F,A_1,B] :
( hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B)))
=> ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,fun(X_b,bool),B,X_2)))
=> ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) ) ),
file('theBenchmark.p',fact_84_PiE) ).
fof(fact_85_complete__Lin,axiom,
! [Aa,Ba] :
( ti(arrow_1212486748le_alt,Aa) != ti(arrow_1212486748le_alt,Ba)
=> ? [X_1] :
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Ba)),X_1))
& hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),X_1),arrow_638930832le_Lin)) ) ),
file('theBenchmark.p',fact_85_complete__Lin) ).
fof(fact_86_PiProf,axiom,
! [Na] : hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combc(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),ord_less(nat)),h)),Na))),lab)),lba)),arrow_1834574746e_Prof)),
file('theBenchmark.p',fact_86_PiProf) ).
fof(fact_87_Pi__mem,axiom,
! [X_a,X_b,X_2,F,A_1,B] :
( hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B)))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
=> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,fun(X_b,bool),B,X_2))) ) ),
file('theBenchmark.p',fact_87_Pi__mem) ).
fof(fact_88_Prof__def,axiom,
arrow_1834574746e_Prof = hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),hAPP(fun(arrow_1384031255e_indi,bool),fun(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool)),pi(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),top_top(fun(arrow_1384031255e_indi,bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),arrow_1384031255e_indi),arrow_638930832le_Lin)),
file('theBenchmark.p',fact_88_Prof__def) ).
fof(fact_89_funcset__mem,axiom,
! [X_a,X_b,X_2,F,A_1,B] :
( hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),combk(fun(X_b,bool),X_a),B))))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
=> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_2)),B)) ) ),
file('theBenchmark.p',fact_89_funcset__mem) ).
fof(fact_90_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_90_funcset__id) ).
fof(fact_91_dictator__def,axiom,
! [Fa,I_1] :
( hBOOL(hAPP(arrow_1384031255e_indi,bool,hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,bool),arrow_1990387629ctator,Fa),I_1))
<=> ! [X_1] :
( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),X_1),arrow_1834574746e_Prof))
=> hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Fa,X_1) = hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),X_1,I_1) ) ),
file('theBenchmark.p',fact_91_dictator__def) ).
fof(fact_92_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_92_Pi__UNIV) ).
fof(fact_93__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_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),ord_less(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1384031255e_indi),arrow_992993526_mktop),p)),e))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),fequal(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),arrow_1726925404_above),p)),c)),e))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1384031255e_indi),arrow_844286440_mkbot),p)),e))))))
<=> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combc(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),ord_less(nat)),h)),n))),lab)),lba)))) ),
file('theBenchmark.p',fact_93__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amk) ).
fof(fact_94__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk,axiom,
! [I] :
( ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,I)),n))
=> ( ( hAPP(arrow_1384031255e_indi,nat,h,I) != n
=> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,I)),e))) )
& ( hAPP(arrow_1384031255e_indi,nat,h,I) = n
=> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,I)),c),e))) ) ) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,I)),n))
=> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,I)),e))) ) )
<=> ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,I)),n))
=> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lba)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,I)),n))
=> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lab)) ) ) ),
file('theBenchmark.p',fact_94__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk) ).
fof(fact_95__096a_A_126_061_Ab_096,axiom,
a != b,
file('theBenchmark.p',fact_95__096a_A_126_061_Ab_096) ).
fof(fact_96__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096,axiom,
hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lba)),
file('theBenchmark.p',fact_96__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096) ).
fof(fact_97__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096,axiom,
hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),a),b)),lab)),
file('theBenchmark.p',fact_97__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096) ).
fof(fact_98__096_Ia_M_Ab_J_A_126_058_ALba_096,axiom,
~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),a),b)),lba)),
file('theBenchmark.p',fact_98__096_Ia_M_Ab_J_A_126_058_ALba_096) ).
fof(fact_99__096_Ib_M_Aa_J_A_126_058_ALab_096,axiom,
~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lab)),
file('theBenchmark.p',fact_99__096_Ib_M_Aa_J_A_126_058_ALab_096) ).
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___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___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___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_HOL_Obool___Orderings_Opreorder,axiom,
preorder(bool),
file('theBenchmark.p',arity_HOL_Obool___Orderings_Opreorder) ).
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(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_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_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_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,p))),
file('theBenchmark.p',conj_0) ).
fof(f_1_1,plain,
ti(fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),arrow_612047104le_IIA) = arrow_612047104le_IIA,
inference(fof_nnf,[status(thm)],[tsy_c_Arrow__Order__Mirabelle__rvjphhsdgg_OIIA_res]) ).
cnf(f_1_2,plain,
ti(fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),arrow_612047104le_IIA) = arrow_612047104le_IIA,
inference(clausify,[status(thm)],[f_1_1]) ).
fof(f_2_1,plain,
ti(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),arrow_638930832le_Lin) = arrow_638930832le_Lin,
inference(fof_nnf,[status(thm)],[tsy_c_Arrow__Order__Mirabelle__rvjphhsdgg_OLin_res]) ).
cnf(f_2_2,plain,
ti(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),arrow_638930832le_Lin) = arrow_638930832le_Lin,
inference(clausify,[status(thm)],[f_2_1]) ).
fof(f_3_1,plain,
ti(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),arrow_1834574746e_Prof) = arrow_1834574746e_Prof,
inference(fof_nnf,[status(thm)],[tsy_c_Arrow__Order__Mirabelle__rvjphhsdgg_OProf_res]) ).
cnf(f_3_2,plain,
ti(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),arrow_1834574746e_Prof) = arrow_1834574746e_Prof,
inference(clausify,[status(thm)],[f_3_1]) ).
fof(f_4_1,plain,
ti(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),arrow_1726925404_above) = arrow_1726925404_above,
inference(fof_nnf,[status(thm)],[tsy_c_Arrow__Order__Mirabelle__rvjphhsdgg_Oabove_res]) ).
cnf(f_4_2,plain,
ti(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),arrow_1726925404_above) = arrow_1726925404_above,
inference(clausify,[status(thm)],[f_4_1]) ).
fof(f_5_1,plain,
ti(fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,bool)),arrow_1990387629ctator) = arrow_1990387629ctator,
inference(fof_nnf,[status(thm)],[tsy_c_Arrow__Order__Mirabelle__rvjphhsdgg_Odictator_res]) ).
cnf(f_5_2,plain,
ti(fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,bool)),arrow_1990387629ctator) = arrow_1990387629ctator,
inference(clausify,[status(thm)],[f_5_1]) ).
fof(f_6_1,plain,
ti(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_844286440_mkbot) = arrow_844286440_mkbot,
inference(fof_nnf,[status(thm)],[tsy_c_Arrow__Order__Mirabelle__rvjphhsdgg_Omkbot_res]) ).
cnf(f_6_2,plain,
ti(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_844286440_mkbot) = arrow_844286440_mkbot,
inference(clausify,[status(thm)],[f_6_1]) ).
fof(f_7_1,plain,
ti(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_992993526_mktop) = arrow_992993526_mktop,
inference(fof_nnf,[status(thm)],[tsy_c_Arrow__Order__Mirabelle__rvjphhsdgg_Omktop_res]) ).
cnf(f_7_2,plain,
ti(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_992993526_mktop) = arrow_992993526_mktop,
inference(clausify,[status(thm)],[f_7_1]) ).
fof(f_8_1,plain,
ti(fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),arrow_1932713123nimity) = arrow_1932713123nimity,
inference(fof_nnf,[status(thm)],[tsy_c_Arrow__Order__Mirabelle__rvjphhsdgg_Ounanimity_res]) ).
cnf(f_8_2,plain,
ti(fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),arrow_1932713123nimity) = arrow_1932713123nimity,
inference(clausify,[status(thm)],[f_8_1]) ).
fof(f_9_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_9_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_9_1]) ).
cnf(f_9_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_9_2]) ).
fof(f_10_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_10_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_10_1]) ).
cnf(f_10_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_10_2]) ).
fof(f_11_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_11_2,plain,
! [U_6] : ti(fun(U_6,U_6),combi(U_6)) = combi(U_6),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
ti(fun(U_6,U_6),combi(U_6)) = combi(U_6),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_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_12_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_12_1]) ).
cnf(f_12_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_12_2]) ).
fof(f_13_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_13_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_13_1]) ).
cnf(f_13_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_13_2]) ).
fof(f_14_1,plain,
ti(fun(fun(arrow_1384031255e_indi,bool),nat),finite_card(arrow_1384031255e_indi)) = finite_card(arrow_1384031255e_indi),
inference(fof_nnf,[status(thm)],[tsy_c_Finite__Set_Ocard_res]) ).
cnf(f_14_2,plain,
ti(fun(fun(arrow_1384031255e_indi,bool),nat),finite_card(arrow_1384031255e_indi)) = finite_card(arrow_1384031255e_indi),
inference(clausify,[status(thm)],[f_14_1]) ).
fof(f_15_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_15_2,plain,
! [U_13,U_12] : ti(fun(fun(U_13,U_12),fun(fun(U_13,bool),bool)),inj_on(U_13,U_12)) = inj_on(U_13,U_12),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
ti(fun(fun(U_13,U_12),fun(fun(U_13,bool),bool)),inj_on(U_13,U_12)) = inj_on(U_13,U_12),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_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_16_2,plain,
! [U_15,U_14] : ti(fun(fun(U_15,bool),fun(fun(U_15,fun(U_14,bool)),fun(fun(U_15,U_14),bool))),pi(U_15,U_14)) = pi(U_15,U_14),
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
ti(fun(fun(U_15,bool),fun(fun(U_15,fun(U_14,bool)),fun(fun(U_15,U_14),bool))),pi(U_15,U_14)) = pi(U_15,U_14),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_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_17_2,plain,
! [U_16] : ti(U_16,undefined(U_16)) = undefined(U_16),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
ti(U_16,undefined(U_16)) = undefined(U_16),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_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_18_2,plain,
! [U_18,U_17] : ti(fun(fun(U_18,bool),fun(fun(U_18,U_17),fun(U_17,U_18))),hilbert_inv_into(U_18,U_17)) = hilbert_inv_into(U_18,U_17),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
ti(fun(fun(U_18,bool),fun(fun(U_18,U_17),fun(U_17,U_18))),hilbert_inv_into(U_18,U_17)) = hilbert_inv_into(U_18,U_17),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_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_19_2,plain,
! [U_19] : ti(fun(bool,fun(U_19,fun(U_19,U_19))),if(U_19)) = if(U_19),
inference(variable_rename,[status(thm)],[f_19_1]) ).
cnf(f_19_3,plain,
ti(fun(bool,fun(U_19,fun(U_19,U_19))),if(U_19)) = if(U_19),
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_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_20_2,plain,
! [U_20] :
( ti(fun(U_20,fun(U_20,bool)),ord_less(U_20)) = ord_less(U_20)
| ~ ord(U_20) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
cnf(f_20_3,plain,
( ti(fun(U_20,fun(U_20,bool)),ord_less(U_20)) = ord_less(U_20)
| ~ ord(U_20) ),
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_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_21_2,plain,
! [U_21] :
( ti(U_21,top_top(U_21)) = top_top(U_21)
| ~ top(U_21) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
cnf(f_21_3,plain,
( ti(U_21,top_top(U_21)) = top_top(U_21)
| ~ top(U_21) ),
inference(clausify,[status(thm)],[f_21_2]) ).
fof(f_22_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_22_2,plain,
! [U_23,U_22] : ti(fun(U_23,fun(U_22,product_prod(U_23,U_22))),product_Pair(U_23,U_22)) = product_Pair(U_23,U_22),
inference(variable_rename,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
ti(fun(U_23,fun(U_22,product_prod(U_23,U_22))),product_Pair(U_23,U_22)) = product_Pair(U_23,U_22),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_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_23_2,plain,
! [U_26,U_25,U_24] : ti(fun(fun(U_26,fun(U_25,U_24)),fun(product_prod(U_26,U_25),U_24)),product_prod_rec(U_26,U_25,U_24)) = product_prod_rec(U_26,U_25,U_24),
inference(variable_rename,[status(thm)],[f_23_1]) ).
cnf(f_23_3,plain,
ti(fun(fun(U_26,fun(U_25,U_24)),fun(product_prod(U_26,U_25),U_24)),product_prod_rec(U_26,U_25,U_24)) = product_prod_rec(U_26,U_25,U_24),
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_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_24_2,plain,
! [U_27] : ti(fun(fun(U_27,bool),fun(U_27,bool)),collect(U_27)) = collect(U_27),
inference(variable_rename,[status(thm)],[f_24_1]) ).
cnf(f_24_3,plain,
ti(fun(fun(U_27,bool),fun(U_27,bool)),collect(U_27)) = collect(U_27),
inference(clausify,[status(thm)],[f_24_2]) ).
fof(f_25_1,plain,
ti(bool,fFalse) = fFalse,
inference(fof_nnf,[status(thm)],[tsy_c_fFalse_res]) ).
cnf(f_25_2,plain,
ti(bool,fFalse) = fFalse,
inference(clausify,[status(thm)],[f_25_1]) ).
fof(f_26_1,plain,
ti(bool,fTrue) = fTrue,
inference(fof_nnf,[status(thm)],[tsy_c_fTrue_res]) ).
cnf(f_26_2,plain,
ti(bool,fTrue) = fTrue,
inference(clausify,[status(thm)],[f_26_1]) ).
fof(f_27_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_27_2,plain,
! [U_28] : ti(fun(U_28,fun(U_28,bool)),fequal(U_28)) = fequal(U_28),
inference(variable_rename,[status(thm)],[f_27_1]) ).
cnf(f_27_3,plain,
ti(fun(U_28,fun(U_28,bool)),fequal(U_28)) = fequal(U_28),
inference(clausify,[status(thm)],[f_27_2]) ).
fof(f_28_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_28_2,plain,
! [U_32,U_31,U_30,U_29] : hAPP(U_32,U_31,ti(fun(U_32,U_31),U_30),U_29) = hAPP(U_32,U_31,U_30,U_29),
inference(variable_rename,[status(thm)],[f_28_1]) ).
cnf(f_28_3,plain,
hAPP(U_32,U_31,ti(fun(U_32,U_31),U_30),U_29) = hAPP(U_32,U_31,U_30,U_29),
inference(clausify,[status(thm)],[f_28_2]) ).
fof(f_29_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_29_2,plain,
! [U_36,U_35,U_34,U_33] : hAPP(U_36,U_35,U_34,ti(U_36,U_33)) = hAPP(U_36,U_35,U_34,U_33),
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
hAPP(U_36,U_35,U_34,ti(U_36,U_33)) = hAPP(U_36,U_35,U_34,U_33),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_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_30_2,plain,
! [U_40,U_39,U_38,U_37] : ti(U_40,hAPP(U_39,U_40,U_38,U_37)) = hAPP(U_39,U_40,U_38,U_37),
inference(variable_rename,[status(thm)],[f_30_1]) ).
cnf(f_30_3,plain,
ti(U_40,hAPP(U_39,U_40,U_38,U_37)) = hAPP(U_39,U_40,U_38,U_37),
inference(clausify,[status(thm)],[f_30_2]) ).
fof(f_31_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_31_2,plain,
! [U_41] :
( ( hBOOL(ti(bool,U_41))
| ~ hBOOL(U_41) )
& ( hBOOL(U_41)
| ~ hBOOL(ti(bool,U_41)) ) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
( ! [U_43] :
( hBOOL(ti(bool,U_43))
| ~ hBOOL(U_43) )
& ! [U_42] :
( hBOOL(U_42)
| ~ hBOOL(ti(bool,U_42)) ) ),
inference(miniscope,[status(thm)],[f_31_2]) ).
cnf(f_31_4,plain,
( hBOOL(U_42)
| ~ hBOOL(ti(bool,U_42)) ),
inference(clausify,[status(thm)],[f_31_3]) ).
cnf(f_31_5,plain,
( hBOOL(ti(bool,U_43))
| ~ hBOOL(U_43) ),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_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_32_2,plain,
! [U_44] : ti(fun(U_44,fun(fun(U_44,bool),bool)),member(U_44)) = member(U_44),
inference(variable_rename,[status(thm)],[f_32_1]) ).
cnf(f_32_3,plain,
ti(fun(U_44,fun(fun(U_44,bool),bool)),member(U_44)) = member(U_44),
inference(clausify,[status(thm)],[f_32_2]) ).
fof(f_33_1,plain,
ti(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),f) = f,
inference(fof_nnf,[status(thm)],[tsy_v_F_res]) ).
cnf(f_33_2,plain,
ti(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),f) = f,
inference(clausify,[status(thm)],[f_33_1]) ).
fof(f_34_1,plain,
ti(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),lab) = lab,
inference(fof_nnf,[status(thm)],[tsy_v_Lab_____res]) ).
cnf(f_34_2,plain,
ti(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),lab) = lab,
inference(clausify,[status(thm)],[f_34_1]) ).
fof(f_35_1,plain,
ti(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),lba) = lba,
inference(fof_nnf,[status(thm)],[tsy_v_Lba_____res]) ).
cnf(f_35_2,plain,
ti(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),lba) = lba,
inference(clausify,[status(thm)],[f_35_1]) ).
fof(f_36_1,plain,
ti(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),p) = p,
inference(fof_nnf,[status(thm)],[tsy_v_P_____res]) ).
cnf(f_36_2,plain,
ti(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),p) = p,
inference(clausify,[status(thm)],[f_36_1]) ).
fof(f_37_1,plain,
ti(arrow_1212486748le_alt,a) = a,
inference(fof_nnf,[status(thm)],[tsy_v_a_____res]) ).
cnf(f_37_2,plain,
ti(arrow_1212486748le_alt,a) = a,
inference(clausify,[status(thm)],[f_37_1]) ).
fof(f_38_1,plain,
ti(arrow_1212486748le_alt,b) = b,
inference(fof_nnf,[status(thm)],[tsy_v_b_____res]) ).
cnf(f_38_2,plain,
ti(arrow_1212486748le_alt,b) = b,
inference(clausify,[status(thm)],[f_38_1]) ).
fof(f_39_1,plain,
ti(arrow_1212486748le_alt,c) = c,
inference(fof_nnf,[status(thm)],[tsy_v_c_____res]) ).
cnf(f_39_2,plain,
ti(arrow_1212486748le_alt,c) = c,
inference(clausify,[status(thm)],[f_39_1]) ).
fof(f_40_1,plain,
ti(arrow_1212486748le_alt,d) = d,
inference(fof_nnf,[status(thm)],[tsy_v_d_____res]) ).
cnf(f_40_2,plain,
ti(arrow_1212486748le_alt,d) = d,
inference(clausify,[status(thm)],[f_40_1]) ).
fof(f_41_1,plain,
ti(arrow_1212486748le_alt,e) = e,
inference(fof_nnf,[status(thm)],[tsy_v_e_____res]) ).
cnf(f_41_2,plain,
ti(arrow_1212486748le_alt,e) = e,
inference(clausify,[status(thm)],[f_41_1]) ).
fof(f_42_1,plain,
ti(fun(arrow_1384031255e_indi,nat),h) = h,
inference(fof_nnf,[status(thm)],[tsy_v_h_____res]) ).
cnf(f_42_2,plain,
ti(fun(arrow_1384031255e_indi,nat),h) = h,
inference(clausify,[status(thm)],[f_42_1]) ).
fof(f_43_1,plain,
ti(nat,n) = n,
inference(fof_nnf,[status(thm)],[tsy_v_n_____res]) ).
cnf(f_43_2,plain,
ti(nat,n) = n,
inference(clausify,[status(thm)],[f_43_1]) ).
fof(f_44_1,plain,
hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_612047104le_IIA,f)),
inference(fof_nnf,[status(thm)],[fact_0_assms_I3_J]) ).
cnf(f_44_2,plain,
hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_612047104le_IIA,f)),
inference(clausify,[status(thm)],[f_44_1]) ).
fof(f_45_1,plain,
hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_1932713123nimity,f)),
inference(fof_nnf,[status(thm)],[fact_1_u]) ).
cnf(f_45_2,plain,
hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_1932713123nimity,f)),
inference(clausify,[status(thm)],[f_45_1]) ).
fof(f_46_1,plain,
c != d,
inference(fof_nnf,[status(thm)],[fact_2__096c_A_126_061_Ad_096]) ).
cnf(f_46_2,plain,
c != d,
inference(clausify,[status(thm)],[f_46_1]) ).
fof(f_47_1,plain,
hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),p),arrow_1834574746e_Prof)),
inference(fof_nnf,[status(thm)],[fact_3__096P_A_058_AProf_096]) ).
cnf(f_47_2,plain,
hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),p),arrow_1834574746e_Prof)),
inference(clausify,[status(thm)],[f_47_1]) ).
fof(f_48_1,plain,
! [X_2,Y_1,L,Z_1] :
( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),X_2),Y_1)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,L),Z_1)))
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),X_2),Y_1)),L))
& ti(arrow_1212486748le_alt,X_2) != ti(arrow_1212486748le_alt,Z_1) )
| ( ti(arrow_1212486748le_alt,X_2) = ti(arrow_1212486748le_alt,Y_1)
& ti(arrow_1212486748le_alt,X_2) = ti(arrow_1212486748le_alt,Z_1) )
| ti(arrow_1212486748le_alt,Y_1) = ti(arrow_1212486748le_alt,Z_1) )
& ( ( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),X_2),Y_1)),L))
| ti(arrow_1212486748le_alt,X_2) = ti(arrow_1212486748le_alt,Z_1) )
& ( ti(arrow_1212486748le_alt,X_2) != ti(arrow_1212486748le_alt,Y_1)
| ti(arrow_1212486748le_alt,X_2) != ti(arrow_1212486748le_alt,Z_1) )
& ti(arrow_1212486748le_alt,Y_1) != ti(arrow_1212486748le_alt,Z_1) )
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),X_2),Y_1)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,L),Z_1))) ) ),
inference(fof_nnf,[status(thm)],[fact_4_in__mkbot]) ).
fof(f_48_2,plain,
! [U_48,U_47,U_46,U_45] :
( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_48),U_47)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,U_46),U_45)))
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_48),U_47)),U_46))
& ti(arrow_1212486748le_alt,U_48) != ti(arrow_1212486748le_alt,U_45) )
| ( ti(arrow_1212486748le_alt,U_48) = ti(arrow_1212486748le_alt,U_47)
& ti(arrow_1212486748le_alt,U_48) = ti(arrow_1212486748le_alt,U_45) )
| ti(arrow_1212486748le_alt,U_47) = ti(arrow_1212486748le_alt,U_45) )
& ( ( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_48),U_47)),U_46))
| ti(arrow_1212486748le_alt,U_48) = ti(arrow_1212486748le_alt,U_45) )
& ( ti(arrow_1212486748le_alt,U_48) != ti(arrow_1212486748le_alt,U_47)
| ti(arrow_1212486748le_alt,U_48) != ti(arrow_1212486748le_alt,U_45) )
& ti(arrow_1212486748le_alt,U_47) != ti(arrow_1212486748le_alt,U_45) )
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_48),U_47)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,U_46),U_45))) ) ),
inference(variable_rename,[status(thm)],[f_48_1]) ).
fof(f_48_3,plain,
( ! [U_56,U_54,U_52,U_50] :
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_56),U_54)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,U_52),U_50)))
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_56),U_54)),U_52))
& ti(arrow_1212486748le_alt,U_56) != ti(arrow_1212486748le_alt,U_50) )
| ( ti(arrow_1212486748le_alt,U_56) = ti(arrow_1212486748le_alt,U_54)
& ti(arrow_1212486748le_alt,U_56) = ti(arrow_1212486748le_alt,U_50) )
| ti(arrow_1212486748le_alt,U_54) = ti(arrow_1212486748le_alt,U_50) )
& ! [U_55,U_53,U_51,U_49] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_55),U_53)),U_51))
| ti(arrow_1212486748le_alt,U_55) = ti(arrow_1212486748le_alt,U_49) )
& ( ti(arrow_1212486748le_alt,U_55) != ti(arrow_1212486748le_alt,U_53)
| ti(arrow_1212486748le_alt,U_55) != ti(arrow_1212486748le_alt,U_49) )
& ti(arrow_1212486748le_alt,U_53) != ti(arrow_1212486748le_alt,U_49) )
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_55),U_53)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,U_51),U_49))) ) ),
inference(miniscope,[status(thm)],[f_48_2]) ).
cnf(f_48_4,plain,
( ti(arrow_1212486748le_alt,U_53) != ti(arrow_1212486748le_alt,U_49)
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_55),U_53)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,U_51),U_49))) ),
inference(clausify,[status(thm)],[f_48_3]) ).
cnf(f_48_5,plain,
( ti(arrow_1212486748le_alt,U_55) != ti(arrow_1212486748le_alt,U_53)
| ti(arrow_1212486748le_alt,U_55) != ti(arrow_1212486748le_alt,U_49)
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_55),U_53)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,U_51),U_49))) ),
inference(clausify,[status(thm)],[f_48_3]) ).
cnf(f_48_6,plain,
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_55),U_53)),U_51))
| ti(arrow_1212486748le_alt,U_55) = ti(arrow_1212486748le_alt,U_49)
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_55),U_53)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,U_51),U_49))) ),
inference(clausify,[status(thm)],[f_48_3]) ).
cnf(f_48_7,plain,
( ti(arrow_1212486748le_alt,U_56) != ti(arrow_1212486748le_alt,U_50)
| ti(arrow_1212486748le_alt,U_56) = ti(arrow_1212486748le_alt,U_50)
| ti(arrow_1212486748le_alt,U_54) = ti(arrow_1212486748le_alt,U_50)
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_56),U_54)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,U_52),U_50))) ),
inference(clausify,[status(thm)],[f_48_3]) ).
cnf(f_48_8,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_56),U_54)),U_52))
| ti(arrow_1212486748le_alt,U_56) = ti(arrow_1212486748le_alt,U_50)
| ti(arrow_1212486748le_alt,U_54) = ti(arrow_1212486748le_alt,U_50)
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_56),U_54)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,U_52),U_50))) ),
inference(clausify,[status(thm)],[f_48_3]) ).
cnf(f_48_9,plain,
( ti(arrow_1212486748le_alt,U_56) != ti(arrow_1212486748le_alt,U_50)
| ti(arrow_1212486748le_alt,U_56) = ti(arrow_1212486748le_alt,U_54)
| ti(arrow_1212486748le_alt,U_54) = ti(arrow_1212486748le_alt,U_50)
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_56),U_54)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,U_52),U_50))) ),
inference(clausify,[status(thm)],[f_48_3]) ).
cnf(f_48_10,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_56),U_54)),U_52))
| ti(arrow_1212486748le_alt,U_56) = ti(arrow_1212486748le_alt,U_54)
| ti(arrow_1212486748le_alt,U_54) = ti(arrow_1212486748le_alt,U_50)
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_56),U_54)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,U_52),U_50))) ),
inference(clausify,[status(thm)],[f_48_3]) ).
fof(f_49_1,plain,
! [X_2,Y_1,L,Z_1] :
( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),X_2),Y_1)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,L),Z_1)))
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),X_2),Y_1)),L))
& ti(arrow_1212486748le_alt,Y_1) != ti(arrow_1212486748le_alt,Z_1) )
| ( ti(arrow_1212486748le_alt,X_2) = ti(arrow_1212486748le_alt,Y_1)
& ti(arrow_1212486748le_alt,Y_1) = ti(arrow_1212486748le_alt,Z_1) )
| ti(arrow_1212486748le_alt,X_2) = ti(arrow_1212486748le_alt,Z_1) )
& ( ( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),X_2),Y_1)),L))
| ti(arrow_1212486748le_alt,Y_1) = ti(arrow_1212486748le_alt,Z_1) )
& ( ti(arrow_1212486748le_alt,X_2) != ti(arrow_1212486748le_alt,Y_1)
| ti(arrow_1212486748le_alt,Y_1) != ti(arrow_1212486748le_alt,Z_1) )
& ti(arrow_1212486748le_alt,X_2) != ti(arrow_1212486748le_alt,Z_1) )
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),X_2),Y_1)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,L),Z_1))) ) ),
inference(fof_nnf,[status(thm)],[fact_5_in__mktop]) ).
fof(f_49_2,plain,
! [U_60,U_59,U_58,U_57] :
( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_60),U_59)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,U_58),U_57)))
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_60),U_59)),U_58))
& ti(arrow_1212486748le_alt,U_59) != ti(arrow_1212486748le_alt,U_57) )
| ( ti(arrow_1212486748le_alt,U_60) = ti(arrow_1212486748le_alt,U_59)
& ti(arrow_1212486748le_alt,U_59) = ti(arrow_1212486748le_alt,U_57) )
| ti(arrow_1212486748le_alt,U_60) = ti(arrow_1212486748le_alt,U_57) )
& ( ( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_60),U_59)),U_58))
| ti(arrow_1212486748le_alt,U_59) = ti(arrow_1212486748le_alt,U_57) )
& ( ti(arrow_1212486748le_alt,U_60) != ti(arrow_1212486748le_alt,U_59)
| ti(arrow_1212486748le_alt,U_59) != ti(arrow_1212486748le_alt,U_57) )
& ti(arrow_1212486748le_alt,U_60) != ti(arrow_1212486748le_alt,U_57) )
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_60),U_59)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,U_58),U_57))) ) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
fof(f_49_3,plain,
( ! [U_68,U_66,U_64,U_62] :
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_68),U_66)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,U_64),U_62)))
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_68),U_66)),U_64))
& ti(arrow_1212486748le_alt,U_66) != ti(arrow_1212486748le_alt,U_62) )
| ( ti(arrow_1212486748le_alt,U_68) = ti(arrow_1212486748le_alt,U_66)
& ti(arrow_1212486748le_alt,U_66) = ti(arrow_1212486748le_alt,U_62) )
| ti(arrow_1212486748le_alt,U_68) = ti(arrow_1212486748le_alt,U_62) )
& ! [U_67,U_65,U_63,U_61] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_67),U_65)),U_63))
| ti(arrow_1212486748le_alt,U_65) = ti(arrow_1212486748le_alt,U_61) )
& ( ti(arrow_1212486748le_alt,U_67) != ti(arrow_1212486748le_alt,U_65)
| ti(arrow_1212486748le_alt,U_65) != ti(arrow_1212486748le_alt,U_61) )
& ti(arrow_1212486748le_alt,U_67) != ti(arrow_1212486748le_alt,U_61) )
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_67),U_65)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,U_63),U_61))) ) ),
inference(miniscope,[status(thm)],[f_49_2]) ).
cnf(f_49_4,plain,
( ti(arrow_1212486748le_alt,U_67) != ti(arrow_1212486748le_alt,U_61)
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_67),U_65)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,U_63),U_61))) ),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_5,plain,
( ti(arrow_1212486748le_alt,U_67) != ti(arrow_1212486748le_alt,U_65)
| ti(arrow_1212486748le_alt,U_65) != ti(arrow_1212486748le_alt,U_61)
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_67),U_65)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,U_63),U_61))) ),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_6,plain,
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_67),U_65)),U_63))
| ti(arrow_1212486748le_alt,U_65) = ti(arrow_1212486748le_alt,U_61)
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_67),U_65)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,U_63),U_61))) ),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_7,plain,
( ti(arrow_1212486748le_alt,U_66) != ti(arrow_1212486748le_alt,U_62)
| ti(arrow_1212486748le_alt,U_66) = ti(arrow_1212486748le_alt,U_62)
| ti(arrow_1212486748le_alt,U_68) = ti(arrow_1212486748le_alt,U_62)
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_68),U_66)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,U_64),U_62))) ),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_8,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_68),U_66)),U_64))
| ti(arrow_1212486748le_alt,U_66) = ti(arrow_1212486748le_alt,U_62)
| ti(arrow_1212486748le_alt,U_68) = ti(arrow_1212486748le_alt,U_62)
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_68),U_66)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,U_64),U_62))) ),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_9,plain,
( ti(arrow_1212486748le_alt,U_66) != ti(arrow_1212486748le_alt,U_62)
| ti(arrow_1212486748le_alt,U_68) = ti(arrow_1212486748le_alt,U_66)
| ti(arrow_1212486748le_alt,U_68) = ti(arrow_1212486748le_alt,U_62)
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_68),U_66)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,U_64),U_62))) ),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_10,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_68),U_66)),U_64))
| ti(arrow_1212486748le_alt,U_68) = ti(arrow_1212486748le_alt,U_66)
| ti(arrow_1212486748le_alt,U_68) = ti(arrow_1212486748le_alt,U_62)
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_68),U_66)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,U_64),U_62))) ),
inference(clausify,[status(thm)],[f_49_3]) ).
fof(f_50_1,plain,
! [P_1,Pa,A_4,B_3,Aa,Ba] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Ba)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,Pa)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_4),B_3)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,P_1))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_4),B_3)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,P_1)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Ba)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,Pa))) ) )
| ? [I] :
( ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Ba)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Pa,I)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_4),B_3)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),P_1,I))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_4),B_3)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),P_1,I)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Ba)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Pa,I))) ) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),P_1),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),Pa),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,Ba) = ti(arrow_1212486748le_alt,A_4)
| ti(arrow_1212486748le_alt,Aa) = ti(arrow_1212486748le_alt,B_3)
| ti(arrow_1212486748le_alt,A_4) = ti(arrow_1212486748le_alt,B_3)
| ti(arrow_1212486748le_alt,Aa) = ti(arrow_1212486748le_alt,Ba) ),
inference(fof_nnf,[status(thm)],[fact_6__C2_C]) ).
fof(f_50_2,plain,
! [U_75,U_74,U_73,U_72,U_71,U_70] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_71),U_70)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_74)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_73),U_72)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_75))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_73),U_72)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_75)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_71),U_70)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_74))) ) )
| ? [U_69] :
( ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_71),U_70)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_74,U_69)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_73),U_72)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_75,U_69))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_73),U_72)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_75,U_69)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_71),U_70)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_74,U_69))) ) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_75),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_74),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_70) = ti(arrow_1212486748le_alt,U_73)
| ti(arrow_1212486748le_alt,U_71) = ti(arrow_1212486748le_alt,U_72)
| ti(arrow_1212486748le_alt,U_73) = ti(arrow_1212486748le_alt,U_72)
| ti(arrow_1212486748le_alt,U_71) = ti(arrow_1212486748le_alt,U_70) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
fof(f_50_3,plain,
! [U_75,U_74,U_73,U_72,U_71,U_70] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_71),U_70)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_74)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_73),U_72)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_75))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_73),U_72)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_75)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_71),U_70)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_74))) ) )
| ? [U_77] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_71),U_70)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_74,U_77)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_73),U_72)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_75,U_77))) )
| ? [U_76] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_73),U_72)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_75,U_76)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_71),U_70)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_74,U_76))) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_75),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_74),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_70) = ti(arrow_1212486748le_alt,U_73)
| ti(arrow_1212486748le_alt,U_71) = ti(arrow_1212486748le_alt,U_72)
| ti(arrow_1212486748le_alt,U_73) = ti(arrow_1212486748le_alt,U_72)
| ti(arrow_1212486748le_alt,U_71) = ti(arrow_1212486748le_alt,U_70) ),
inference(miniscope,[status(thm)],[f_50_2]) ).
fof(f_50_4,plain,
! [U_75,U_74,U_73,U_72,U_71,U_70] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_71),U_70)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_74)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_73),U_72)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_75))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_73),U_72)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_75)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_71),U_70)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_74))) ) )
| ? [U_77] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_71),U_70)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_74,U_77)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_73),U_72)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_75,U_77))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_73),U_72)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_75,sK1(U_75,U_74,U_73,U_72,U_71,U_70))))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_71),U_70)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_74,sK1(U_75,U_74,U_73,U_72,U_71,U_70)))) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_75),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_74),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_70) = ti(arrow_1212486748le_alt,U_73)
| ti(arrow_1212486748le_alt,U_71) = ti(arrow_1212486748le_alt,U_72)
| ti(arrow_1212486748le_alt,U_73) = ti(arrow_1212486748le_alt,U_72)
| ti(arrow_1212486748le_alt,U_71) = ti(arrow_1212486748le_alt,U_70) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_76,sK1(U_75,U_74,U_73,U_72,U_71,U_70))],[f_50_3]) ).
fof(f_50_5,plain,
! [U_75,U_74,U_73,U_72,U_71,U_70] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_71),U_70)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_74)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_73),U_72)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_75))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_73),U_72)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_75)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_71),U_70)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_74))) ) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_71),U_70)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_74,sK2(U_75,U_74,U_73,U_72,U_71,U_70))))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_73),U_72)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_75,sK2(U_75,U_74,U_73,U_72,U_71,U_70)))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_73),U_72)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_75,sK1(U_75,U_74,U_73,U_72,U_71,U_70))))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_71),U_70)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_74,sK1(U_75,U_74,U_73,U_72,U_71,U_70)))) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_75),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_74),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_70) = ti(arrow_1212486748le_alt,U_73)
| ti(arrow_1212486748le_alt,U_71) = ti(arrow_1212486748le_alt,U_72)
| ti(arrow_1212486748le_alt,U_73) = ti(arrow_1212486748le_alt,U_72)
| ti(arrow_1212486748le_alt,U_71) = ti(arrow_1212486748le_alt,U_70) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_77,sK2(U_75,U_74,U_73,U_72,U_71,U_70))],[f_50_4]) ).
cnf(f_50_6,plain,
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_73),U_72)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_75,sK2(U_75,U_74,U_73,U_72,U_71,U_70))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_71),U_70)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_74,sK1(U_75,U_74,U_73,U_72,U_71,U_70))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_73),U_72)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_75)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_71),U_70)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_74)))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_75),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_74),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_70) = ti(arrow_1212486748le_alt,U_73)
| ti(arrow_1212486748le_alt,U_71) = ti(arrow_1212486748le_alt,U_72)
| ti(arrow_1212486748le_alt,U_73) = ti(arrow_1212486748le_alt,U_72)
| ti(arrow_1212486748le_alt,U_71) = ti(arrow_1212486748le_alt,U_70) ),
inference(clausify,[status(thm)],[f_50_5]) ).
cnf(f_50_7,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_71),U_70)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_74,sK2(U_75,U_74,U_73,U_72,U_71,U_70))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_71),U_70)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_74,sK1(U_75,U_74,U_73,U_72,U_71,U_70))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_73),U_72)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_75)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_71),U_70)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_74)))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_75),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_74),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_70) = ti(arrow_1212486748le_alt,U_73)
| ti(arrow_1212486748le_alt,U_71) = ti(arrow_1212486748le_alt,U_72)
| ti(arrow_1212486748le_alt,U_73) = ti(arrow_1212486748le_alt,U_72)
| ti(arrow_1212486748le_alt,U_71) = ti(arrow_1212486748le_alt,U_70) ),
inference(clausify,[status(thm)],[f_50_5]) ).
cnf(f_50_8,plain,
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_73),U_72)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_75,sK2(U_75,U_74,U_73,U_72,U_71,U_70))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_73),U_72)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_75,sK1(U_75,U_74,U_73,U_72,U_71,U_70))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_73),U_72)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_75)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_71),U_70)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_74)))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_75),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_74),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_70) = ti(arrow_1212486748le_alt,U_73)
| ti(arrow_1212486748le_alt,U_71) = ti(arrow_1212486748le_alt,U_72)
| ti(arrow_1212486748le_alt,U_73) = ti(arrow_1212486748le_alt,U_72)
| ti(arrow_1212486748le_alt,U_71) = ti(arrow_1212486748le_alt,U_70) ),
inference(clausify,[status(thm)],[f_50_5]) ).
cnf(f_50_9,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_71),U_70)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_74,sK2(U_75,U_74,U_73,U_72,U_71,U_70))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_73),U_72)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_75,sK1(U_75,U_74,U_73,U_72,U_71,U_70))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_73),U_72)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_75)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_71),U_70)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_74)))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_75),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_74),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_70) = ti(arrow_1212486748le_alt,U_73)
| ti(arrow_1212486748le_alt,U_71) = ti(arrow_1212486748le_alt,U_72)
| ti(arrow_1212486748le_alt,U_73) = ti(arrow_1212486748le_alt,U_72)
| ti(arrow_1212486748le_alt,U_71) = ti(arrow_1212486748le_alt,U_70) ),
inference(clausify,[status(thm)],[f_50_5]) ).
cnf(f_50_10,plain,
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_73),U_72)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_75,sK2(U_75,U_74,U_73,U_72,U_71,U_70))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_71),U_70)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_74,sK1(U_75,U_74,U_73,U_72,U_71,U_70))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_71),U_70)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_74)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_73),U_72)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_75)))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_75),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_74),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_70) = ti(arrow_1212486748le_alt,U_73)
| ti(arrow_1212486748le_alt,U_71) = ti(arrow_1212486748le_alt,U_72)
| ti(arrow_1212486748le_alt,U_73) = ti(arrow_1212486748le_alt,U_72)
| ti(arrow_1212486748le_alt,U_71) = ti(arrow_1212486748le_alt,U_70) ),
inference(clausify,[status(thm)],[f_50_5]) ).
cnf(f_50_11,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_71),U_70)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_74,sK2(U_75,U_74,U_73,U_72,U_71,U_70))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_71),U_70)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_74,sK1(U_75,U_74,U_73,U_72,U_71,U_70))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_71),U_70)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_74)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_73),U_72)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_75)))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_75),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_74),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_70) = ti(arrow_1212486748le_alt,U_73)
| ti(arrow_1212486748le_alt,U_71) = ti(arrow_1212486748le_alt,U_72)
| ti(arrow_1212486748le_alt,U_73) = ti(arrow_1212486748le_alt,U_72)
| ti(arrow_1212486748le_alt,U_71) = ti(arrow_1212486748le_alt,U_70) ),
inference(clausify,[status(thm)],[f_50_5]) ).
cnf(f_50_12,plain,
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_73),U_72)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_75,sK2(U_75,U_74,U_73,U_72,U_71,U_70))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_73),U_72)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_75,sK1(U_75,U_74,U_73,U_72,U_71,U_70))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_71),U_70)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_74)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_73),U_72)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_75)))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_75),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_74),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_70) = ti(arrow_1212486748le_alt,U_73)
| ti(arrow_1212486748le_alt,U_71) = ti(arrow_1212486748le_alt,U_72)
| ti(arrow_1212486748le_alt,U_73) = ti(arrow_1212486748le_alt,U_72)
| ti(arrow_1212486748le_alt,U_71) = ti(arrow_1212486748le_alt,U_70) ),
inference(clausify,[status(thm)],[f_50_5]) ).
cnf(f_50_13,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_71),U_70)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_74,sK2(U_75,U_74,U_73,U_72,U_71,U_70))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_73),U_72)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_75,sK1(U_75,U_74,U_73,U_72,U_71,U_70))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_71),U_70)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_74)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_73),U_72)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_75)))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_75),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_74),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_70) = ti(arrow_1212486748le_alt,U_73)
| ti(arrow_1212486748le_alt,U_71) = ti(arrow_1212486748le_alt,U_72)
| ti(arrow_1212486748le_alt,U_73) = ti(arrow_1212486748le_alt,U_72)
| ti(arrow_1212486748le_alt,U_71) = ti(arrow_1212486748le_alt,U_70) ),
inference(clausify,[status(thm)],[f_50_5]) ).
fof(f_51_1,plain,
! [P_1,Pa,A_4,B_3,Aa,Ba] :
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_4),B_3)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,P_1)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Ba)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,Pa)))
| ? [I] :
( ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Ba)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Pa,I)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_4),B_3)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),P_1,I))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_4),B_3)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),P_1,I)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Ba)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Pa,I))) ) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),P_1),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),Pa),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,Ba) = ti(arrow_1212486748le_alt,A_4)
| ti(arrow_1212486748le_alt,Aa) = ti(arrow_1212486748le_alt,B_3)
| ti(arrow_1212486748le_alt,A_4) = ti(arrow_1212486748le_alt,B_3)
| ti(arrow_1212486748le_alt,Aa) = ti(arrow_1212486748le_alt,Ba) ),
inference(fof_nnf,[status(thm)],[fact_7__C1_C]) ).
fof(f_51_2,plain,
! [U_84,U_83,U_82,U_81,U_80,U_79] :
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_82),U_81)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_84)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_80),U_79)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_83)))
| ? [U_78] :
( ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_80),U_79)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_83,U_78)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_82),U_81)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_84,U_78))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_82),U_81)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_84,U_78)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_80),U_79)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_83,U_78))) ) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_84),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_83),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_79) = ti(arrow_1212486748le_alt,U_82)
| ti(arrow_1212486748le_alt,U_80) = ti(arrow_1212486748le_alt,U_81)
| ti(arrow_1212486748le_alt,U_82) = ti(arrow_1212486748le_alt,U_81)
| ti(arrow_1212486748le_alt,U_80) = ti(arrow_1212486748le_alt,U_79) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
fof(f_51_3,plain,
! [U_84,U_83,U_82,U_81,U_80,U_79] :
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_82),U_81)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_84)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_80),U_79)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_83)))
| ? [U_86] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_80),U_79)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_83,U_86)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_82),U_81)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_84,U_86))) )
| ? [U_85] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_82),U_81)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_84,U_85)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_80),U_79)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_83,U_85))) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_84),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_83),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_79) = ti(arrow_1212486748le_alt,U_82)
| ti(arrow_1212486748le_alt,U_80) = ti(arrow_1212486748le_alt,U_81)
| ti(arrow_1212486748le_alt,U_82) = ti(arrow_1212486748le_alt,U_81)
| ti(arrow_1212486748le_alt,U_80) = ti(arrow_1212486748le_alt,U_79) ),
inference(miniscope,[status(thm)],[f_51_2]) ).
fof(f_51_4,plain,
! [U_84,U_83,U_82,U_81,U_80,U_79] :
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_82),U_81)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_84)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_80),U_79)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_83)))
| ? [U_86] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_80),U_79)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_83,U_86)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_82),U_81)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_84,U_86))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_82),U_81)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_84,sK3(U_84,U_83,U_82,U_81,U_80,U_79))))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_80),U_79)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_83,sK3(U_84,U_83,U_82,U_81,U_80,U_79)))) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_84),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_83),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_79) = ti(arrow_1212486748le_alt,U_82)
| ti(arrow_1212486748le_alt,U_80) = ti(arrow_1212486748le_alt,U_81)
| ti(arrow_1212486748le_alt,U_82) = ti(arrow_1212486748le_alt,U_81)
| ti(arrow_1212486748le_alt,U_80) = ti(arrow_1212486748le_alt,U_79) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_85,sK3(U_84,U_83,U_82,U_81,U_80,U_79))],[f_51_3]) ).
fof(f_51_5,plain,
! [U_84,U_83,U_82,U_81,U_80,U_79] :
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_82),U_81)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_84)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_80),U_79)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_83)))
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_80),U_79)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_83,sK4(U_84,U_83,U_82,U_81,U_80,U_79))))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_82),U_81)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_84,sK4(U_84,U_83,U_82,U_81,U_80,U_79)))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_82),U_81)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_84,sK3(U_84,U_83,U_82,U_81,U_80,U_79))))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_80),U_79)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_83,sK3(U_84,U_83,U_82,U_81,U_80,U_79)))) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_84),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_83),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_79) = ti(arrow_1212486748le_alt,U_82)
| ti(arrow_1212486748le_alt,U_80) = ti(arrow_1212486748le_alt,U_81)
| ti(arrow_1212486748le_alt,U_82) = ti(arrow_1212486748le_alt,U_81)
| ti(arrow_1212486748le_alt,U_80) = ti(arrow_1212486748le_alt,U_79) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_86,sK4(U_84,U_83,U_82,U_81,U_80,U_79))],[f_51_4]) ).
cnf(f_51_6,plain,
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_82),U_81)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_84,sK4(U_84,U_83,U_82,U_81,U_80,U_79))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_80),U_79)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_83,sK3(U_84,U_83,U_82,U_81,U_80,U_79))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_82),U_81)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_84)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_80),U_79)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_83)))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_84),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_83),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_79) = ti(arrow_1212486748le_alt,U_82)
| ti(arrow_1212486748le_alt,U_80) = ti(arrow_1212486748le_alt,U_81)
| ti(arrow_1212486748le_alt,U_82) = ti(arrow_1212486748le_alt,U_81)
| ti(arrow_1212486748le_alt,U_80) = ti(arrow_1212486748le_alt,U_79) ),
inference(clausify,[status(thm)],[f_51_5]) ).
cnf(f_51_7,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_80),U_79)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_83,sK4(U_84,U_83,U_82,U_81,U_80,U_79))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_80),U_79)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_83,sK3(U_84,U_83,U_82,U_81,U_80,U_79))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_82),U_81)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_84)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_80),U_79)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_83)))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_84),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_83),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_79) = ti(arrow_1212486748le_alt,U_82)
| ti(arrow_1212486748le_alt,U_80) = ti(arrow_1212486748le_alt,U_81)
| ti(arrow_1212486748le_alt,U_82) = ti(arrow_1212486748le_alt,U_81)
| ti(arrow_1212486748le_alt,U_80) = ti(arrow_1212486748le_alt,U_79) ),
inference(clausify,[status(thm)],[f_51_5]) ).
cnf(f_51_8,plain,
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_82),U_81)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_84,sK4(U_84,U_83,U_82,U_81,U_80,U_79))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_82),U_81)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_84,sK3(U_84,U_83,U_82,U_81,U_80,U_79))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_82),U_81)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_84)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_80),U_79)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_83)))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_84),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_83),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_79) = ti(arrow_1212486748le_alt,U_82)
| ti(arrow_1212486748le_alt,U_80) = ti(arrow_1212486748le_alt,U_81)
| ti(arrow_1212486748le_alt,U_82) = ti(arrow_1212486748le_alt,U_81)
| ti(arrow_1212486748le_alt,U_80) = ti(arrow_1212486748le_alt,U_79) ),
inference(clausify,[status(thm)],[f_51_5]) ).
cnf(f_51_9,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_80),U_79)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_83,sK4(U_84,U_83,U_82,U_81,U_80,U_79))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_82),U_81)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_84,sK3(U_84,U_83,U_82,U_81,U_80,U_79))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_82),U_81)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_84)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_80),U_79)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_83)))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_84),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_83),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_79) = ti(arrow_1212486748le_alt,U_82)
| ti(arrow_1212486748le_alt,U_80) = ti(arrow_1212486748le_alt,U_81)
| ti(arrow_1212486748le_alt,U_82) = ti(arrow_1212486748le_alt,U_81)
| ti(arrow_1212486748le_alt,U_80) = ti(arrow_1212486748le_alt,U_79) ),
inference(clausify,[status(thm)],[f_51_5]) ).
fof(f_52_1,plain,
! [P_1,Pa,Ca,Aa,Ba] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Ba)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,Pa)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Ba),Ca)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,P_1))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Ba),Ca)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,P_1)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Ba)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,Pa))) ) )
| ? [I] :
( ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Ba)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Pa,I)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Ba),Ca)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),P_1,I))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Ba),Ca)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),P_1,I)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Ba)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Pa,I))) ) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),P_1),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),Pa),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,Aa) = ti(arrow_1212486748le_alt,Ca)
| ti(arrow_1212486748le_alt,Ba) = ti(arrow_1212486748le_alt,Ca)
| ti(arrow_1212486748le_alt,Aa) = ti(arrow_1212486748le_alt,Ba) ),
inference(fof_nnf,[status(thm)],[fact_8__C4_C]) ).
fof(f_52_2,plain,
! [U_92,U_91,U_90,U_89,U_88] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_89),U_88)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_91)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_88),U_90)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_92))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_88),U_90)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_92)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_89),U_88)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_91))) ) )
| ? [U_87] :
( ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_89),U_88)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_91,U_87)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_88),U_90)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_92,U_87))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_88),U_90)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_92,U_87)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_89),U_88)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_91,U_87))) ) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_92),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_91),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_89) = ti(arrow_1212486748le_alt,U_90)
| ti(arrow_1212486748le_alt,U_88) = ti(arrow_1212486748le_alt,U_90)
| ti(arrow_1212486748le_alt,U_89) = ti(arrow_1212486748le_alt,U_88) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
fof(f_52_3,plain,
! [U_92,U_91,U_90,U_89,U_88] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_89),U_88)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_91)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_88),U_90)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_92))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_88),U_90)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_92)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_89),U_88)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_91))) ) )
| ? [U_94] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_89),U_88)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_91,U_94)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_88),U_90)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_92,U_94))) )
| ? [U_93] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_88),U_90)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_92,U_93)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_89),U_88)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_91,U_93))) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_92),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_91),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_89) = ti(arrow_1212486748le_alt,U_90)
| ti(arrow_1212486748le_alt,U_88) = ti(arrow_1212486748le_alt,U_90)
| ti(arrow_1212486748le_alt,U_89) = ti(arrow_1212486748le_alt,U_88) ),
inference(miniscope,[status(thm)],[f_52_2]) ).
fof(f_52_4,plain,
! [U_92,U_91,U_90,U_89,U_88] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_89),U_88)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_91)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_88),U_90)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_92))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_88),U_90)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_92)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_89),U_88)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_91))) ) )
| ? [U_94] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_89),U_88)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_91,U_94)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_88),U_90)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_92,U_94))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_88),U_90)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_92,sK5(U_92,U_91,U_90,U_89,U_88))))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_89),U_88)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_91,sK5(U_92,U_91,U_90,U_89,U_88)))) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_92),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_91),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_89) = ti(arrow_1212486748le_alt,U_90)
| ti(arrow_1212486748le_alt,U_88) = ti(arrow_1212486748le_alt,U_90)
| ti(arrow_1212486748le_alt,U_89) = ti(arrow_1212486748le_alt,U_88) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_93,sK5(U_92,U_91,U_90,U_89,U_88))],[f_52_3]) ).
fof(f_52_5,plain,
! [U_92,U_91,U_90,U_89,U_88] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_89),U_88)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_91)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_88),U_90)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_92))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_88),U_90)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_92)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_89),U_88)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_91))) ) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_89),U_88)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_91,sK6(U_92,U_91,U_90,U_89,U_88))))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_88),U_90)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_92,sK6(U_92,U_91,U_90,U_89,U_88)))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_88),U_90)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_92,sK5(U_92,U_91,U_90,U_89,U_88))))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_89),U_88)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_91,sK5(U_92,U_91,U_90,U_89,U_88)))) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_92),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_91),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_89) = ti(arrow_1212486748le_alt,U_90)
| ti(arrow_1212486748le_alt,U_88) = ti(arrow_1212486748le_alt,U_90)
| ti(arrow_1212486748le_alt,U_89) = ti(arrow_1212486748le_alt,U_88) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_94,sK6(U_92,U_91,U_90,U_89,U_88))],[f_52_4]) ).
cnf(f_52_6,plain,
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_88),U_90)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_92,sK6(U_92,U_91,U_90,U_89,U_88))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_89),U_88)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_91,sK5(U_92,U_91,U_90,U_89,U_88))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_88),U_90)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_92)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_89),U_88)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_91)))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_92),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_91),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_89) = ti(arrow_1212486748le_alt,U_90)
| ti(arrow_1212486748le_alt,U_88) = ti(arrow_1212486748le_alt,U_90)
| ti(arrow_1212486748le_alt,U_89) = ti(arrow_1212486748le_alt,U_88) ),
inference(clausify,[status(thm)],[f_52_5]) ).
cnf(f_52_7,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_89),U_88)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_91,sK6(U_92,U_91,U_90,U_89,U_88))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_89),U_88)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_91,sK5(U_92,U_91,U_90,U_89,U_88))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_88),U_90)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_92)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_89),U_88)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_91)))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_92),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_91),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_89) = ti(arrow_1212486748le_alt,U_90)
| ti(arrow_1212486748le_alt,U_88) = ti(arrow_1212486748le_alt,U_90)
| ti(arrow_1212486748le_alt,U_89) = ti(arrow_1212486748le_alt,U_88) ),
inference(clausify,[status(thm)],[f_52_5]) ).
cnf(f_52_8,plain,
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_88),U_90)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_92,sK6(U_92,U_91,U_90,U_89,U_88))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_88),U_90)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_92,sK5(U_92,U_91,U_90,U_89,U_88))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_88),U_90)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_92)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_89),U_88)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_91)))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_92),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_91),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_89) = ti(arrow_1212486748le_alt,U_90)
| ti(arrow_1212486748le_alt,U_88) = ti(arrow_1212486748le_alt,U_90)
| ti(arrow_1212486748le_alt,U_89) = ti(arrow_1212486748le_alt,U_88) ),
inference(clausify,[status(thm)],[f_52_5]) ).
cnf(f_52_9,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_89),U_88)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_91,sK6(U_92,U_91,U_90,U_89,U_88))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_88),U_90)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_92,sK5(U_92,U_91,U_90,U_89,U_88))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_88),U_90)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_92)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_89),U_88)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_91)))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_92),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_91),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_89) = ti(arrow_1212486748le_alt,U_90)
| ti(arrow_1212486748le_alt,U_88) = ti(arrow_1212486748le_alt,U_90)
| ti(arrow_1212486748le_alt,U_89) = ti(arrow_1212486748le_alt,U_88) ),
inference(clausify,[status(thm)],[f_52_5]) ).
cnf(f_52_10,plain,
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_88),U_90)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_92,sK6(U_92,U_91,U_90,U_89,U_88))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_89),U_88)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_91,sK5(U_92,U_91,U_90,U_89,U_88))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_89),U_88)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_91)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_88),U_90)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_92)))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_92),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_91),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_89) = ti(arrow_1212486748le_alt,U_90)
| ti(arrow_1212486748le_alt,U_88) = ti(arrow_1212486748le_alt,U_90)
| ti(arrow_1212486748le_alt,U_89) = ti(arrow_1212486748le_alt,U_88) ),
inference(clausify,[status(thm)],[f_52_5]) ).
cnf(f_52_11,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_89),U_88)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_91,sK6(U_92,U_91,U_90,U_89,U_88))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_89),U_88)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_91,sK5(U_92,U_91,U_90,U_89,U_88))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_89),U_88)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_91)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_88),U_90)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_92)))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_92),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_91),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_89) = ti(arrow_1212486748le_alt,U_90)
| ti(arrow_1212486748le_alt,U_88) = ti(arrow_1212486748le_alt,U_90)
| ti(arrow_1212486748le_alt,U_89) = ti(arrow_1212486748le_alt,U_88) ),
inference(clausify,[status(thm)],[f_52_5]) ).
cnf(f_52_12,plain,
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_88),U_90)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_92,sK6(U_92,U_91,U_90,U_89,U_88))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_88),U_90)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_92,sK5(U_92,U_91,U_90,U_89,U_88))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_89),U_88)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_91)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_88),U_90)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_92)))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_92),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_91),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_89) = ti(arrow_1212486748le_alt,U_90)
| ti(arrow_1212486748le_alt,U_88) = ti(arrow_1212486748le_alt,U_90)
| ti(arrow_1212486748le_alt,U_89) = ti(arrow_1212486748le_alt,U_88) ),
inference(clausify,[status(thm)],[f_52_5]) ).
cnf(f_52_13,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_89),U_88)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_91,sK6(U_92,U_91,U_90,U_89,U_88))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_88),U_90)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_92,sK5(U_92,U_91,U_90,U_89,U_88))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_89),U_88)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_91)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_88),U_90)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_92)))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_92),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_91),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_89) = ti(arrow_1212486748le_alt,U_90)
| ti(arrow_1212486748le_alt,U_88) = ti(arrow_1212486748le_alt,U_90)
| ti(arrow_1212486748le_alt,U_89) = ti(arrow_1212486748le_alt,U_88) ),
inference(clausify,[status(thm)],[f_52_5]) ).
fof(f_53_1,plain,
! [P_1,Pa,A_4,B_3,Aa,Ba] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Ba)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,Pa)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_4),B_3)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,P_1))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_4),B_3)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,P_1)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Ba)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,Pa))) ) )
| ? [I] :
( ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Ba)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Pa,I)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_4),B_3)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),P_1,I))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_4),B_3)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),P_1,I)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Ba)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Pa,I))) ) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),P_1),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),Pa),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,A_4) = ti(arrow_1212486748le_alt,B_3)
| ti(arrow_1212486748le_alt,Aa) = ti(arrow_1212486748le_alt,Ba) ),
inference(fof_nnf,[status(thm)],[fact_9_pairwise__neutrality]) ).
fof(f_53_2,plain,
! [U_101,U_100,U_99,U_98,U_97,U_96] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_97),U_96)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_100)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_99),U_98)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_101))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_99),U_98)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_101)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_97),U_96)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_100))) ) )
| ? [U_95] :
( ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_97),U_96)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_100,U_95)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_99),U_98)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_101,U_95))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_99),U_98)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_101,U_95)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_97),U_96)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_100,U_95))) ) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_101),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_100),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_99) = ti(arrow_1212486748le_alt,U_98)
| ti(arrow_1212486748le_alt,U_97) = ti(arrow_1212486748le_alt,U_96) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
fof(f_53_3,plain,
! [U_101,U_100,U_99,U_98,U_97,U_96] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_97),U_96)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_100)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_99),U_98)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_101))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_99),U_98)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_101)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_97),U_96)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_100))) ) )
| ? [U_103] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_97),U_96)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_100,U_103)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_99),U_98)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_101,U_103))) )
| ? [U_102] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_99),U_98)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_101,U_102)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_97),U_96)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_100,U_102))) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_101),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_100),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_99) = ti(arrow_1212486748le_alt,U_98)
| ti(arrow_1212486748le_alt,U_97) = ti(arrow_1212486748le_alt,U_96) ),
inference(miniscope,[status(thm)],[f_53_2]) ).
fof(f_53_4,plain,
! [U_101,U_100,U_99,U_98,U_97,U_96] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_97),U_96)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_100)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_99),U_98)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_101))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_99),U_98)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_101)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_97),U_96)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_100))) ) )
| ? [U_103] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_97),U_96)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_100,U_103)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_99),U_98)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_101,U_103))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_99),U_98)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_101,sK7(U_101,U_100,U_99,U_98,U_97,U_96))))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_97),U_96)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_100,sK7(U_101,U_100,U_99,U_98,U_97,U_96)))) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_101),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_100),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_99) = ti(arrow_1212486748le_alt,U_98)
| ti(arrow_1212486748le_alt,U_97) = ti(arrow_1212486748le_alt,U_96) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_102,sK7(U_101,U_100,U_99,U_98,U_97,U_96))],[f_53_3]) ).
fof(f_53_5,plain,
! [U_101,U_100,U_99,U_98,U_97,U_96] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_97),U_96)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_100)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_99),U_98)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_101))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_99),U_98)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_101)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_97),U_96)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_100))) ) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_97),U_96)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_100,sK8(U_101,U_100,U_99,U_98,U_97,U_96))))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_99),U_98)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_101,sK8(U_101,U_100,U_99,U_98,U_97,U_96)))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_99),U_98)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_101,sK7(U_101,U_100,U_99,U_98,U_97,U_96))))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_97),U_96)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_100,sK7(U_101,U_100,U_99,U_98,U_97,U_96)))) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_101),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_100),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_99) = ti(arrow_1212486748le_alt,U_98)
| ti(arrow_1212486748le_alt,U_97) = ti(arrow_1212486748le_alt,U_96) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_103,sK8(U_101,U_100,U_99,U_98,U_97,U_96))],[f_53_4]) ).
cnf(f_53_6,plain,
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_99),U_98)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_101,sK8(U_101,U_100,U_99,U_98,U_97,U_96))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_97),U_96)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_100,sK7(U_101,U_100,U_99,U_98,U_97,U_96))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_99),U_98)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_101)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_97),U_96)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_100)))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_101),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_100),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_99) = ti(arrow_1212486748le_alt,U_98)
| ti(arrow_1212486748le_alt,U_97) = ti(arrow_1212486748le_alt,U_96) ),
inference(clausify,[status(thm)],[f_53_5]) ).
cnf(f_53_7,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_97),U_96)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_100,sK8(U_101,U_100,U_99,U_98,U_97,U_96))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_97),U_96)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_100,sK7(U_101,U_100,U_99,U_98,U_97,U_96))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_99),U_98)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_101)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_97),U_96)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_100)))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_101),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_100),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_99) = ti(arrow_1212486748le_alt,U_98)
| ti(arrow_1212486748le_alt,U_97) = ti(arrow_1212486748le_alt,U_96) ),
inference(clausify,[status(thm)],[f_53_5]) ).
cnf(f_53_8,plain,
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_99),U_98)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_101,sK8(U_101,U_100,U_99,U_98,U_97,U_96))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_99),U_98)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_101,sK7(U_101,U_100,U_99,U_98,U_97,U_96))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_99),U_98)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_101)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_97),U_96)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_100)))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_101),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_100),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_99) = ti(arrow_1212486748le_alt,U_98)
| ti(arrow_1212486748le_alt,U_97) = ti(arrow_1212486748le_alt,U_96) ),
inference(clausify,[status(thm)],[f_53_5]) ).
cnf(f_53_9,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_97),U_96)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_100,sK8(U_101,U_100,U_99,U_98,U_97,U_96))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_99),U_98)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_101,sK7(U_101,U_100,U_99,U_98,U_97,U_96))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_99),U_98)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_101)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_97),U_96)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_100)))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_101),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_100),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_99) = ti(arrow_1212486748le_alt,U_98)
| ti(arrow_1212486748le_alt,U_97) = ti(arrow_1212486748le_alt,U_96) ),
inference(clausify,[status(thm)],[f_53_5]) ).
cnf(f_53_10,plain,
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_99),U_98)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_101,sK8(U_101,U_100,U_99,U_98,U_97,U_96))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_97),U_96)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_100,sK7(U_101,U_100,U_99,U_98,U_97,U_96))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_97),U_96)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_100)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_99),U_98)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_101)))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_101),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_100),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_99) = ti(arrow_1212486748le_alt,U_98)
| ti(arrow_1212486748le_alt,U_97) = ti(arrow_1212486748le_alt,U_96) ),
inference(clausify,[status(thm)],[f_53_5]) ).
cnf(f_53_11,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_97),U_96)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_100,sK8(U_101,U_100,U_99,U_98,U_97,U_96))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_97),U_96)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_100,sK7(U_101,U_100,U_99,U_98,U_97,U_96))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_97),U_96)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_100)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_99),U_98)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_101)))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_101),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_100),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_99) = ti(arrow_1212486748le_alt,U_98)
| ti(arrow_1212486748le_alt,U_97) = ti(arrow_1212486748le_alt,U_96) ),
inference(clausify,[status(thm)],[f_53_5]) ).
cnf(f_53_12,plain,
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_99),U_98)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_101,sK8(U_101,U_100,U_99,U_98,U_97,U_96))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_99),U_98)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_101,sK7(U_101,U_100,U_99,U_98,U_97,U_96))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_97),U_96)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_100)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_99),U_98)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_101)))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_101),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_100),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_99) = ti(arrow_1212486748le_alt,U_98)
| ti(arrow_1212486748le_alt,U_97) = ti(arrow_1212486748le_alt,U_96) ),
inference(clausify,[status(thm)],[f_53_5]) ).
cnf(f_53_13,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_97),U_96)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_100,sK8(U_101,U_100,U_99,U_98,U_97,U_96))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_99),U_98)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_101,sK7(U_101,U_100,U_99,U_98,U_97,U_96))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_97),U_96)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_100)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_99),U_98)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_101)))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_101),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_100),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_99) = ti(arrow_1212486748le_alt,U_98)
| ti(arrow_1212486748le_alt,U_97) = ti(arrow_1212486748le_alt,U_96) ),
inference(clausify,[status(thm)],[f_53_5]) ).
fof(f_54_1,plain,
! [P_1,Pa,Aa,Ba] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Ba)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,Pa)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Ba),Aa)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,P_1))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Ba),Aa)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,P_1)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Ba)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,Pa))) ) )
| ? [I] :
( ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Ba)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Pa,I)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Ba),Aa)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),P_1,I))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Ba),Aa)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),P_1,I)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Ba)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Pa,I))) ) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),P_1),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),Pa),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,Aa) = ti(arrow_1212486748le_alt,Ba) ),
inference(fof_nnf,[status(thm)],[fact_10__C3_C]) ).
fof(f_54_2,plain,
! [U_108,U_107,U_106,U_105] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_106),U_105)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_107)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_105),U_106)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_108))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_105),U_106)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_108)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_106),U_105)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_107))) ) )
| ? [U_104] :
( ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_106),U_105)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_107,U_104)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_105),U_106)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_108,U_104))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_105),U_106)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_108,U_104)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_106),U_105)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_107,U_104))) ) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_108),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_107),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_106) = ti(arrow_1212486748le_alt,U_105) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
fof(f_54_3,plain,
! [U_108,U_107,U_106,U_105] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_106),U_105)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_107)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_105),U_106)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_108))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_105),U_106)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_108)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_106),U_105)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_107))) ) )
| ? [U_110] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_106),U_105)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_107,U_110)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_105),U_106)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_108,U_110))) )
| ? [U_109] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_105),U_106)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_108,U_109)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_106),U_105)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_107,U_109))) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_108),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_107),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_106) = ti(arrow_1212486748le_alt,U_105) ),
inference(miniscope,[status(thm)],[f_54_2]) ).
fof(f_54_4,plain,
! [U_108,U_107,U_106,U_105] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_106),U_105)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_107)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_105),U_106)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_108))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_105),U_106)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_108)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_106),U_105)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_107))) ) )
| ? [U_110] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_106),U_105)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_107,U_110)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_105),U_106)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_108,U_110))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_105),U_106)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_108,sK9(U_108,U_107,U_106,U_105))))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_106),U_105)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_107,sK9(U_108,U_107,U_106,U_105)))) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_108),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_107),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_106) = ti(arrow_1212486748le_alt,U_105) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_109,sK9(U_108,U_107,U_106,U_105))],[f_54_3]) ).
fof(f_54_5,plain,
! [U_108,U_107,U_106,U_105] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_106),U_105)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_107)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_105),U_106)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_108))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_105),U_106)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_108)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_106),U_105)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_107))) ) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_106),U_105)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_107,sK10(U_108,U_107,U_106,U_105))))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_105),U_106)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_108,sK10(U_108,U_107,U_106,U_105)))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_105),U_106)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_108,sK9(U_108,U_107,U_106,U_105))))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_106),U_105)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_107,sK9(U_108,U_107,U_106,U_105)))) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_108),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_107),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_106) = ti(arrow_1212486748le_alt,U_105) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_110,sK10(U_108,U_107,U_106,U_105))],[f_54_4]) ).
cnf(f_54_6,plain,
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_105),U_106)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_108,sK10(U_108,U_107,U_106,U_105))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_106),U_105)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_107,sK9(U_108,U_107,U_106,U_105))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_105),U_106)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_108)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_106),U_105)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_107)))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_108),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_107),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_106) = ti(arrow_1212486748le_alt,U_105) ),
inference(clausify,[status(thm)],[f_54_5]) ).
cnf(f_54_7,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_106),U_105)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_107,sK10(U_108,U_107,U_106,U_105))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_106),U_105)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_107,sK9(U_108,U_107,U_106,U_105))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_105),U_106)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_108)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_106),U_105)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_107)))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_108),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_107),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_106) = ti(arrow_1212486748le_alt,U_105) ),
inference(clausify,[status(thm)],[f_54_5]) ).
cnf(f_54_8,plain,
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_105),U_106)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_108,sK10(U_108,U_107,U_106,U_105))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_105),U_106)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_108,sK9(U_108,U_107,U_106,U_105))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_105),U_106)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_108)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_106),U_105)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_107)))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_108),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_107),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_106) = ti(arrow_1212486748le_alt,U_105) ),
inference(clausify,[status(thm)],[f_54_5]) ).
cnf(f_54_9,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_106),U_105)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_107,sK10(U_108,U_107,U_106,U_105))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_105),U_106)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_108,sK9(U_108,U_107,U_106,U_105))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_105),U_106)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_108)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_106),U_105)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_107)))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_108),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_107),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_106) = ti(arrow_1212486748le_alt,U_105) ),
inference(clausify,[status(thm)],[f_54_5]) ).
cnf(f_54_10,plain,
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_105),U_106)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_108,sK10(U_108,U_107,U_106,U_105))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_106),U_105)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_107,sK9(U_108,U_107,U_106,U_105))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_106),U_105)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_107)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_105),U_106)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_108)))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_108),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_107),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_106) = ti(arrow_1212486748le_alt,U_105) ),
inference(clausify,[status(thm)],[f_54_5]) ).
cnf(f_54_11,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_106),U_105)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_107,sK10(U_108,U_107,U_106,U_105))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_106),U_105)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_107,sK9(U_108,U_107,U_106,U_105))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_106),U_105)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_107)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_105),U_106)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_108)))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_108),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_107),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_106) = ti(arrow_1212486748le_alt,U_105) ),
inference(clausify,[status(thm)],[f_54_5]) ).
cnf(f_54_12,plain,
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_105),U_106)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_108,sK10(U_108,U_107,U_106,U_105))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_105),U_106)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_108,sK9(U_108,U_107,U_106,U_105))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_106),U_105)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_107)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_105),U_106)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_108)))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_108),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_107),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_106) = ti(arrow_1212486748le_alt,U_105) ),
inference(clausify,[status(thm)],[f_54_5]) ).
cnf(f_54_13,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_106),U_105)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_107,sK10(U_108,U_107,U_106,U_105))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_105),U_106)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_108,sK9(U_108,U_107,U_106,U_105))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_106),U_105)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_107)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_105),U_106)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,U_108)))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_108),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_107),arrow_1834574746e_Prof))
| ti(arrow_1212486748le_alt,U_106) = ti(arrow_1212486748le_alt,U_105) ),
inference(clausify,[status(thm)],[f_54_5]) ).
fof(f_55_1,plain,
! [I] :
( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,I)))
| ( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,I)),e)))
& hAPP(arrow_1384031255e_indi,nat,h,I) != n )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,I)),c),e)))
& hAPP(arrow_1384031255e_indi,nat,h,I) = n ) )
& ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,I)),n)) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,I)),e)))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,I)),n)) ) )
& ( ( ( ( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,I)),e)))
| hAPP(arrow_1384031255e_indi,nat,h,I) = n )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,I)),c),e)))
| hAPP(arrow_1384031255e_indi,nat,h,I) != n ) )
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,I)),n)) )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,I)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,I)),n)) ) )
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,I))) ) ),
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_55_2,plain,
! [U_111] :
( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_111)))
| ( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_111)),e)))
& hAPP(arrow_1384031255e_indi,nat,h,U_111) != n )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_111)),c),e)))
& hAPP(arrow_1384031255e_indi,nat,h,U_111) = n ) )
& ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_111)),n)) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_111)),e)))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_111)),n)) ) )
& ( ( ( ( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_111)),e)))
| hAPP(arrow_1384031255e_indi,nat,h,U_111) = n )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_111)),c),e)))
| hAPP(arrow_1384031255e_indi,nat,h,U_111) != n ) )
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_111)),n)) )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_111)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_111)),n)) ) )
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_111))) ) ),
inference(variable_rename,[status(thm)],[f_55_1]) ).
fof(f_55_3,plain,
( ! [U_113] :
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_113)))
| ( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_113)),e)))
& hAPP(arrow_1384031255e_indi,nat,h,U_113) != n )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_113)),c),e)))
& hAPP(arrow_1384031255e_indi,nat,h,U_113) = n ) )
& ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_113)),n)) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_113)),e)))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_113)),n)) ) )
& ! [U_112] :
( ( ( ( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_112)),e)))
| hAPP(arrow_1384031255e_indi,nat,h,U_112) = n )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_112)),c),e)))
| hAPP(arrow_1384031255e_indi,nat,h,U_112) != n ) )
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_112)),n)) )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_112)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_112)),n)) ) )
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_112))) ) ),
inference(miniscope,[status(thm)],[f_55_2]) ).
cnf(f_55_4,plain,
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_112)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_112)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_112))) ),
inference(clausify,[status(thm)],[f_55_3]) ).
cnf(f_55_5,plain,
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_112)),c),e)))
| hAPP(arrow_1384031255e_indi,nat,h,U_112) != n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_112)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_112))) ),
inference(clausify,[status(thm)],[f_55_3]) ).
cnf(f_55_6,plain,
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_112)),e)))
| hAPP(arrow_1384031255e_indi,nat,h,U_112) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_112)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_112))) ),
inference(clausify,[status(thm)],[f_55_3]) ).
cnf(f_55_7,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_113)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_113)),n))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_113))) ),
inference(clausify,[status(thm)],[f_55_3]) ).
cnf(f_55_8,plain,
( hAPP(arrow_1384031255e_indi,nat,h,U_113) != n
| hAPP(arrow_1384031255e_indi,nat,h,U_113) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_113)),n))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_113))) ),
inference(clausify,[status(thm)],[f_55_3]) ).
cnf(f_55_9,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_113)),e)))
| hAPP(arrow_1384031255e_indi,nat,h,U_113) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_113)),n))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_113))) ),
inference(clausify,[status(thm)],[f_55_3]) ).
cnf(f_55_10,plain,
( hAPP(arrow_1384031255e_indi,nat,h,U_113) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_113)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_113)),n))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_113))) ),
inference(clausify,[status(thm)],[f_55_3]) ).
cnf(f_55_11,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_113)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_113)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_113)),n))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_113))) ),
inference(clausify,[status(thm)],[f_55_3]) ).
cnf(f_55_12,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_113)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_113)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_113))) ),
inference(clausify,[status(thm)],[f_55_3]) ).
cnf(f_55_13,plain,
( hAPP(arrow_1384031255e_indi,nat,h,U_113) != n
| hAPP(arrow_1384031255e_indi,nat,h,U_113) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_113)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_113))) ),
inference(clausify,[status(thm)],[f_55_3]) ).
cnf(f_55_14,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_113)),e)))
| hAPP(arrow_1384031255e_indi,nat,h,U_113) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_113)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_113))) ),
inference(clausify,[status(thm)],[f_55_3]) ).
cnf(f_55_15,plain,
( hAPP(arrow_1384031255e_indi,nat,h,U_113) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_113)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_113)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_113))) ),
inference(clausify,[status(thm)],[f_55_3]) ).
cnf(f_55_16,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_113)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_113)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_113)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_113))) ),
inference(clausify,[status(thm)],[f_55_3]) ).
fof(f_56_1,plain,
hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,hAPP(nat,arrow_1384031255e_indi,hAPP(fun(arrow_1384031255e_indi,nat),fun(nat,arrow_1384031255e_indi),hAPP(fun(arrow_1384031255e_indi,bool),fun(fun(arrow_1384031255e_indi,nat),fun(nat,arrow_1384031255e_indi)),hilbert_inv_into(arrow_1384031255e_indi,nat),top_top(fun(arrow_1384031255e_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_56_2,plain,
hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,hAPP(nat,arrow_1384031255e_indi,hAPP(fun(arrow_1384031255e_indi,nat),fun(nat,arrow_1384031255e_indi),hAPP(fun(arrow_1384031255e_indi,bool),fun(fun(arrow_1384031255e_indi,nat),fun(nat,arrow_1384031255e_indi)),hilbert_inv_into(arrow_1384031255e_indi,nat),top_top(fun(arrow_1384031255e_indi,bool))),h),n)))),
inference(clausify,[status(thm)],[f_56_1]) ).
fof(f_57_1,plain,
hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),ord_less(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1384031255e_indi),arrow_992993526_mktop),p)),e))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),fequal(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),arrow_1726925404_above),p)),c)),e))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1384031255e_indi),arrow_844286440_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_57_2,plain,
hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),ord_less(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1384031255e_indi),arrow_992993526_mktop),p)),e))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),fequal(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),arrow_1726925404_above),p)),c)),e))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1384031255e_indi),arrow_844286440_mkbot),p)),e)))))),
inference(clausify,[status(thm)],[f_57_1]) ).
fof(f_58_1,plain,
( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,p)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),ord_less(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_121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,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),arrow_1726925404_above),p)),c)),e))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1384031255e_indi),arrow_844286440_mkbot),p)),e)))))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),ord_less(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1384031255e_indi),arrow_992993526_mktop),p)),e))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),fequal(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),arrow_1726925404_above),p)),c)),e))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1384031255e_indi),arrow_844286440_mkbot),p)),e))))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,p))) ) ),
inference(fof_nnf,[status(thm)],[fact_14_PW]) ).
cnf(f_58_2,plain,
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),ord_less(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1384031255e_indi),arrow_992993526_mktop),p)),e))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),fequal(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),arrow_1726925404_above),p)),c)),e))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1384031255e_indi),arrow_844286440_mkbot),p)),e))))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,p))) ),
inference(clausify,[status(thm)],[f_58_1]) ).
cnf(f_58_3,plain,
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,p)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),ord_less(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1384031255e_indi),arrow_992993526_mktop),p)),e))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),fequal(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),arrow_1726925404_above),p)),c)),e))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1384031255e_indi),arrow_844286440_mkbot),p)),e)))))) ),
inference(clausify,[status(thm)],[f_58_1]) ).
fof(f_59_1,plain,
! [X_a,X_b,Pa] :
( ( ! [X1] : hBOOL(hAPP(product_prod(X_a,X_b),bool,Pa,X1))
| ? [A_2,B_1] : ~ 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_2),B_1))) )
& ( ! [A_2,B_1] : 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_2),B_1)))
| ? [X1] : ~ hBOOL(hAPP(product_prod(X_a,X_b),bool,Pa,X1)) ) ),
inference(fof_nnf,[status(thm)],[fact_15_split__paired__All]) ).
fof(f_59_2,plain,
! [U_122,U_121,U_120] :
( ( ! [U_119] : hBOOL(hAPP(product_prod(U_122,U_121),bool,U_120,U_119))
| ? [U_118,U_117] : ~ hBOOL(hAPP(product_prod(U_122,U_121),bool,U_120,hAPP(U_121,product_prod(U_122,U_121),hAPP(U_122,fun(U_121,product_prod(U_122,U_121)),product_Pair(U_122,U_121),U_118),U_117))) )
& ( ! [U_116,U_115] : hBOOL(hAPP(product_prod(U_122,U_121),bool,U_120,hAPP(U_121,product_prod(U_122,U_121),hAPP(U_122,fun(U_121,product_prod(U_122,U_121)),product_Pair(U_122,U_121),U_116),U_115)))
| ? [U_114] : ~ hBOOL(hAPP(product_prod(U_122,U_121),bool,U_120,U_114)) ) ),
inference(variable_rename,[status(thm)],[f_59_1]) ).
fof(f_59_3,plain,
( ! [U_128,U_126,U_124] :
( ! [U_119] : hBOOL(hAPP(product_prod(U_128,U_126),bool,U_124,U_119))
| ? [U_118,U_117] : ~ hBOOL(hAPP(product_prod(U_128,U_126),bool,U_124,hAPP(U_126,product_prod(U_128,U_126),hAPP(U_128,fun(U_126,product_prod(U_128,U_126)),product_Pair(U_128,U_126),U_118),U_117))) )
& ! [U_127,U_125,U_123] :
( ! [U_116,U_115] : hBOOL(hAPP(product_prod(U_127,U_125),bool,U_123,hAPP(U_125,product_prod(U_127,U_125),hAPP(U_127,fun(U_125,product_prod(U_127,U_125)),product_Pair(U_127,U_125),U_116),U_115)))
| ? [U_114] : ~ hBOOL(hAPP(product_prod(U_127,U_125),bool,U_123,U_114)) ) ),
inference(miniscope,[status(thm)],[f_59_2]) ).
fof(f_59_4,plain,
( ! [U_128,U_126,U_124] :
( ! [U_119] : hBOOL(hAPP(product_prod(U_128,U_126),bool,U_124,U_119))
| ? [U_118,U_117] : ~ hBOOL(hAPP(product_prod(U_128,U_126),bool,U_124,hAPP(U_126,product_prod(U_128,U_126),hAPP(U_128,fun(U_126,product_prod(U_128,U_126)),product_Pair(U_128,U_126),U_118),U_117))) )
& ! [U_127,U_125,U_123] :
( ! [U_116,U_115] : hBOOL(hAPP(product_prod(U_127,U_125),bool,U_123,hAPP(U_125,product_prod(U_127,U_125),hAPP(U_127,fun(U_125,product_prod(U_127,U_125)),product_Pair(U_127,U_125),U_116),U_115)))
| ~ hBOOL(hAPP(product_prod(U_127,U_125),bool,U_123,sK11(U_127,U_125,U_123))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_114,sK11(U_127,U_125,U_123))],[f_59_3]) ).
fof(f_59_5,plain,
( ! [U_128,U_126,U_124] :
( ! [U_119] : hBOOL(hAPP(product_prod(U_128,U_126),bool,U_124,U_119))
| ? [U_117] : ~ hBOOL(hAPP(product_prod(U_128,U_126),bool,U_124,hAPP(U_126,product_prod(U_128,U_126),hAPP(U_128,fun(U_126,product_prod(U_128,U_126)),product_Pair(U_128,U_126),sK12(U_128,U_126,U_124)),U_117))) )
& ! [U_127,U_125,U_123] :
( ! [U_116,U_115] : hBOOL(hAPP(product_prod(U_127,U_125),bool,U_123,hAPP(U_125,product_prod(U_127,U_125),hAPP(U_127,fun(U_125,product_prod(U_127,U_125)),product_Pair(U_127,U_125),U_116),U_115)))
| ~ hBOOL(hAPP(product_prod(U_127,U_125),bool,U_123,sK11(U_127,U_125,U_123))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_118,sK12(U_128,U_126,U_124))],[f_59_4]) ).
fof(f_59_6,plain,
( ! [U_128,U_126,U_124] :
( ! [U_119] : hBOOL(hAPP(product_prod(U_128,U_126),bool,U_124,U_119))
| ~ hBOOL(hAPP(product_prod(U_128,U_126),bool,U_124,hAPP(U_126,product_prod(U_128,U_126),hAPP(U_128,fun(U_126,product_prod(U_128,U_126)),product_Pair(U_128,U_126),sK12(U_128,U_126,U_124)),sK13(U_128,U_126,U_124)))) )
& ! [U_127,U_125,U_123] :
( ! [U_116,U_115] : hBOOL(hAPP(product_prod(U_127,U_125),bool,U_123,hAPP(U_125,product_prod(U_127,U_125),hAPP(U_127,fun(U_125,product_prod(U_127,U_125)),product_Pair(U_127,U_125),U_116),U_115)))
| ~ hBOOL(hAPP(product_prod(U_127,U_125),bool,U_123,sK11(U_127,U_125,U_123))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_117,sK13(U_128,U_126,U_124))],[f_59_5]) ).
cnf(f_59_7,plain,
( hBOOL(hAPP(product_prod(U_127,U_125),bool,U_123,hAPP(U_125,product_prod(U_127,U_125),hAPP(U_127,fun(U_125,product_prod(U_127,U_125)),product_Pair(U_127,U_125),U_116),U_115)))
| ~ hBOOL(hAPP(product_prod(U_127,U_125),bool,U_123,sK11(U_127,U_125,U_123))) ),
inference(clausify,[status(thm)],[f_59_6]) ).
cnf(f_59_8,plain,
( hBOOL(hAPP(product_prod(U_128,U_126),bool,U_124,U_119))
| ~ hBOOL(hAPP(product_prod(U_128,U_126),bool,U_124,hAPP(U_126,product_prod(U_128,U_126),hAPP(U_128,fun(U_126,product_prod(U_128,U_126)),product_Pair(U_128,U_126),sK12(U_128,U_126,U_124)),sK13(U_128,U_126,U_124)))) ),
inference(clausify,[status(thm)],[f_59_6]) ).
fof(f_60_1,plain,
hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),ord_less(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1384031255e_indi),arrow_992993526_mktop),p)),e))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),fequal(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),arrow_1726925404_above),p)),c)),e))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1384031255e_indi),arrow_844286440_mkbot),p)),e)))),arrow_1834574746e_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_60_2,plain,
hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),ord_less(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1384031255e_indi),arrow_992993526_mktop),p)),e))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),fequal(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),arrow_1726925404_above),p)),c)),e))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1384031255e_indi),arrow_844286440_mkbot),p)),e)))),arrow_1834574746e_Prof)),
inference(clausify,[status(thm)],[f_60_1]) ).
fof(f_61_1,plain,
hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),e)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),ord_less(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1384031255e_indi),arrow_992993526_mktop),p)),e))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),fequal(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),arrow_1726925404_above),p)),c)),e))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1384031255e_indi),arrow_844286440_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_61_2,plain,
hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),e)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),ord_less(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1384031255e_indi),arrow_992993526_mktop),p)),e))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),fequal(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),arrow_1726925404_above),p)),c)),e))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1384031255e_indi),arrow_844286440_mkbot),p)),e)))))),
inference(clausify,[status(thm)],[f_61_1]) ).
fof(f_62_1,plain,
hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),ord_less(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1384031255e_indi),arrow_992993526_mktop),p)),e))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),fequal(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),arrow_1726925404_above),p)),c)),e))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1384031255e_indi),arrow_844286440_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_62_2,plain,
hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),ord_less(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1384031255e_indi),arrow_992993526_mktop),p)),e))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),fequal(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),arrow_1726925404_above),p)),c)),e))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1384031255e_indi),arrow_844286440_mkbot),p)),e)))))),
inference(clausify,[status(thm)],[f_62_1]) ).
fof(f_63_1,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),n),hAPP(fun(arrow_1384031255e_indi,bool),nat,finite_card(arrow_1384031255e_indi),top_top(fun(arrow_1384031255e_indi,bool))))),
inference(fof_nnf,[status(thm)],[fact_19_n_I1_J]) ).
cnf(f_63_2,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),n),hAPP(fun(arrow_1384031255e_indi,bool),nat,finite_card(arrow_1384031255e_indi),top_top(fun(arrow_1384031255e_indi,bool))))),
inference(clausify,[status(thm)],[f_63_1]) ).
fof(f_64_1,plain,
hBOOL(hAPP(fun(arrow_1384031255e_indi,bool),bool,hAPP(fun(arrow_1384031255e_indi,nat),fun(fun(arrow_1384031255e_indi,bool),bool),inj_on(arrow_1384031255e_indi,nat),h),top_top(fun(arrow_1384031255e_indi,bool)))),
inference(fof_nnf,[status(thm)],[fact_20_injh]) ).
cnf(f_64_2,plain,
hBOOL(hAPP(fun(arrow_1384031255e_indi,bool),bool,hAPP(fun(arrow_1384031255e_indi,nat),fun(fun(arrow_1384031255e_indi,bool),bool),inj_on(arrow_1384031255e_indi,nat),h),top_top(fun(arrow_1384031255e_indi,bool)))),
inference(clausify,[status(thm)],[f_64_1]) ).
fof(f_65_1,plain,
! [X_b,X_a,A_3,B_2,A_5,B_4] :
( ( ti(X_b,B_2) = ti(X_b,B_4)
& ti(X_a,A_3) = 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),A_3),B_2) != hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_5),B_4) ),
inference(fof_nnf,[status(thm)],[fact_21_Pair__inject]) ).
fof(f_65_2,plain,
! [U_134,U_133,U_132,U_131,U_130,U_129] :
( ( ti(U_134,U_131) = ti(U_134,U_129)
& ti(U_133,U_132) = ti(U_133,U_130) )
| hAPP(U_134,product_prod(U_133,U_134),hAPP(U_133,fun(U_134,product_prod(U_133,U_134)),product_Pair(U_133,U_134),U_132),U_131) != hAPP(U_134,product_prod(U_133,U_134),hAPP(U_133,fun(U_134,product_prod(U_133,U_134)),product_Pair(U_133,U_134),U_130),U_129) ),
inference(variable_rename,[status(thm)],[f_65_1]) ).
cnf(f_65_3,plain,
( ti(U_133,U_132) = ti(U_133,U_130)
| hAPP(U_134,product_prod(U_133,U_134),hAPP(U_133,fun(U_134,product_prod(U_133,U_134)),product_Pair(U_133,U_134),U_132),U_131) != hAPP(U_134,product_prod(U_133,U_134),hAPP(U_133,fun(U_134,product_prod(U_133,U_134)),product_Pair(U_133,U_134),U_130),U_129) ),
inference(clausify,[status(thm)],[f_65_2]) ).
cnf(f_65_4,plain,
( ti(U_134,U_131) = ti(U_134,U_129)
| hAPP(U_134,product_prod(U_133,U_134),hAPP(U_133,fun(U_134,product_prod(U_133,U_134)),product_Pair(U_133,U_134),U_132),U_131) != hAPP(U_134,product_prod(U_133,U_134),hAPP(U_133,fun(U_134,product_prod(U_133,U_134)),product_Pair(U_133,U_134),U_130),U_129) ),
inference(clausify,[status(thm)],[f_65_2]) ).
fof(f_66_1,plain,
! [X_b,X_a,Aa,Ba,A_4,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_4),B_3)
| ti(X_b,Ba) != ti(X_b,B_3)
| ti(X_a,Aa) != ti(X_a,A_4) )
& ( ( ti(X_b,Ba) = ti(X_b,B_3)
& ti(X_a,Aa) = ti(X_a,A_4) )
| hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba) != hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_4),B_3) ) ),
inference(fof_nnf,[status(thm)],[fact_22_Pair__eq]) ).
fof(f_66_2,plain,
! [U_140,U_139,U_138,U_137,U_136,U_135] :
( ( hAPP(U_140,product_prod(U_139,U_140),hAPP(U_139,fun(U_140,product_prod(U_139,U_140)),product_Pair(U_139,U_140),U_138),U_137) = hAPP(U_140,product_prod(U_139,U_140),hAPP(U_139,fun(U_140,product_prod(U_139,U_140)),product_Pair(U_139,U_140),U_136),U_135)
| ti(U_140,U_137) != ti(U_140,U_135)
| ti(U_139,U_138) != ti(U_139,U_136) )
& ( ( ti(U_140,U_137) = ti(U_140,U_135)
& ti(U_139,U_138) = ti(U_139,U_136) )
| hAPP(U_140,product_prod(U_139,U_140),hAPP(U_139,fun(U_140,product_prod(U_139,U_140)),product_Pair(U_139,U_140),U_138),U_137) != hAPP(U_140,product_prod(U_139,U_140),hAPP(U_139,fun(U_140,product_prod(U_139,U_140)),product_Pair(U_139,U_140),U_136),U_135) ) ),
inference(variable_rename,[status(thm)],[f_66_1]) ).
fof(f_66_3,plain,
( ! [U_152,U_150,U_148,U_146,U_144,U_142] :
( hAPP(U_152,product_prod(U_150,U_152),hAPP(U_150,fun(U_152,product_prod(U_150,U_152)),product_Pair(U_150,U_152),U_148),U_146) = hAPP(U_152,product_prod(U_150,U_152),hAPP(U_150,fun(U_152,product_prod(U_150,U_152)),product_Pair(U_150,U_152),U_144),U_142)
| ti(U_152,U_146) != ti(U_152,U_142)
| ti(U_150,U_148) != ti(U_150,U_144) )
& ! [U_151,U_149,U_147,U_145,U_143,U_141] :
( ( ti(U_151,U_145) = ti(U_151,U_141)
& ti(U_149,U_147) = ti(U_149,U_143) )
| hAPP(U_151,product_prod(U_149,U_151),hAPP(U_149,fun(U_151,product_prod(U_149,U_151)),product_Pair(U_149,U_151),U_147),U_145) != hAPP(U_151,product_prod(U_149,U_151),hAPP(U_149,fun(U_151,product_prod(U_149,U_151)),product_Pair(U_149,U_151),U_143),U_141) ) ),
inference(miniscope,[status(thm)],[f_66_2]) ).
cnf(f_66_4,plain,
( ti(U_149,U_147) = ti(U_149,U_143)
| hAPP(U_151,product_prod(U_149,U_151),hAPP(U_149,fun(U_151,product_prod(U_149,U_151)),product_Pair(U_149,U_151),U_147),U_145) != hAPP(U_151,product_prod(U_149,U_151),hAPP(U_149,fun(U_151,product_prod(U_149,U_151)),product_Pair(U_149,U_151),U_143),U_141) ),
inference(clausify,[status(thm)],[f_66_3]) ).
cnf(f_66_5,plain,
( ti(U_151,U_145) = ti(U_151,U_141)
| hAPP(U_151,product_prod(U_149,U_151),hAPP(U_149,fun(U_151,product_prod(U_149,U_151)),product_Pair(U_149,U_151),U_147),U_145) != hAPP(U_151,product_prod(U_149,U_151),hAPP(U_149,fun(U_151,product_prod(U_149,U_151)),product_Pair(U_149,U_151),U_143),U_141) ),
inference(clausify,[status(thm)],[f_66_3]) ).
cnf(f_66_6,plain,
( hAPP(U_152,product_prod(U_150,U_152),hAPP(U_150,fun(U_152,product_prod(U_150,U_152)),product_Pair(U_150,U_152),U_148),U_146) = hAPP(U_152,product_prod(U_150,U_152),hAPP(U_150,fun(U_152,product_prod(U_150,U_152)),product_Pair(U_150,U_152),U_144),U_142)
| ti(U_152,U_146) != ti(U_152,U_142)
| ti(U_150,U_148) != ti(U_150,U_144) ),
inference(clausify,[status(thm)],[f_66_3]) ).
fof(f_67_1,plain,
! [Fa] :
( ( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_612047104le_IIA,Fa))
| ? [X_1] :
( ? [Xa] :
( ? [A_2,B_1] :
( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_2),B_1)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Fa,X_1)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_2),B_1)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Fa,Xa))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_2),B_1)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Fa,Xa)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_2),B_1)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Fa,X_1))) ) )
& ! [I] :
( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_2),B_1)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),X_1,I)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_2),B_1)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Xa,I))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_2),B_1)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Xa,I)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_2),B_1)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),X_1,I))) ) ) )
& hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),Xa),arrow_1834574746e_Prof)) )
& hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),X_1),arrow_1834574746e_Prof)) ) )
& ( ! [X_1] :
( ! [Xa] :
( ! [A_2,B_1] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_2),B_1)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Fa,X_1)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_2),B_1)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Fa,Xa))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_2),B_1)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Fa,Xa)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_2),B_1)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Fa,X_1))) ) )
| ? [I] :
( ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_2),B_1)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),X_1,I)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_2),B_1)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Xa,I))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_2),B_1)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Xa,I)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_2),B_1)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),X_1,I))) ) ) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),Xa),arrow_1834574746e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),X_1),arrow_1834574746e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_612047104le_IIA,Fa)) ) ),
inference(fof_nnf,[status(thm)],[fact_23_IIA__def]) ).
fof(f_67_2,plain,
! [U_163] :
( ( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_612047104le_IIA,U_163))
| ? [U_162] :
( ? [U_161] :
( ? [U_160,U_159] :
( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_160),U_159)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_163,U_162)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_160),U_159)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_163,U_161))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_160),U_159)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_163,U_161)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_160),U_159)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_163,U_162))) ) )
& ! [U_158] :
( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_160),U_159)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_162,U_158)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_160),U_159)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_161,U_158))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_160),U_159)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_161,U_158)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_160),U_159)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_162,U_158))) ) ) )
& hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_161),arrow_1834574746e_Prof)) )
& hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_162),arrow_1834574746e_Prof)) ) )
& ( ! [U_157] :
( ! [U_156] :
( ! [U_155,U_154] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_163,U_157)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_163,U_156))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_163,U_156)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_163,U_157))) ) )
| ? [U_153] :
( ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_157,U_153)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_156,U_153))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_156,U_153)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_157,U_153))) ) ) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_156),arrow_1834574746e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_157),arrow_1834574746e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_612047104le_IIA,U_163)) ) ),
inference(variable_rename,[status(thm)],[f_67_1]) ).
fof(f_67_3,plain,
( ! [U_169] :
( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_612047104le_IIA,U_169))
| ? [U_162] :
( ? [U_161] :
( ? [U_160,U_159] :
( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_160),U_159)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_169,U_162)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_160),U_159)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_169,U_161))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_160),U_159)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_169,U_161)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_160),U_159)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_169,U_162))) ) )
& ! [U_167] :
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_160),U_159)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_162,U_167)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_160),U_159)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_161,U_167))) )
& ! [U_166] :
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_160),U_159)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_161,U_166)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_160),U_159)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_162,U_166))) ) )
& hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_161),arrow_1834574746e_Prof)) )
& hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_162),arrow_1834574746e_Prof)) ) )
& ! [U_168] :
( ! [U_157] :
( ! [U_156] :
( ! [U_155,U_154] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_168,U_157)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_168,U_156))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_168,U_156)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_168,U_157))) ) )
| ? [U_165] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_157,U_165)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_156,U_165))) )
| ? [U_164] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_156,U_164)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_157,U_164))) ) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_156),arrow_1834574746e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_157),arrow_1834574746e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_612047104le_IIA,U_168)) ) ),
inference(miniscope,[status(thm)],[f_67_2]) ).
fof(f_67_4,plain,
( ! [U_169] :
( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_612047104le_IIA,U_169))
| ? [U_162] :
( ? [U_161] :
( ? [U_160,U_159] :
( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_160),U_159)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_169,U_162)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_160),U_159)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_169,U_161))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_160),U_159)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_169,U_161)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_160),U_159)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_169,U_162))) ) )
& ! [U_167] :
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_160),U_159)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_162,U_167)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_160),U_159)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_161,U_167))) )
& ! [U_166] :
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_160),U_159)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_161,U_166)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_160),U_159)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_162,U_166))) ) )
& hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_161),arrow_1834574746e_Prof)) )
& hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_162),arrow_1834574746e_Prof)) ) )
& ! [U_168] :
( ! [U_157] :
( ! [U_156] :
( ! [U_155,U_154] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_168,U_157)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_168,U_156))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_168,U_156)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_168,U_157))) ) )
| ? [U_165] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_157,U_165)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_156,U_165))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_156,sK14(U_168,U_157,U_156,U_155,U_154))))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_157,sK14(U_168,U_157,U_156,U_155,U_154)))) ) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_156),arrow_1834574746e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_157),arrow_1834574746e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_612047104le_IIA,U_168)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_164,sK14(U_168,U_157,U_156,U_155,U_154))],[f_67_3]) ).
fof(f_67_5,plain,
( ! [U_169] :
( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_612047104le_IIA,U_169))
| ? [U_162] :
( ? [U_161] :
( ? [U_160,U_159] :
( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_160),U_159)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_169,U_162)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_160),U_159)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_169,U_161))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_160),U_159)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_169,U_161)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_160),U_159)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_169,U_162))) ) )
& ! [U_167] :
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_160),U_159)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_162,U_167)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_160),U_159)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_161,U_167))) )
& ! [U_166] :
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_160),U_159)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_161,U_166)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_160),U_159)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_162,U_166))) ) )
& hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_161),arrow_1834574746e_Prof)) )
& hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_162),arrow_1834574746e_Prof)) ) )
& ! [U_168] :
( ! [U_157] :
( ! [U_156] :
( ! [U_155,U_154] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_168,U_157)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_168,U_156))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_168,U_156)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_168,U_157))) ) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_157,sK15(U_168,U_157,U_156,U_155,U_154))))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_156,sK15(U_168,U_157,U_156,U_155,U_154)))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_156,sK14(U_168,U_157,U_156,U_155,U_154))))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_157,sK14(U_168,U_157,U_156,U_155,U_154)))) ) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_156),arrow_1834574746e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_157),arrow_1834574746e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_612047104le_IIA,U_168)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_165,sK15(U_168,U_157,U_156,U_155,U_154))],[f_67_4]) ).
fof(f_67_6,plain,
( ! [U_169] :
( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_612047104le_IIA,U_169))
| ( ? [U_161] :
( ? [U_160,U_159] :
( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_160),U_159)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_169,sK16(U_169))))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_160),U_159)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_169,U_161))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_160),U_159)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_169,U_161)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_160),U_159)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_169,sK16(U_169)))) ) )
& ! [U_167] :
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_160),U_159)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),sK16(U_169),U_167)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_160),U_159)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_161,U_167))) )
& ! [U_166] :
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_160),U_159)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_161,U_166)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_160),U_159)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),sK16(U_169),U_166))) ) )
& hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_161),arrow_1834574746e_Prof)) )
& hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),sK16(U_169)),arrow_1834574746e_Prof)) ) )
& ! [U_168] :
( ! [U_157] :
( ! [U_156] :
( ! [U_155,U_154] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_168,U_157)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_168,U_156))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_168,U_156)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_168,U_157))) ) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_157,sK15(U_168,U_157,U_156,U_155,U_154))))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_156,sK15(U_168,U_157,U_156,U_155,U_154)))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_156,sK14(U_168,U_157,U_156,U_155,U_154))))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_157,sK14(U_168,U_157,U_156,U_155,U_154)))) ) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_156),arrow_1834574746e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_157),arrow_1834574746e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_612047104le_IIA,U_168)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_162,sK16(U_169))],[f_67_5]) ).
fof(f_67_7,plain,
( ! [U_169] :
( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_612047104le_IIA,U_169))
| ( ? [U_160,U_159] :
( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_160),U_159)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_169,sK16(U_169))))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_160),U_159)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_169,sK17(U_169)))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_160),U_159)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_169,sK17(U_169))))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_160),U_159)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_169,sK16(U_169)))) ) )
& ! [U_167] :
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_160),U_159)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),sK16(U_169),U_167)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_160),U_159)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),sK17(U_169),U_167))) )
& ! [U_166] :
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_160),U_159)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),sK17(U_169),U_166)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_160),U_159)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),sK16(U_169),U_166))) ) )
& hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),sK17(U_169)),arrow_1834574746e_Prof))
& hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),sK16(U_169)),arrow_1834574746e_Prof)) ) )
& ! [U_168] :
( ! [U_157] :
( ! [U_156] :
( ! [U_155,U_154] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_168,U_157)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_168,U_156))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_168,U_156)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_168,U_157))) ) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_157,sK15(U_168,U_157,U_156,U_155,U_154))))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_156,sK15(U_168,U_157,U_156,U_155,U_154)))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_156,sK14(U_168,U_157,U_156,U_155,U_154))))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_157,sK14(U_168,U_157,U_156,U_155,U_154)))) ) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_156),arrow_1834574746e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_157),arrow_1834574746e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_612047104le_IIA,U_168)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_161,sK17(U_169))],[f_67_6]) ).
fof(f_67_8,plain,
( ! [U_169] :
( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_612047104le_IIA,U_169))
| ( ? [U_159] :
( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),sK18(U_169)),U_159)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_169,sK16(U_169))))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),sK18(U_169)),U_159)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_169,sK17(U_169)))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),sK18(U_169)),U_159)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_169,sK17(U_169))))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),sK18(U_169)),U_159)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_169,sK16(U_169)))) ) )
& ! [U_167] :
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),sK18(U_169)),U_159)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),sK16(U_169),U_167)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),sK18(U_169)),U_159)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),sK17(U_169),U_167))) )
& ! [U_166] :
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),sK18(U_169)),U_159)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),sK17(U_169),U_166)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),sK18(U_169)),U_159)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),sK16(U_169),U_166))) ) )
& hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),sK17(U_169)),arrow_1834574746e_Prof))
& hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),sK16(U_169)),arrow_1834574746e_Prof)) ) )
& ! [U_168] :
( ! [U_157] :
( ! [U_156] :
( ! [U_155,U_154] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_168,U_157)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_168,U_156))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_168,U_156)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_168,U_157))) ) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_157,sK15(U_168,U_157,U_156,U_155,U_154))))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_156,sK15(U_168,U_157,U_156,U_155,U_154)))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_156,sK14(U_168,U_157,U_156,U_155,U_154))))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_157,sK14(U_168,U_157,U_156,U_155,U_154)))) ) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_156),arrow_1834574746e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_157),arrow_1834574746e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_612047104le_IIA,U_168)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_160,sK18(U_169))],[f_67_7]) ).
fof(f_67_9,plain,
( ! [U_169] :
( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_612047104le_IIA,U_169))
| ( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),sK18(U_169)),sK19(U_169))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_169,sK16(U_169))))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),sK18(U_169)),sK19(U_169))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_169,sK17(U_169)))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),sK18(U_169)),sK19(U_169))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_169,sK17(U_169))))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),sK18(U_169)),sK19(U_169))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_169,sK16(U_169)))) ) )
& ! [U_167] :
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),sK18(U_169)),sK19(U_169))),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),sK16(U_169),U_167)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),sK18(U_169)),sK19(U_169))),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),sK17(U_169),U_167))) )
& ! [U_166] :
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),sK18(U_169)),sK19(U_169))),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),sK17(U_169),U_166)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),sK18(U_169)),sK19(U_169))),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),sK16(U_169),U_166))) )
& hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),sK17(U_169)),arrow_1834574746e_Prof))
& hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),sK16(U_169)),arrow_1834574746e_Prof)) ) )
& ! [U_168] :
( ! [U_157] :
( ! [U_156] :
( ! [U_155,U_154] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_168,U_157)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_168,U_156))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_168,U_156)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_168,U_157))) ) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_157,sK15(U_168,U_157,U_156,U_155,U_154))))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_156,sK15(U_168,U_157,U_156,U_155,U_154)))) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_156,sK14(U_168,U_157,U_156,U_155,U_154))))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_157,sK14(U_168,U_157,U_156,U_155,U_154)))) ) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_156),arrow_1834574746e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_157),arrow_1834574746e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_612047104le_IIA,U_168)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_159,sK19(U_169))],[f_67_8]) ).
cnf(f_67_10,plain,
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_156,sK15(U_168,U_157,U_156,U_155,U_154))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_157,sK14(U_168,U_157,U_156,U_155,U_154))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_168,U_156)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_168,U_157)))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_156),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_157),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_612047104le_IIA,U_168)) ),
inference(clausify,[status(thm)],[f_67_9]) ).
cnf(f_67_11,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_157,sK15(U_168,U_157,U_156,U_155,U_154))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_157,sK14(U_168,U_157,U_156,U_155,U_154))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_168,U_156)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_168,U_157)))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_156),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_157),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_612047104le_IIA,U_168)) ),
inference(clausify,[status(thm)],[f_67_9]) ).
cnf(f_67_12,plain,
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_156,sK15(U_168,U_157,U_156,U_155,U_154))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_156,sK14(U_168,U_157,U_156,U_155,U_154))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_168,U_156)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_168,U_157)))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_156),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_157),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_612047104le_IIA,U_168)) ),
inference(clausify,[status(thm)],[f_67_9]) ).
cnf(f_67_13,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_157,sK15(U_168,U_157,U_156,U_155,U_154))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_156,sK14(U_168,U_157,U_156,U_155,U_154))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_168,U_156)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_168,U_157)))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_156),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_157),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_612047104le_IIA,U_168)) ),
inference(clausify,[status(thm)],[f_67_9]) ).
cnf(f_67_14,plain,
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_156,sK15(U_168,U_157,U_156,U_155,U_154))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_157,sK14(U_168,U_157,U_156,U_155,U_154))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_168,U_157)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_168,U_156)))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_156),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_157),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_612047104le_IIA,U_168)) ),
inference(clausify,[status(thm)],[f_67_9]) ).
cnf(f_67_15,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_157,sK15(U_168,U_157,U_156,U_155,U_154))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_157,sK14(U_168,U_157,U_156,U_155,U_154))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_168,U_157)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_168,U_156)))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_156),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_157),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_612047104le_IIA,U_168)) ),
inference(clausify,[status(thm)],[f_67_9]) ).
cnf(f_67_16,plain,
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_156,sK15(U_168,U_157,U_156,U_155,U_154))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_156,sK14(U_168,U_157,U_156,U_155,U_154))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_168,U_157)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_168,U_156)))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_156),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_157),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_612047104le_IIA,U_168)) ),
inference(clausify,[status(thm)],[f_67_9]) ).
cnf(f_67_17,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_157,sK15(U_168,U_157,U_156,U_155,U_154))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_156,sK14(U_168,U_157,U_156,U_155,U_154))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_168,U_157)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_155),U_154)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_168,U_156)))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_156),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_157),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_612047104le_IIA,U_168)) ),
inference(clausify,[status(thm)],[f_67_9]) ).
cnf(f_67_18,plain,
( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),sK16(U_169)),arrow_1834574746e_Prof))
| hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_612047104le_IIA,U_169)) ),
inference(clausify,[status(thm)],[f_67_9]) ).
cnf(f_67_19,plain,
( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),sK17(U_169)),arrow_1834574746e_Prof))
| hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_612047104le_IIA,U_169)) ),
inference(clausify,[status(thm)],[f_67_9]) ).
cnf(f_67_20,plain,
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),sK18(U_169)),sK19(U_169))),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),sK17(U_169),U_166)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),sK18(U_169)),sK19(U_169))),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),sK16(U_169),U_166)))
| hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_612047104le_IIA,U_169)) ),
inference(clausify,[status(thm)],[f_67_9]) ).
cnf(f_67_21,plain,
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),sK18(U_169)),sK19(U_169))),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),sK16(U_169),U_167)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),sK18(U_169)),sK19(U_169))),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),sK17(U_169),U_167)))
| hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_612047104le_IIA,U_169)) ),
inference(clausify,[status(thm)],[f_67_9]) ).
cnf(f_67_22,plain,
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),sK18(U_169)),sK19(U_169))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_169,sK17(U_169))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),sK18(U_169)),sK19(U_169))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_169,sK16(U_169))))
| hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_612047104le_IIA,U_169)) ),
inference(clausify,[status(thm)],[f_67_9]) ).
cnf(f_67_23,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),sK18(U_169)),sK19(U_169))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_169,sK16(U_169))))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),sK18(U_169)),sK19(U_169))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_169,sK16(U_169))))
| hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_612047104le_IIA,U_169)) ),
inference(clausify,[status(thm)],[f_67_9]) ).
cnf(f_67_24,plain,
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),sK18(U_169)),sK19(U_169))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_169,sK17(U_169))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),sK18(U_169)),sK19(U_169))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_169,sK17(U_169))))
| hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_612047104le_IIA,U_169)) ),
inference(clausify,[status(thm)],[f_67_9]) ).
cnf(f_67_25,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),sK18(U_169)),sK19(U_169))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_169,sK16(U_169))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),sK18(U_169)),sK19(U_169))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_169,sK17(U_169))))
| hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_612047104le_IIA,U_169)) ),
inference(clausify,[status(thm)],[f_67_9]) ).
fof(f_68_1,plain,
! [Fa] :
( ( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_1932713123nimity,Fa))
| ? [X_1] :
( ? [A_2,B_1] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_2),B_1)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Fa,X_1)))
& ! [I] : hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_2),B_1)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),X_1,I))) )
& hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),X_1),arrow_1834574746e_Prof)) ) )
& ( ! [X_1] :
( ! [A_2,B_1] :
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_2),B_1)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Fa,X_1)))
| ? [I] : ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_2),B_1)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),X_1,I))) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),X_1),arrow_1834574746e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_1932713123nimity,Fa)) ) ),
inference(fof_nnf,[status(thm)],[fact_24_unanimity__def]) ).
fof(f_68_2,plain,
! [U_178] :
( ( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_1932713123nimity,U_178))
| ? [U_177] :
( ? [U_176,U_175] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_176),U_175)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_178,U_177)))
& ! [U_174] : hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_176),U_175)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_177,U_174))) )
& hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_177),arrow_1834574746e_Prof)) ) )
& ( ! [U_173] :
( ! [U_172,U_171] :
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_172),U_171)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_178,U_173)))
| ? [U_170] : ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_172),U_171)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_173,U_170))) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_173),arrow_1834574746e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_1932713123nimity,U_178)) ) ),
inference(variable_rename,[status(thm)],[f_68_1]) ).
fof(f_68_3,plain,
( ! [U_180] :
( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_1932713123nimity,U_180))
| ? [U_177] :
( ? [U_176,U_175] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_176),U_175)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_180,U_177)))
& ! [U_174] : hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_176),U_175)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_177,U_174))) )
& hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_177),arrow_1834574746e_Prof)) ) )
& ! [U_179] :
( ! [U_173] :
( ! [U_172,U_171] :
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_172),U_171)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_179,U_173)))
| ? [U_170] : ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_172),U_171)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_173,U_170))) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_173),arrow_1834574746e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_1932713123nimity,U_179)) ) ),
inference(miniscope,[status(thm)],[f_68_2]) ).
fof(f_68_4,plain,
( ! [U_180] :
( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_1932713123nimity,U_180))
| ? [U_177] :
( ? [U_176,U_175] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_176),U_175)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_180,U_177)))
& ! [U_174] : hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_176),U_175)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_177,U_174))) )
& hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_177),arrow_1834574746e_Prof)) ) )
& ! [U_179] :
( ! [U_173] :
( ! [U_172,U_171] :
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_172),U_171)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_179,U_173)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_172),U_171)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_173,sK20(U_179,U_173,U_172,U_171)))) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_173),arrow_1834574746e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_1932713123nimity,U_179)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_170,sK20(U_179,U_173,U_172,U_171))],[f_68_3]) ).
fof(f_68_5,plain,
( ! [U_180] :
( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_1932713123nimity,U_180))
| ( ? [U_176,U_175] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_176),U_175)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_180,sK21(U_180))))
& ! [U_174] : hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_176),U_175)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),sK21(U_180),U_174))) )
& hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),sK21(U_180)),arrow_1834574746e_Prof)) ) )
& ! [U_179] :
( ! [U_173] :
( ! [U_172,U_171] :
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_172),U_171)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_179,U_173)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_172),U_171)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_173,sK20(U_179,U_173,U_172,U_171)))) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_173),arrow_1834574746e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_1932713123nimity,U_179)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_177,sK21(U_180))],[f_68_4]) ).
fof(f_68_6,plain,
( ! [U_180] :
( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_1932713123nimity,U_180))
| ( ? [U_175] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),sK22(U_180)),U_175)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_180,sK21(U_180))))
& ! [U_174] : hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),sK22(U_180)),U_175)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),sK21(U_180),U_174))) )
& hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),sK21(U_180)),arrow_1834574746e_Prof)) ) )
& ! [U_179] :
( ! [U_173] :
( ! [U_172,U_171] :
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_172),U_171)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_179,U_173)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_172),U_171)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_173,sK20(U_179,U_173,U_172,U_171)))) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_173),arrow_1834574746e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_1932713123nimity,U_179)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_176,sK22(U_180))],[f_68_5]) ).
fof(f_68_7,plain,
( ! [U_180] :
( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_1932713123nimity,U_180))
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),sK22(U_180)),sK23(U_180))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_180,sK21(U_180))))
& ! [U_174] : hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),sK22(U_180)),sK23(U_180))),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),sK21(U_180),U_174)))
& hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),sK21(U_180)),arrow_1834574746e_Prof)) ) )
& ! [U_179] :
( ! [U_173] :
( ! [U_172,U_171] :
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_172),U_171)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_179,U_173)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_172),U_171)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_173,sK20(U_179,U_173,U_172,U_171)))) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_173),arrow_1834574746e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_1932713123nimity,U_179)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_175,sK23(U_180))],[f_68_6]) ).
cnf(f_68_8,plain,
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_172),U_171)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_179,U_173)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_172),U_171)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_173,sK20(U_179,U_173,U_172,U_171))))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_173),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_1932713123nimity,U_179)) ),
inference(clausify,[status(thm)],[f_68_7]) ).
cnf(f_68_9,plain,
( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),sK21(U_180)),arrow_1834574746e_Prof))
| hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_1932713123nimity,U_180)) ),
inference(clausify,[status(thm)],[f_68_7]) ).
cnf(f_68_10,plain,
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),sK22(U_180)),sK23(U_180))),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),sK21(U_180),U_174)))
| hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_1932713123nimity,U_180)) ),
inference(clausify,[status(thm)],[f_68_7]) ).
cnf(f_68_11,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),sK22(U_180)),sK23(U_180))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_180,sK21(U_180))))
| hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_1932713123nimity,U_180)) ),
inference(clausify,[status(thm)],[f_68_7]) ).
fof(f_69_1,plain,
! [X_a,X_2] : hBOOL(hAPP(X_a,bool,top_top(fun(X_a,bool)),X_2)),
inference(fof_nnf,[status(thm)],[fact_25_top1I]) ).
fof(f_69_2,plain,
! [U_182,U_181] : hBOOL(hAPP(U_182,bool,top_top(fun(U_182,bool)),U_181)),
inference(variable_rename,[status(thm)],[f_69_1]) ).
cnf(f_69_3,plain,
hBOOL(hAPP(U_182,bool,top_top(fun(U_182,bool)),U_181)),
inference(clausify,[status(thm)],[f_69_2]) ).
fof(f_70_1,plain,
! [X_a,X_2] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),top_top(fun(X_a,bool)))),
inference(fof_nnf,[status(thm)],[fact_26_UNIV__I]) ).
fof(f_70_2,plain,
! [U_184,U_183] : hBOOL(hAPP(fun(U_184,bool),bool,hAPP(U_184,fun(fun(U_184,bool),bool),member(U_184),U_183),top_top(fun(U_184,bool)))),
inference(variable_rename,[status(thm)],[f_70_1]) ).
cnf(f_70_3,plain,
hBOOL(hAPP(fun(U_184,bool),bool,hAPP(U_184,fun(fun(U_184,bool),bool),member(U_184),U_183),top_top(fun(U_184,bool)))),
inference(clausify,[status(thm)],[f_70_2]) ).
fof(f_71_1,plain,
! [X_a,X_2] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),top_top(fun(X_a,bool)))),
inference(fof_nnf,[status(thm)],[fact_27_iso__tuple__UNIV__I]) ).
fof(f_71_2,plain,
! [U_186,U_185] : hBOOL(hAPP(fun(U_186,bool),bool,hAPP(U_186,fun(fun(U_186,bool),bool),member(U_186),U_185),top_top(fun(U_186,bool)))),
inference(variable_rename,[status(thm)],[f_71_1]) ).
cnf(f_71_3,plain,
hBOOL(hAPP(fun(U_186,bool),bool,hAPP(U_186,fun(fun(U_186,bool),bool),member(U_186),U_185),top_top(fun(U_186,bool)))),
inference(clausify,[status(thm)],[f_71_2]) ).
fof(f_72_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_72_2,plain,
! [U_192,U_191,U_190,U_189,U_188,U_187] : hAPP(product_prod(U_192,U_191),U_190,hAPP(fun(U_192,fun(U_191,U_190)),fun(product_prod(U_192,U_191),U_190),product_prod_rec(U_192,U_191,U_190),U_189),hAPP(U_191,product_prod(U_192,U_191),hAPP(U_192,fun(U_191,product_prod(U_192,U_191)),product_Pair(U_192,U_191),U_188),U_187)) = hAPP(U_191,U_190,hAPP(U_192,fun(U_191,U_190),U_189,U_188),U_187),
inference(variable_rename,[status(thm)],[f_72_1]) ).
cnf(f_72_3,plain,
hAPP(product_prod(U_192,U_191),U_190,hAPP(fun(U_192,fun(U_191,U_190)),fun(product_prod(U_192,U_191),U_190),product_prod_rec(U_192,U_191,U_190),U_189),hAPP(U_191,product_prod(U_192,U_191),hAPP(U_192,fun(U_191,product_prod(U_192,U_191)),product_Pair(U_192,U_191),U_188),U_187)) = hAPP(U_191,U_190,hAPP(U_192,fun(U_191,U_190),U_189,U_188),U_187),
inference(clausify,[status(thm)],[f_72_2]) ).
fof(f_73_1,plain,
! [X_b,X_a] :
( ! [X_2] : hAPP(X_b,X_a,top_top(fun(X_b,X_a)),X_2) = top_top(X_a)
| ~ top(X_a) ),
inference(fof_nnf,[status(thm)],[fact_29_top__apply]) ).
fof(f_73_2,plain,
! [U_195,U_194] :
( ! [U_193] : hAPP(U_195,U_194,top_top(fun(U_195,U_194)),U_193) = top_top(U_194)
| ~ top(U_194) ),
inference(variable_rename,[status(thm)],[f_73_1]) ).
cnf(f_73_3,plain,
( hAPP(U_195,U_194,top_top(fun(U_195,U_194)),U_193) = top_top(U_194)
| ~ top(U_194) ),
inference(clausify,[status(thm)],[f_73_2]) ).
fof(f_74_1,plain,
! [X_a] :
( ! [A_3] : ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),top_top(X_a)),A_3))
| ~ top(X_a) ),
inference(fof_nnf,[status(thm)],[fact_30_not__top__less]) ).
fof(f_74_2,plain,
! [U_197] :
( ! [U_196] : ~ hBOOL(hAPP(U_197,bool,hAPP(U_197,fun(U_197,bool),ord_less(U_197),top_top(U_197)),U_196))
| ~ top(U_197) ),
inference(variable_rename,[status(thm)],[f_74_1]) ).
cnf(f_74_3,plain,
( ~ hBOOL(hAPP(U_197,bool,hAPP(U_197,fun(U_197,bool),ord_less(U_197),top_top(U_197)),U_196))
| ~ top(U_197) ),
inference(clausify,[status(thm)],[f_74_2]) ).
fof(f_75_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_31_linorder__cases]) ).
fof(f_75_2,plain,
! [U_200] :
( ! [U_199,U_198] :
( hBOOL(hAPP(U_200,bool,hAPP(U_200,fun(U_200,bool),ord_less(U_200),U_198),U_199))
| ti(U_200,U_199) = ti(U_200,U_198)
| hBOOL(hAPP(U_200,bool,hAPP(U_200,fun(U_200,bool),ord_less(U_200),U_199),U_198)) )
| ~ linorder(U_200) ),
inference(variable_rename,[status(thm)],[f_75_1]) ).
cnf(f_75_3,plain,
( hBOOL(hAPP(U_200,bool,hAPP(U_200,fun(U_200,bool),ord_less(U_200),U_198),U_199))
| ti(U_200,U_199) = ti(U_200,U_198)
| hBOOL(hAPP(U_200,bool,hAPP(U_200,fun(U_200,bool),ord_less(U_200),U_199),U_198))
| ~ linorder(U_200) ),
inference(clausify,[status(thm)],[f_75_2]) ).
fof(f_76_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_32_order__less__asym]) ).
fof(f_76_2,plain,
! [U_203] :
( ! [U_202,U_201] :
( ~ hBOOL(hAPP(U_203,bool,hAPP(U_203,fun(U_203,bool),ord_less(U_203),U_201),U_202))
| ~ hBOOL(hAPP(U_203,bool,hAPP(U_203,fun(U_203,bool),ord_less(U_203),U_202),U_201)) )
| ~ preorder(U_203) ),
inference(variable_rename,[status(thm)],[f_76_1]) ).
cnf(f_76_3,plain,
( ~ hBOOL(hAPP(U_203,bool,hAPP(U_203,fun(U_203,bool),ord_less(U_203),U_201),U_202))
| ~ hBOOL(hAPP(U_203,bool,hAPP(U_203,fun(U_203,bool),ord_less(U_203),U_202),U_201))
| ~ preorder(U_203) ),
inference(clausify,[status(thm)],[f_76_2]) ).
fof(f_77_1,plain,
! [X_a] :
( ! [Z,Y,X] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X))
| ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),Y))
| ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) )
| ~ order(X_a) ),
inference(fof_nnf,[status(thm)],[fact_33_xt1_I10_J]) ).
fof(f_77_2,plain,
! [U_207] :
( ! [U_206,U_205,U_204] :
( hBOOL(hAPP(U_207,bool,hAPP(U_207,fun(U_207,bool),ord_less(U_207),U_206),U_204))
| ~ hBOOL(hAPP(U_207,bool,hAPP(U_207,fun(U_207,bool),ord_less(U_207),U_206),U_205))
| ~ hBOOL(hAPP(U_207,bool,hAPP(U_207,fun(U_207,bool),ord_less(U_207),U_205),U_204)) )
| ~ order(U_207) ),
inference(variable_rename,[status(thm)],[f_77_1]) ).
cnf(f_77_3,plain,
( hBOOL(hAPP(U_207,bool,hAPP(U_207,fun(U_207,bool),ord_less(U_207),U_206),U_204))
| ~ hBOOL(hAPP(U_207,bool,hAPP(U_207,fun(U_207,bool),ord_less(U_207),U_206),U_205))
| ~ hBOOL(hAPP(U_207,bool,hAPP(U_207,fun(U_207,bool),ord_less(U_207),U_205),U_204))
| ~ order(U_207) ),
inference(clausify,[status(thm)],[f_77_2]) ).
fof(f_78_1,plain,
! [X_a] :
( ! [Z,X,Y] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z))
| ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),Z))
| ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) )
| ~ preorder(X_a) ),
inference(fof_nnf,[status(thm)],[fact_34_order__less__trans]) ).
fof(f_78_2,plain,
! [U_211] :
( ! [U_210,U_209,U_208] :
( hBOOL(hAPP(U_211,bool,hAPP(U_211,fun(U_211,bool),ord_less(U_211),U_209),U_210))
| ~ hBOOL(hAPP(U_211,bool,hAPP(U_211,fun(U_211,bool),ord_less(U_211),U_208),U_210))
| ~ hBOOL(hAPP(U_211,bool,hAPP(U_211,fun(U_211,bool),ord_less(U_211),U_209),U_208)) )
| ~ preorder(U_211) ),
inference(variable_rename,[status(thm)],[f_78_1]) ).
cnf(f_78_3,plain,
( hBOOL(hAPP(U_211,bool,hAPP(U_211,fun(U_211,bool),ord_less(U_211),U_209),U_210))
| ~ hBOOL(hAPP(U_211,bool,hAPP(U_211,fun(U_211,bool),ord_less(U_211),U_208),U_210))
| ~ hBOOL(hAPP(U_211,bool,hAPP(U_211,fun(U_211,bool),ord_less(U_211),U_209),U_208))
| ~ preorder(U_211) ),
inference(clausify,[status(thm)],[f_78_2]) ).
fof(f_79_1,plain,
! [X_a] :
( ! [C,B_2,A_3] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),A_3))
| B_2 != C
| ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),A_3)) )
| ~ order(X_a) ),
inference(fof_nnf,[status(thm)],[fact_35_xt1_I2_J]) ).
fof(f_79_2,plain,
! [U_215] :
( ! [U_214,U_213,U_212] :
( hBOOL(hAPP(U_215,bool,hAPP(U_215,fun(U_215,bool),ord_less(U_215),U_214),U_212))
| U_213 != U_214
| ~ hBOOL(hAPP(U_215,bool,hAPP(U_215,fun(U_215,bool),ord_less(U_215),U_213),U_212)) )
| ~ order(U_215) ),
inference(variable_rename,[status(thm)],[f_79_1]) ).
cnf(f_79_3,plain,
( hBOOL(hAPP(U_215,bool,hAPP(U_215,fun(U_215,bool),ord_less(U_215),U_214),U_212))
| U_213 != U_214
| ~ hBOOL(hAPP(U_215,bool,hAPP(U_215,fun(U_215,bool),ord_less(U_215),U_213),U_212))
| ~ order(U_215) ),
inference(clausify,[status(thm)],[f_79_2]) ).
fof(f_80_1,plain,
! [X_a] :
( ! [C,A_3,B_2] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),C))
| B_2 != C
| ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2)) )
| ~ ord(X_a) ),
inference(fof_nnf,[status(thm)],[fact_36_ord__less__eq__trans]) ).
fof(f_80_2,plain,
! [U_219] :
( ! [U_218,U_217,U_216] :
( hBOOL(hAPP(U_219,bool,hAPP(U_219,fun(U_219,bool),ord_less(U_219),U_217),U_218))
| U_216 != U_218
| ~ hBOOL(hAPP(U_219,bool,hAPP(U_219,fun(U_219,bool),ord_less(U_219),U_217),U_216)) )
| ~ ord(U_219) ),
inference(variable_rename,[status(thm)],[f_80_1]) ).
cnf(f_80_3,plain,
( hBOOL(hAPP(U_219,bool,hAPP(U_219,fun(U_219,bool),ord_less(U_219),U_217),U_218))
| U_216 != U_218
| ~ hBOOL(hAPP(U_219,bool,hAPP(U_219,fun(U_219,bool),ord_less(U_219),U_217),U_216))
| ~ ord(U_219) ),
inference(clausify,[status(thm)],[f_80_2]) ).
fof(f_81_1,plain,
! [X_a] :
( ! [C,A_3,B_2] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),A_3))
| ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),B_2))
| A_3 != B_2 )
| ~ order(X_a) ),
inference(fof_nnf,[status(thm)],[fact_37_xt1_I1_J]) ).
fof(f_81_2,plain,
! [U_223] :
( ! [U_222,U_221,U_220] :
( hBOOL(hAPP(U_223,bool,hAPP(U_223,fun(U_223,bool),ord_less(U_223),U_222),U_221))
| ~ hBOOL(hAPP(U_223,bool,hAPP(U_223,fun(U_223,bool),ord_less(U_223),U_222),U_220))
| U_221 != U_220 )
| ~ order(U_223) ),
inference(variable_rename,[status(thm)],[f_81_1]) ).
cnf(f_81_3,plain,
( hBOOL(hAPP(U_223,bool,hAPP(U_223,fun(U_223,bool),ord_less(U_223),U_222),U_221))
| ~ hBOOL(hAPP(U_223,bool,hAPP(U_223,fun(U_223,bool),ord_less(U_223),U_222),U_220))
| U_221 != U_220
| ~ order(U_223) ),
inference(clausify,[status(thm)],[f_81_2]) ).
fof(f_82_1,plain,
! [X_a] :
( ! [C,A_3,B_2] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),C))
| ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),C))
| A_3 != B_2 )
| ~ ord(X_a) ),
inference(fof_nnf,[status(thm)],[fact_38_ord__eq__less__trans]) ).
fof(f_82_2,plain,
! [U_227] :
( ! [U_226,U_225,U_224] :
( hBOOL(hAPP(U_227,bool,hAPP(U_227,fun(U_227,bool),ord_less(U_227),U_225),U_226))
| ~ hBOOL(hAPP(U_227,bool,hAPP(U_227,fun(U_227,bool),ord_less(U_227),U_224),U_226))
| U_225 != U_224 )
| ~ ord(U_227) ),
inference(variable_rename,[status(thm)],[f_82_1]) ).
cnf(f_82_3,plain,
( hBOOL(hAPP(U_227,bool,hAPP(U_227,fun(U_227,bool),ord_less(U_227),U_225),U_226))
| ~ hBOOL(hAPP(U_227,bool,hAPP(U_227,fun(U_227,bool),ord_less(U_227),U_224),U_226))
| U_225 != U_224
| ~ ord(U_227) ),
inference(clausify,[status(thm)],[f_82_2]) ).
fof(f_83_1,plain,
! [X_a] :
( ! [B_2,A_3] :
( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2))
| ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),A_3)) )
| ~ order(X_a) ),
inference(fof_nnf,[status(thm)],[fact_39_xt1_I9_J]) ).
fof(f_83_2,plain,
! [U_230] :
( ! [U_229,U_228] :
( ~ hBOOL(hAPP(U_230,bool,hAPP(U_230,fun(U_230,bool),ord_less(U_230),U_228),U_229))
| ~ hBOOL(hAPP(U_230,bool,hAPP(U_230,fun(U_230,bool),ord_less(U_230),U_229),U_228)) )
| ~ order(U_230) ),
inference(variable_rename,[status(thm)],[f_83_1]) ).
cnf(f_83_3,plain,
( ~ hBOOL(hAPP(U_230,bool,hAPP(U_230,fun(U_230,bool),ord_less(U_230),U_228),U_229))
| ~ hBOOL(hAPP(U_230,bool,hAPP(U_230,fun(U_230,bool),ord_less(U_230),U_229),U_228))
| ~ order(U_230) ),
inference(clausify,[status(thm)],[f_83_2]) ).
fof(f_84_1,plain,
! [X_a] :
( ! [A_3,B_2] :
( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),A_3))
| ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2)) )
| ~ preorder(X_a) ),
inference(fof_nnf,[status(thm)],[fact_40_order__less__asym_H]) ).
fof(f_84_2,plain,
! [U_233] :
( ! [U_232,U_231] :
( ~ hBOOL(hAPP(U_233,bool,hAPP(U_233,fun(U_233,bool),ord_less(U_233),U_231),U_232))
| ~ hBOOL(hAPP(U_233,bool,hAPP(U_233,fun(U_233,bool),ord_less(U_233),U_232),U_231)) )
| ~ preorder(U_233) ),
inference(variable_rename,[status(thm)],[f_84_1]) ).
cnf(f_84_3,plain,
( ~ hBOOL(hAPP(U_233,bool,hAPP(U_233,fun(U_233,bool),ord_less(U_233),U_231),U_232))
| ~ hBOOL(hAPP(U_233,bool,hAPP(U_233,fun(U_233,bool),ord_less(U_233),U_232),U_231))
| ~ preorder(U_233) ),
inference(clausify,[status(thm)],[f_84_2]) ).
fof(f_85_1,plain,
! [X_a] :
( ! [Pa,X_2,Y_1] :
( hBOOL(Pa)
| ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_2))
| ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_1)) )
| ~ preorder(X_a) ),
inference(fof_nnf,[status(thm)],[fact_41_order__less__imp__triv]) ).
fof(f_85_2,plain,
! [U_237] :
( ! [U_236,U_235,U_234] :
( hBOOL(U_236)
| ~ hBOOL(hAPP(U_237,bool,hAPP(U_237,fun(U_237,bool),ord_less(U_237),U_234),U_235))
| ~ hBOOL(hAPP(U_237,bool,hAPP(U_237,fun(U_237,bool),ord_less(U_237),U_235),U_234)) )
| ~ preorder(U_237) ),
inference(variable_rename,[status(thm)],[f_85_1]) ).
cnf(f_85_3,plain,
( hBOOL(U_236)
| ~ hBOOL(hAPP(U_237,bool,hAPP(U_237,fun(U_237,bool),ord_less(U_237),U_234),U_235))
| ~ hBOOL(hAPP(U_237,bool,hAPP(U_237,fun(U_237,bool),ord_less(U_237),U_235),U_234))
| ~ preorder(U_237) ),
inference(clausify,[status(thm)],[f_85_2]) ).
fof(f_86_1,plain,
! [X_a] :
( ! [X,Y] :
( Y != 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_42_order__less__imp__not__eq2]) ).
fof(f_86_2,plain,
! [U_240] :
( ! [U_239,U_238] :
( U_238 != U_239
| ~ hBOOL(hAPP(U_240,bool,hAPP(U_240,fun(U_240,bool),ord_less(U_240),U_239),U_238)) )
| ~ order(U_240) ),
inference(variable_rename,[status(thm)],[f_86_1]) ).
cnf(f_86_3,plain,
( U_238 != U_239
| ~ hBOOL(hAPP(U_240,bool,hAPP(U_240,fun(U_240,bool),ord_less(U_240),U_239),U_238))
| ~ order(U_240) ),
inference(clausify,[status(thm)],[f_86_2]) ).
fof(f_87_1,plain,
! [X_a] :
( ! [X,Y] :
( X != 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_43_order__less__imp__not__eq]) ).
fof(f_87_2,plain,
! [U_243] :
( ! [U_242,U_241] :
( U_242 != U_241
| ~ hBOOL(hAPP(U_243,bool,hAPP(U_243,fun(U_243,bool),ord_less(U_243),U_242),U_241)) )
| ~ order(U_243) ),
inference(variable_rename,[status(thm)],[f_87_1]) ).
cnf(f_87_3,plain,
( U_242 != U_241
| ~ hBOOL(hAPP(U_243,bool,hAPP(U_243,fun(U_243,bool),ord_less(U_243),U_242),U_241))
| ~ order(U_243) ),
inference(clausify,[status(thm)],[f_87_2]) ).
fof(f_88_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_44_order__less__imp__not__less]) ).
fof(f_88_2,plain,
! [U_246] :
( ! [U_245,U_244] :
( ~ hBOOL(hAPP(U_246,bool,hAPP(U_246,fun(U_246,bool),ord_less(U_246),U_244),U_245))
| ~ hBOOL(hAPP(U_246,bool,hAPP(U_246,fun(U_246,bool),ord_less(U_246),U_245),U_244)) )
| ~ preorder(U_246) ),
inference(variable_rename,[status(thm)],[f_88_1]) ).
cnf(f_88_3,plain,
( ~ hBOOL(hAPP(U_246,bool,hAPP(U_246,fun(U_246,bool),ord_less(U_246),U_244),U_245))
| ~ hBOOL(hAPP(U_246,bool,hAPP(U_246,fun(U_246,bool),ord_less(U_246),U_245),U_244))
| ~ preorder(U_246) ),
inference(clausify,[status(thm)],[f_88_2]) ).
fof(f_89_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_45_order__less__not__sym]) ).
fof(f_89_2,plain,
! [U_249] :
( ! [U_248,U_247] :
( ~ hBOOL(hAPP(U_249,bool,hAPP(U_249,fun(U_249,bool),ord_less(U_249),U_247),U_248))
| ~ hBOOL(hAPP(U_249,bool,hAPP(U_249,fun(U_249,bool),ord_less(U_249),U_248),U_247)) )
| ~ preorder(U_249) ),
inference(variable_rename,[status(thm)],[f_89_1]) ).
cnf(f_89_3,plain,
( ~ hBOOL(hAPP(U_249,bool,hAPP(U_249,fun(U_249,bool),ord_less(U_249),U_247),U_248))
| ~ hBOOL(hAPP(U_249,bool,hAPP(U_249,fun(U_249,bool),ord_less(U_249),U_248),U_247))
| ~ preorder(U_249) ),
inference(clausify,[status(thm)],[f_89_2]) ).
fof(f_90_1,plain,
! [X_a] :
( ! [X,Y] :
( X != 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_46_less__imp__neq]) ).
fof(f_90_2,plain,
! [U_252] :
( ! [U_251,U_250] :
( U_251 != U_250
| ~ hBOOL(hAPP(U_252,bool,hAPP(U_252,fun(U_252,bool),ord_less(U_252),U_251),U_250)) )
| ~ order(U_252) ),
inference(variable_rename,[status(thm)],[f_90_1]) ).
cnf(f_90_3,plain,
( U_251 != U_250
| ~ hBOOL(hAPP(U_252,bool,hAPP(U_252,fun(U_252,bool),ord_less(U_252),U_251),U_250))
| ~ order(U_252) ),
inference(clausify,[status(thm)],[f_90_2]) ).
fof(f_91_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_47_linorder__neqE]) ).
fof(f_91_2,plain,
! [U_255] :
( ! [U_254,U_253] :
( 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_254),U_253))
| ti(U_255,U_254) = ti(U_255,U_253) )
| ~ linorder(U_255) ),
inference(variable_rename,[status(thm)],[f_91_1]) ).
cnf(f_91_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_254),U_253))
| ti(U_255,U_254) = ti(U_255,U_253)
| ~ linorder(U_255) ),
inference(clausify,[status(thm)],[f_91_2]) ).
fof(f_92_1,plain,
! [X_a] :
( ! [Y_1,X_2] :
( ( ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_1))
| ti(X_a,X_2) != ti(X_a,Y_1) )
& ( ti(X_a,X_2) = ti(X_a,Y_1)
| hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_1)) ) )
| hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_2)) )
| ~ linorder(X_a) ),
inference(fof_nnf,[status(thm)],[fact_48_linorder__antisym__conv3]) ).
fof(f_92_2,plain,
! [U_258] :
( ! [U_257,U_256] :
( ( ( ~ hBOOL(hAPP(U_258,bool,hAPP(U_258,fun(U_258,bool),ord_less(U_258),U_256),U_257))
| ti(U_258,U_256) != ti(U_258,U_257) )
& ( ti(U_258,U_256) = ti(U_258,U_257)
| hBOOL(hAPP(U_258,bool,hAPP(U_258,fun(U_258,bool),ord_less(U_258),U_256),U_257)) ) )
| hBOOL(hAPP(U_258,bool,hAPP(U_258,fun(U_258,bool),ord_less(U_258),U_257),U_256)) )
| ~ linorder(U_258) ),
inference(variable_rename,[status(thm)],[f_92_1]) ).
cnf(f_92_3,plain,
( ti(U_258,U_256) = ti(U_258,U_257)
| hBOOL(hAPP(U_258,bool,hAPP(U_258,fun(U_258,bool),ord_less(U_258),U_256),U_257))
| hBOOL(hAPP(U_258,bool,hAPP(U_258,fun(U_258,bool),ord_less(U_258),U_257),U_256))
| ~ linorder(U_258) ),
inference(clausify,[status(thm)],[f_92_2]) ).
cnf(f_92_4,plain,
( ~ hBOOL(hAPP(U_258,bool,hAPP(U_258,fun(U_258,bool),ord_less(U_258),U_256),U_257))
| ti(U_258,U_256) != ti(U_258,U_257)
| hBOOL(hAPP(U_258,bool,hAPP(U_258,fun(U_258,bool),ord_less(U_258),U_257),U_256))
| ~ linorder(U_258) ),
inference(clausify,[status(thm)],[f_92_2]) ).
fof(f_93_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_49_linorder__less__linear]) ).
fof(f_93_2,plain,
! [U_261] :
( ! [U_260,U_259] :
( hBOOL(hAPP(U_261,bool,hAPP(U_261,fun(U_261,bool),ord_less(U_261),U_259),U_260))
| ti(U_261,U_260) = ti(U_261,U_259)
| hBOOL(hAPP(U_261,bool,hAPP(U_261,fun(U_261,bool),ord_less(U_261),U_260),U_259)) )
| ~ linorder(U_261) ),
inference(variable_rename,[status(thm)],[f_93_1]) ).
cnf(f_93_3,plain,
( hBOOL(hAPP(U_261,bool,hAPP(U_261,fun(U_261,bool),ord_less(U_261),U_259),U_260))
| ti(U_261,U_260) = ti(U_261,U_259)
| hBOOL(hAPP(U_261,bool,hAPP(U_261,fun(U_261,bool),ord_less(U_261),U_260),U_259))
| ~ linorder(U_261) ),
inference(clausify,[status(thm)],[f_93_2]) ).
fof(f_94_1,plain,
! [X_a] :
( ! [X_2,Y_1] :
( ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_1))
| ( ti(X_a,X_2) != ti(X_a,Y_1)
& ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_2)) ) )
& ( ti(X_a,X_2) = ti(X_a,Y_1)
| hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_2))
| hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_1)) ) )
| ~ linorder(X_a) ),
inference(fof_nnf,[status(thm)],[fact_50_not__less__iff__gr__or__eq]) ).
fof(f_94_2,plain,
! [U_264] :
( ! [U_263,U_262] :
( ( ~ hBOOL(hAPP(U_264,bool,hAPP(U_264,fun(U_264,bool),ord_less(U_264),U_263),U_262))
| ( ti(U_264,U_263) != ti(U_264,U_262)
& ~ hBOOL(hAPP(U_264,bool,hAPP(U_264,fun(U_264,bool),ord_less(U_264),U_262),U_263)) ) )
& ( ti(U_264,U_263) = ti(U_264,U_262)
| hBOOL(hAPP(U_264,bool,hAPP(U_264,fun(U_264,bool),ord_less(U_264),U_262),U_263))
| hBOOL(hAPP(U_264,bool,hAPP(U_264,fun(U_264,bool),ord_less(U_264),U_263),U_262)) ) )
| ~ linorder(U_264) ),
inference(variable_rename,[status(thm)],[f_94_1]) ).
fof(f_94_3,plain,
! [U_264] :
( ( ! [U_268,U_266] :
( ~ hBOOL(hAPP(U_264,bool,hAPP(U_264,fun(U_264,bool),ord_less(U_264),U_268),U_266))
| ( ti(U_264,U_268) != ti(U_264,U_266)
& ~ hBOOL(hAPP(U_264,bool,hAPP(U_264,fun(U_264,bool),ord_less(U_264),U_266),U_268)) ) )
& ! [U_267,U_265] :
( ti(U_264,U_267) = ti(U_264,U_265)
| hBOOL(hAPP(U_264,bool,hAPP(U_264,fun(U_264,bool),ord_less(U_264),U_265),U_267))
| hBOOL(hAPP(U_264,bool,hAPP(U_264,fun(U_264,bool),ord_less(U_264),U_267),U_265)) ) )
| ~ linorder(U_264) ),
inference(miniscope,[status(thm)],[f_94_2]) ).
cnf(f_94_4,plain,
( ti(U_264,U_267) = ti(U_264,U_265)
| hBOOL(hAPP(U_264,bool,hAPP(U_264,fun(U_264,bool),ord_less(U_264),U_265),U_267))
| hBOOL(hAPP(U_264,bool,hAPP(U_264,fun(U_264,bool),ord_less(U_264),U_267),U_265))
| ~ linorder(U_264) ),
inference(clausify,[status(thm)],[f_94_3]) ).
cnf(f_94_5,plain,
( ~ hBOOL(hAPP(U_264,bool,hAPP(U_264,fun(U_264,bool),ord_less(U_264),U_266),U_268))
| ~ hBOOL(hAPP(U_264,bool,hAPP(U_264,fun(U_264,bool),ord_less(U_264),U_268),U_266))
| ~ linorder(U_264) ),
inference(clausify,[status(thm)],[f_94_3]) ).
cnf(f_94_6,plain,
( ti(U_264,U_268) != ti(U_264,U_266)
| ~ hBOOL(hAPP(U_264,bool,hAPP(U_264,fun(U_264,bool),ord_less(U_264),U_268),U_266))
| ~ linorder(U_264) ),
inference(clausify,[status(thm)],[f_94_3]) ).
fof(f_95_1,plain,
! [X_a] :
( ! [X_2,Y_1] :
( ( ti(X_a,X_2) != ti(X_a,Y_1)
| ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_2))
& ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_1)) ) )
& ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_2))
| hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_1))
| ti(X_a,X_2) = ti(X_a,Y_1) ) )
| ~ linorder(X_a) ),
inference(fof_nnf,[status(thm)],[fact_51_linorder__neq__iff]) ).
fof(f_95_2,plain,
! [U_271] :
( ! [U_270,U_269] :
( ( ti(U_271,U_270) != ti(U_271,U_269)
| ( ~ 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_270),U_269)) ) )
& ( 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_270),U_269))
| ti(U_271,U_270) = ti(U_271,U_269) ) )
| ~ linorder(U_271) ),
inference(variable_rename,[status(thm)],[f_95_1]) ).
fof(f_95_3,plain,
! [U_271] :
( ( ! [U_275,U_273] :
( ti(U_271,U_275) != ti(U_271,U_273)
| ( ~ hBOOL(hAPP(U_271,bool,hAPP(U_271,fun(U_271,bool),ord_less(U_271),U_273),U_275))
& ~ hBOOL(hAPP(U_271,bool,hAPP(U_271,fun(U_271,bool),ord_less(U_271),U_275),U_273)) ) )
& ! [U_274,U_272] :
( hBOOL(hAPP(U_271,bool,hAPP(U_271,fun(U_271,bool),ord_less(U_271),U_272),U_274))
| hBOOL(hAPP(U_271,bool,hAPP(U_271,fun(U_271,bool),ord_less(U_271),U_274),U_272))
| ti(U_271,U_274) = ti(U_271,U_272) ) )
| ~ linorder(U_271) ),
inference(miniscope,[status(thm)],[f_95_2]) ).
cnf(f_95_4,plain,
( hBOOL(hAPP(U_271,bool,hAPP(U_271,fun(U_271,bool),ord_less(U_271),U_272),U_274))
| hBOOL(hAPP(U_271,bool,hAPP(U_271,fun(U_271,bool),ord_less(U_271),U_274),U_272))
| ti(U_271,U_274) = ti(U_271,U_272)
| ~ linorder(U_271) ),
inference(clausify,[status(thm)],[f_95_3]) ).
cnf(f_95_5,plain,
( ~ hBOOL(hAPP(U_271,bool,hAPP(U_271,fun(U_271,bool),ord_less(U_271),U_275),U_273))
| ti(U_271,U_275) != ti(U_271,U_273)
| ~ linorder(U_271) ),
inference(clausify,[status(thm)],[f_95_3]) ).
cnf(f_95_6,plain,
( ~ hBOOL(hAPP(U_271,bool,hAPP(U_271,fun(U_271,bool),ord_less(U_271),U_273),U_275))
| ti(U_271,U_275) != ti(U_271,U_273)
| ~ linorder(U_271) ),
inference(clausify,[status(thm)],[f_95_3]) ).
fof(f_96_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_52_order__less__irrefl]) ).
fof(f_96_2,plain,
! [U_277] :
( ! [U_276] : ~ hBOOL(hAPP(U_277,bool,hAPP(U_277,fun(U_277,bool),ord_less(U_277),U_276),U_276))
| ~ preorder(U_277) ),
inference(variable_rename,[status(thm)],[f_96_1]) ).
cnf(f_96_3,plain,
( ~ hBOOL(hAPP(U_277,bool,hAPP(U_277,fun(U_277,bool),ord_less(U_277),U_276),U_276))
| ~ preorder(U_277) ),
inference(clausify,[status(thm)],[f_96_2]) ).
fof(f_97_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_53_UNIV__def]) ).
fof(f_97_2,plain,
! [U_278] : top_top(fun(U_278,bool)) = hAPP(fun(U_278,bool),fun(U_278,bool),collect(U_278),hAPP(bool,fun(U_278,bool),combk(bool,U_278),fTrue)),
inference(variable_rename,[status(thm)],[f_97_1]) ).
cnf(f_97_3,plain,
top_top(fun(U_278,bool)) = hAPP(fun(U_278,bool),fun(U_278,bool),collect(U_278),hAPP(bool,fun(U_278,bool),combk(bool,U_278),fTrue)),
inference(clausify,[status(thm)],[f_97_2]) ).
fof(f_98_1,plain,
! [X_a,X_b,S,R_1] :
( ( ! [X_1,Xa] :
( ( hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_1),Xa)),R_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),Xa)),S)) )
& ( hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_1),Xa)),S))
| ~ hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_1),Xa)),R_1)) ) )
| ti(fun(product_prod(X_a,X_b),bool),R_1) != ti(fun(product_prod(X_a,X_b),bool),S) )
& ( ti(fun(product_prod(X_a,X_b),bool),R_1) = ti(fun(product_prod(X_a,X_b),bool),S)
| ? [X_1,Xa] :
( ( ~ hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_1),Xa)),R_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),Xa)),S)) )
| ( ~ hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_1),Xa)),S))
& hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_1),Xa)),R_1)) ) ) ) ),
inference(fof_nnf,[status(thm)],[fact_54_pred__equals__eq2]) ).
fof(f_98_2,plain,
! [U_286,U_285,U_284,U_283] :
( ( ! [U_282,U_281] :
( ( hBOOL(hAPP(fun(product_prod(U_286,U_285),bool),bool,hAPP(product_prod(U_286,U_285),fun(fun(product_prod(U_286,U_285),bool),bool),member(product_prod(U_286,U_285)),hAPP(U_285,product_prod(U_286,U_285),hAPP(U_286,fun(U_285,product_prod(U_286,U_285)),product_Pair(U_286,U_285),U_282),U_281)),U_283))
| ~ hBOOL(hAPP(fun(product_prod(U_286,U_285),bool),bool,hAPP(product_prod(U_286,U_285),fun(fun(product_prod(U_286,U_285),bool),bool),member(product_prod(U_286,U_285)),hAPP(U_285,product_prod(U_286,U_285),hAPP(U_286,fun(U_285,product_prod(U_286,U_285)),product_Pair(U_286,U_285),U_282),U_281)),U_284)) )
& ( hBOOL(hAPP(fun(product_prod(U_286,U_285),bool),bool,hAPP(product_prod(U_286,U_285),fun(fun(product_prod(U_286,U_285),bool),bool),member(product_prod(U_286,U_285)),hAPP(U_285,product_prod(U_286,U_285),hAPP(U_286,fun(U_285,product_prod(U_286,U_285)),product_Pair(U_286,U_285),U_282),U_281)),U_284))
| ~ hBOOL(hAPP(fun(product_prod(U_286,U_285),bool),bool,hAPP(product_prod(U_286,U_285),fun(fun(product_prod(U_286,U_285),bool),bool),member(product_prod(U_286,U_285)),hAPP(U_285,product_prod(U_286,U_285),hAPP(U_286,fun(U_285,product_prod(U_286,U_285)),product_Pair(U_286,U_285),U_282),U_281)),U_283)) ) )
| ti(fun(product_prod(U_286,U_285),bool),U_283) != ti(fun(product_prod(U_286,U_285),bool),U_284) )
& ( ti(fun(product_prod(U_286,U_285),bool),U_283) = ti(fun(product_prod(U_286,U_285),bool),U_284)
| ? [U_280,U_279] :
( ( ~ hBOOL(hAPP(fun(product_prod(U_286,U_285),bool),bool,hAPP(product_prod(U_286,U_285),fun(fun(product_prod(U_286,U_285),bool),bool),member(product_prod(U_286,U_285)),hAPP(U_285,product_prod(U_286,U_285),hAPP(U_286,fun(U_285,product_prod(U_286,U_285)),product_Pair(U_286,U_285),U_280),U_279)),U_283))
& hBOOL(hAPP(fun(product_prod(U_286,U_285),bool),bool,hAPP(product_prod(U_286,U_285),fun(fun(product_prod(U_286,U_285),bool),bool),member(product_prod(U_286,U_285)),hAPP(U_285,product_prod(U_286,U_285),hAPP(U_286,fun(U_285,product_prod(U_286,U_285)),product_Pair(U_286,U_285),U_280),U_279)),U_284)) )
| ( ~ hBOOL(hAPP(fun(product_prod(U_286,U_285),bool),bool,hAPP(product_prod(U_286,U_285),fun(fun(product_prod(U_286,U_285),bool),bool),member(product_prod(U_286,U_285)),hAPP(U_285,product_prod(U_286,U_285),hAPP(U_286,fun(U_285,product_prod(U_286,U_285)),product_Pair(U_286,U_285),U_280),U_279)),U_284))
& hBOOL(hAPP(fun(product_prod(U_286,U_285),bool),bool,hAPP(product_prod(U_286,U_285),fun(fun(product_prod(U_286,U_285),bool),bool),member(product_prod(U_286,U_285)),hAPP(U_285,product_prod(U_286,U_285),hAPP(U_286,fun(U_285,product_prod(U_286,U_285)),product_Pair(U_286,U_285),U_280),U_279)),U_283)) ) ) ) ),
inference(variable_rename,[status(thm)],[f_98_1]) ).
fof(f_98_3,plain,
( ! [U_302,U_300,U_298,U_296] :
( ( ! [U_294,U_292] :
( hBOOL(hAPP(fun(product_prod(U_302,U_300),bool),bool,hAPP(product_prod(U_302,U_300),fun(fun(product_prod(U_302,U_300),bool),bool),member(product_prod(U_302,U_300)),hAPP(U_300,product_prod(U_302,U_300),hAPP(U_302,fun(U_300,product_prod(U_302,U_300)),product_Pair(U_302,U_300),U_294),U_292)),U_296))
| ~ hBOOL(hAPP(fun(product_prod(U_302,U_300),bool),bool,hAPP(product_prod(U_302,U_300),fun(fun(product_prod(U_302,U_300),bool),bool),member(product_prod(U_302,U_300)),hAPP(U_300,product_prod(U_302,U_300),hAPP(U_302,fun(U_300,product_prod(U_302,U_300)),product_Pair(U_302,U_300),U_294),U_292)),U_298)) )
& ! [U_293,U_291] :
( hBOOL(hAPP(fun(product_prod(U_302,U_300),bool),bool,hAPP(product_prod(U_302,U_300),fun(fun(product_prod(U_302,U_300),bool),bool),member(product_prod(U_302,U_300)),hAPP(U_300,product_prod(U_302,U_300),hAPP(U_302,fun(U_300,product_prod(U_302,U_300)),product_Pair(U_302,U_300),U_293),U_291)),U_298))
| ~ hBOOL(hAPP(fun(product_prod(U_302,U_300),bool),bool,hAPP(product_prod(U_302,U_300),fun(fun(product_prod(U_302,U_300),bool),bool),member(product_prod(U_302,U_300)),hAPP(U_300,product_prod(U_302,U_300),hAPP(U_302,fun(U_300,product_prod(U_302,U_300)),product_Pair(U_302,U_300),U_293),U_291)),U_296)) ) )
| ti(fun(product_prod(U_302,U_300),bool),U_296) != ti(fun(product_prod(U_302,U_300),bool),U_298) )
& ! [U_301,U_299,U_297,U_295] :
( ti(fun(product_prod(U_301,U_299),bool),U_295) = ti(fun(product_prod(U_301,U_299),bool),U_297)
| ? [U_290,U_288] :
( ~ hBOOL(hAPP(fun(product_prod(U_301,U_299),bool),bool,hAPP(product_prod(U_301,U_299),fun(fun(product_prod(U_301,U_299),bool),bool),member(product_prod(U_301,U_299)),hAPP(U_299,product_prod(U_301,U_299),hAPP(U_301,fun(U_299,product_prod(U_301,U_299)),product_Pair(U_301,U_299),U_290),U_288)),U_295))
& hBOOL(hAPP(fun(product_prod(U_301,U_299),bool),bool,hAPP(product_prod(U_301,U_299),fun(fun(product_prod(U_301,U_299),bool),bool),member(product_prod(U_301,U_299)),hAPP(U_299,product_prod(U_301,U_299),hAPP(U_301,fun(U_299,product_prod(U_301,U_299)),product_Pair(U_301,U_299),U_290),U_288)),U_297)) )
| ? [U_289,U_287] :
( ~ hBOOL(hAPP(fun(product_prod(U_301,U_299),bool),bool,hAPP(product_prod(U_301,U_299),fun(fun(product_prod(U_301,U_299),bool),bool),member(product_prod(U_301,U_299)),hAPP(U_299,product_prod(U_301,U_299),hAPP(U_301,fun(U_299,product_prod(U_301,U_299)),product_Pair(U_301,U_299),U_289),U_287)),U_297))
& hBOOL(hAPP(fun(product_prod(U_301,U_299),bool),bool,hAPP(product_prod(U_301,U_299),fun(fun(product_prod(U_301,U_299),bool),bool),member(product_prod(U_301,U_299)),hAPP(U_299,product_prod(U_301,U_299),hAPP(U_301,fun(U_299,product_prod(U_301,U_299)),product_Pair(U_301,U_299),U_289),U_287)),U_295)) ) ) ),
inference(miniscope,[status(thm)],[f_98_2]) ).
fof(f_98_4,plain,
( ! [U_302,U_300,U_298,U_296] :
( ( ! [U_294,U_292] :
( hBOOL(hAPP(fun(product_prod(U_302,U_300),bool),bool,hAPP(product_prod(U_302,U_300),fun(fun(product_prod(U_302,U_300),bool),bool),member(product_prod(U_302,U_300)),hAPP(U_300,product_prod(U_302,U_300),hAPP(U_302,fun(U_300,product_prod(U_302,U_300)),product_Pair(U_302,U_300),U_294),U_292)),U_296))
| ~ hBOOL(hAPP(fun(product_prod(U_302,U_300),bool),bool,hAPP(product_prod(U_302,U_300),fun(fun(product_prod(U_302,U_300),bool),bool),member(product_prod(U_302,U_300)),hAPP(U_300,product_prod(U_302,U_300),hAPP(U_302,fun(U_300,product_prod(U_302,U_300)),product_Pair(U_302,U_300),U_294),U_292)),U_298)) )
& ! [U_293,U_291] :
( hBOOL(hAPP(fun(product_prod(U_302,U_300),bool),bool,hAPP(product_prod(U_302,U_300),fun(fun(product_prod(U_302,U_300),bool),bool),member(product_prod(U_302,U_300)),hAPP(U_300,product_prod(U_302,U_300),hAPP(U_302,fun(U_300,product_prod(U_302,U_300)),product_Pair(U_302,U_300),U_293),U_291)),U_298))
| ~ hBOOL(hAPP(fun(product_prod(U_302,U_300),bool),bool,hAPP(product_prod(U_302,U_300),fun(fun(product_prod(U_302,U_300),bool),bool),member(product_prod(U_302,U_300)),hAPP(U_300,product_prod(U_302,U_300),hAPP(U_302,fun(U_300,product_prod(U_302,U_300)),product_Pair(U_302,U_300),U_293),U_291)),U_296)) ) )
| ti(fun(product_prod(U_302,U_300),bool),U_296) != ti(fun(product_prod(U_302,U_300),bool),U_298) )
& ! [U_301,U_299,U_297,U_295] :
( ti(fun(product_prod(U_301,U_299),bool),U_295) = ti(fun(product_prod(U_301,U_299),bool),U_297)
| ? [U_290,U_288] :
( ~ hBOOL(hAPP(fun(product_prod(U_301,U_299),bool),bool,hAPP(product_prod(U_301,U_299),fun(fun(product_prod(U_301,U_299),bool),bool),member(product_prod(U_301,U_299)),hAPP(U_299,product_prod(U_301,U_299),hAPP(U_301,fun(U_299,product_prod(U_301,U_299)),product_Pair(U_301,U_299),U_290),U_288)),U_295))
& hBOOL(hAPP(fun(product_prod(U_301,U_299),bool),bool,hAPP(product_prod(U_301,U_299),fun(fun(product_prod(U_301,U_299),bool),bool),member(product_prod(U_301,U_299)),hAPP(U_299,product_prod(U_301,U_299),hAPP(U_301,fun(U_299,product_prod(U_301,U_299)),product_Pair(U_301,U_299),U_290),U_288)),U_297)) )
| ? [U_287] :
( ~ hBOOL(hAPP(fun(product_prod(U_301,U_299),bool),bool,hAPP(product_prod(U_301,U_299),fun(fun(product_prod(U_301,U_299),bool),bool),member(product_prod(U_301,U_299)),hAPP(U_299,product_prod(U_301,U_299),hAPP(U_301,fun(U_299,product_prod(U_301,U_299)),product_Pair(U_301,U_299),sK24(U_301,U_299,U_297,U_295)),U_287)),U_297))
& hBOOL(hAPP(fun(product_prod(U_301,U_299),bool),bool,hAPP(product_prod(U_301,U_299),fun(fun(product_prod(U_301,U_299),bool),bool),member(product_prod(U_301,U_299)),hAPP(U_299,product_prod(U_301,U_299),hAPP(U_301,fun(U_299,product_prod(U_301,U_299)),product_Pair(U_301,U_299),sK24(U_301,U_299,U_297,U_295)),U_287)),U_295)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_289,sK24(U_301,U_299,U_297,U_295))],[f_98_3]) ).
fof(f_98_5,plain,
( ! [U_302,U_300,U_298,U_296] :
( ( ! [U_294,U_292] :
( hBOOL(hAPP(fun(product_prod(U_302,U_300),bool),bool,hAPP(product_prod(U_302,U_300),fun(fun(product_prod(U_302,U_300),bool),bool),member(product_prod(U_302,U_300)),hAPP(U_300,product_prod(U_302,U_300),hAPP(U_302,fun(U_300,product_prod(U_302,U_300)),product_Pair(U_302,U_300),U_294),U_292)),U_296))
| ~ hBOOL(hAPP(fun(product_prod(U_302,U_300),bool),bool,hAPP(product_prod(U_302,U_300),fun(fun(product_prod(U_302,U_300),bool),bool),member(product_prod(U_302,U_300)),hAPP(U_300,product_prod(U_302,U_300),hAPP(U_302,fun(U_300,product_prod(U_302,U_300)),product_Pair(U_302,U_300),U_294),U_292)),U_298)) )
& ! [U_293,U_291] :
( hBOOL(hAPP(fun(product_prod(U_302,U_300),bool),bool,hAPP(product_prod(U_302,U_300),fun(fun(product_prod(U_302,U_300),bool),bool),member(product_prod(U_302,U_300)),hAPP(U_300,product_prod(U_302,U_300),hAPP(U_302,fun(U_300,product_prod(U_302,U_300)),product_Pair(U_302,U_300),U_293),U_291)),U_298))
| ~ hBOOL(hAPP(fun(product_prod(U_302,U_300),bool),bool,hAPP(product_prod(U_302,U_300),fun(fun(product_prod(U_302,U_300),bool),bool),member(product_prod(U_302,U_300)),hAPP(U_300,product_prod(U_302,U_300),hAPP(U_302,fun(U_300,product_prod(U_302,U_300)),product_Pair(U_302,U_300),U_293),U_291)),U_296)) ) )
| ti(fun(product_prod(U_302,U_300),bool),U_296) != ti(fun(product_prod(U_302,U_300),bool),U_298) )
& ! [U_301,U_299,U_297,U_295] :
( ti(fun(product_prod(U_301,U_299),bool),U_295) = ti(fun(product_prod(U_301,U_299),bool),U_297)
| ? [U_290,U_288] :
( ~ hBOOL(hAPP(fun(product_prod(U_301,U_299),bool),bool,hAPP(product_prod(U_301,U_299),fun(fun(product_prod(U_301,U_299),bool),bool),member(product_prod(U_301,U_299)),hAPP(U_299,product_prod(U_301,U_299),hAPP(U_301,fun(U_299,product_prod(U_301,U_299)),product_Pair(U_301,U_299),U_290),U_288)),U_295))
& hBOOL(hAPP(fun(product_prod(U_301,U_299),bool),bool,hAPP(product_prod(U_301,U_299),fun(fun(product_prod(U_301,U_299),bool),bool),member(product_prod(U_301,U_299)),hAPP(U_299,product_prod(U_301,U_299),hAPP(U_301,fun(U_299,product_prod(U_301,U_299)),product_Pair(U_301,U_299),U_290),U_288)),U_297)) )
| ( ~ hBOOL(hAPP(fun(product_prod(U_301,U_299),bool),bool,hAPP(product_prod(U_301,U_299),fun(fun(product_prod(U_301,U_299),bool),bool),member(product_prod(U_301,U_299)),hAPP(U_299,product_prod(U_301,U_299),hAPP(U_301,fun(U_299,product_prod(U_301,U_299)),product_Pair(U_301,U_299),sK24(U_301,U_299,U_297,U_295)),sK25(U_301,U_299,U_297,U_295))),U_297))
& hBOOL(hAPP(fun(product_prod(U_301,U_299),bool),bool,hAPP(product_prod(U_301,U_299),fun(fun(product_prod(U_301,U_299),bool),bool),member(product_prod(U_301,U_299)),hAPP(U_299,product_prod(U_301,U_299),hAPP(U_301,fun(U_299,product_prod(U_301,U_299)),product_Pair(U_301,U_299),sK24(U_301,U_299,U_297,U_295)),sK25(U_301,U_299,U_297,U_295))),U_295)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_287,sK25(U_301,U_299,U_297,U_295))],[f_98_4]) ).
fof(f_98_6,plain,
( ! [U_302,U_300,U_298,U_296] :
( ( ! [U_294,U_292] :
( hBOOL(hAPP(fun(product_prod(U_302,U_300),bool),bool,hAPP(product_prod(U_302,U_300),fun(fun(product_prod(U_302,U_300),bool),bool),member(product_prod(U_302,U_300)),hAPP(U_300,product_prod(U_302,U_300),hAPP(U_302,fun(U_300,product_prod(U_302,U_300)),product_Pair(U_302,U_300),U_294),U_292)),U_296))
| ~ hBOOL(hAPP(fun(product_prod(U_302,U_300),bool),bool,hAPP(product_prod(U_302,U_300),fun(fun(product_prod(U_302,U_300),bool),bool),member(product_prod(U_302,U_300)),hAPP(U_300,product_prod(U_302,U_300),hAPP(U_302,fun(U_300,product_prod(U_302,U_300)),product_Pair(U_302,U_300),U_294),U_292)),U_298)) )
& ! [U_293,U_291] :
( hBOOL(hAPP(fun(product_prod(U_302,U_300),bool),bool,hAPP(product_prod(U_302,U_300),fun(fun(product_prod(U_302,U_300),bool),bool),member(product_prod(U_302,U_300)),hAPP(U_300,product_prod(U_302,U_300),hAPP(U_302,fun(U_300,product_prod(U_302,U_300)),product_Pair(U_302,U_300),U_293),U_291)),U_298))
| ~ hBOOL(hAPP(fun(product_prod(U_302,U_300),bool),bool,hAPP(product_prod(U_302,U_300),fun(fun(product_prod(U_302,U_300),bool),bool),member(product_prod(U_302,U_300)),hAPP(U_300,product_prod(U_302,U_300),hAPP(U_302,fun(U_300,product_prod(U_302,U_300)),product_Pair(U_302,U_300),U_293),U_291)),U_296)) ) )
| ti(fun(product_prod(U_302,U_300),bool),U_296) != ti(fun(product_prod(U_302,U_300),bool),U_298) )
& ! [U_301,U_299,U_297,U_295] :
( ti(fun(product_prod(U_301,U_299),bool),U_295) = ti(fun(product_prod(U_301,U_299),bool),U_297)
| ? [U_288] :
( ~ hBOOL(hAPP(fun(product_prod(U_301,U_299),bool),bool,hAPP(product_prod(U_301,U_299),fun(fun(product_prod(U_301,U_299),bool),bool),member(product_prod(U_301,U_299)),hAPP(U_299,product_prod(U_301,U_299),hAPP(U_301,fun(U_299,product_prod(U_301,U_299)),product_Pair(U_301,U_299),sK26(U_301,U_299,U_297,U_295)),U_288)),U_295))
& hBOOL(hAPP(fun(product_prod(U_301,U_299),bool),bool,hAPP(product_prod(U_301,U_299),fun(fun(product_prod(U_301,U_299),bool),bool),member(product_prod(U_301,U_299)),hAPP(U_299,product_prod(U_301,U_299),hAPP(U_301,fun(U_299,product_prod(U_301,U_299)),product_Pair(U_301,U_299),sK26(U_301,U_299,U_297,U_295)),U_288)),U_297)) )
| ( ~ hBOOL(hAPP(fun(product_prod(U_301,U_299),bool),bool,hAPP(product_prod(U_301,U_299),fun(fun(product_prod(U_301,U_299),bool),bool),member(product_prod(U_301,U_299)),hAPP(U_299,product_prod(U_301,U_299),hAPP(U_301,fun(U_299,product_prod(U_301,U_299)),product_Pair(U_301,U_299),sK24(U_301,U_299,U_297,U_295)),sK25(U_301,U_299,U_297,U_295))),U_297))
& hBOOL(hAPP(fun(product_prod(U_301,U_299),bool),bool,hAPP(product_prod(U_301,U_299),fun(fun(product_prod(U_301,U_299),bool),bool),member(product_prod(U_301,U_299)),hAPP(U_299,product_prod(U_301,U_299),hAPP(U_301,fun(U_299,product_prod(U_301,U_299)),product_Pair(U_301,U_299),sK24(U_301,U_299,U_297,U_295)),sK25(U_301,U_299,U_297,U_295))),U_295)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_290,sK26(U_301,U_299,U_297,U_295))],[f_98_5]) ).
fof(f_98_7,plain,
( ! [U_302,U_300,U_298,U_296] :
( ( ! [U_294,U_292] :
( hBOOL(hAPP(fun(product_prod(U_302,U_300),bool),bool,hAPP(product_prod(U_302,U_300),fun(fun(product_prod(U_302,U_300),bool),bool),member(product_prod(U_302,U_300)),hAPP(U_300,product_prod(U_302,U_300),hAPP(U_302,fun(U_300,product_prod(U_302,U_300)),product_Pair(U_302,U_300),U_294),U_292)),U_296))
| ~ hBOOL(hAPP(fun(product_prod(U_302,U_300),bool),bool,hAPP(product_prod(U_302,U_300),fun(fun(product_prod(U_302,U_300),bool),bool),member(product_prod(U_302,U_300)),hAPP(U_300,product_prod(U_302,U_300),hAPP(U_302,fun(U_300,product_prod(U_302,U_300)),product_Pair(U_302,U_300),U_294),U_292)),U_298)) )
& ! [U_293,U_291] :
( hBOOL(hAPP(fun(product_prod(U_302,U_300),bool),bool,hAPP(product_prod(U_302,U_300),fun(fun(product_prod(U_302,U_300),bool),bool),member(product_prod(U_302,U_300)),hAPP(U_300,product_prod(U_302,U_300),hAPP(U_302,fun(U_300,product_prod(U_302,U_300)),product_Pair(U_302,U_300),U_293),U_291)),U_298))
| ~ hBOOL(hAPP(fun(product_prod(U_302,U_300),bool),bool,hAPP(product_prod(U_302,U_300),fun(fun(product_prod(U_302,U_300),bool),bool),member(product_prod(U_302,U_300)),hAPP(U_300,product_prod(U_302,U_300),hAPP(U_302,fun(U_300,product_prod(U_302,U_300)),product_Pair(U_302,U_300),U_293),U_291)),U_296)) ) )
| ti(fun(product_prod(U_302,U_300),bool),U_296) != ti(fun(product_prod(U_302,U_300),bool),U_298) )
& ! [U_301,U_299,U_297,U_295] :
( ti(fun(product_prod(U_301,U_299),bool),U_295) = ti(fun(product_prod(U_301,U_299),bool),U_297)
| ( ~ hBOOL(hAPP(fun(product_prod(U_301,U_299),bool),bool,hAPP(product_prod(U_301,U_299),fun(fun(product_prod(U_301,U_299),bool),bool),member(product_prod(U_301,U_299)),hAPP(U_299,product_prod(U_301,U_299),hAPP(U_301,fun(U_299,product_prod(U_301,U_299)),product_Pair(U_301,U_299),sK26(U_301,U_299,U_297,U_295)),sK27(U_301,U_299,U_297,U_295))),U_295))
& hBOOL(hAPP(fun(product_prod(U_301,U_299),bool),bool,hAPP(product_prod(U_301,U_299),fun(fun(product_prod(U_301,U_299),bool),bool),member(product_prod(U_301,U_299)),hAPP(U_299,product_prod(U_301,U_299),hAPP(U_301,fun(U_299,product_prod(U_301,U_299)),product_Pair(U_301,U_299),sK26(U_301,U_299,U_297,U_295)),sK27(U_301,U_299,U_297,U_295))),U_297)) )
| ( ~ hBOOL(hAPP(fun(product_prod(U_301,U_299),bool),bool,hAPP(product_prod(U_301,U_299),fun(fun(product_prod(U_301,U_299),bool),bool),member(product_prod(U_301,U_299)),hAPP(U_299,product_prod(U_301,U_299),hAPP(U_301,fun(U_299,product_prod(U_301,U_299)),product_Pair(U_301,U_299),sK24(U_301,U_299,U_297,U_295)),sK25(U_301,U_299,U_297,U_295))),U_297))
& hBOOL(hAPP(fun(product_prod(U_301,U_299),bool),bool,hAPP(product_prod(U_301,U_299),fun(fun(product_prod(U_301,U_299),bool),bool),member(product_prod(U_301,U_299)),hAPP(U_299,product_prod(U_301,U_299),hAPP(U_301,fun(U_299,product_prod(U_301,U_299)),product_Pair(U_301,U_299),sK24(U_301,U_299,U_297,U_295)),sK25(U_301,U_299,U_297,U_295))),U_295)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_288,sK27(U_301,U_299,U_297,U_295))],[f_98_6]) ).
cnf(f_98_8,plain,
( hBOOL(hAPP(fun(product_prod(U_301,U_299),bool),bool,hAPP(product_prod(U_301,U_299),fun(fun(product_prod(U_301,U_299),bool),bool),member(product_prod(U_301,U_299)),hAPP(U_299,product_prod(U_301,U_299),hAPP(U_301,fun(U_299,product_prod(U_301,U_299)),product_Pair(U_301,U_299),sK26(U_301,U_299,U_297,U_295)),sK27(U_301,U_299,U_297,U_295))),U_297))
| hBOOL(hAPP(fun(product_prod(U_301,U_299),bool),bool,hAPP(product_prod(U_301,U_299),fun(fun(product_prod(U_301,U_299),bool),bool),member(product_prod(U_301,U_299)),hAPP(U_299,product_prod(U_301,U_299),hAPP(U_301,fun(U_299,product_prod(U_301,U_299)),product_Pair(U_301,U_299),sK24(U_301,U_299,U_297,U_295)),sK25(U_301,U_299,U_297,U_295))),U_295))
| ti(fun(product_prod(U_301,U_299),bool),U_295) = ti(fun(product_prod(U_301,U_299),bool),U_297) ),
inference(clausify,[status(thm)],[f_98_7]) ).
cnf(f_98_9,plain,
( ~ hBOOL(hAPP(fun(product_prod(U_301,U_299),bool),bool,hAPP(product_prod(U_301,U_299),fun(fun(product_prod(U_301,U_299),bool),bool),member(product_prod(U_301,U_299)),hAPP(U_299,product_prod(U_301,U_299),hAPP(U_301,fun(U_299,product_prod(U_301,U_299)),product_Pair(U_301,U_299),sK26(U_301,U_299,U_297,U_295)),sK27(U_301,U_299,U_297,U_295))),U_295))
| hBOOL(hAPP(fun(product_prod(U_301,U_299),bool),bool,hAPP(product_prod(U_301,U_299),fun(fun(product_prod(U_301,U_299),bool),bool),member(product_prod(U_301,U_299)),hAPP(U_299,product_prod(U_301,U_299),hAPP(U_301,fun(U_299,product_prod(U_301,U_299)),product_Pair(U_301,U_299),sK24(U_301,U_299,U_297,U_295)),sK25(U_301,U_299,U_297,U_295))),U_295))
| ti(fun(product_prod(U_301,U_299),bool),U_295) = ti(fun(product_prod(U_301,U_299),bool),U_297) ),
inference(clausify,[status(thm)],[f_98_7]) ).
cnf(f_98_10,plain,
( hBOOL(hAPP(fun(product_prod(U_301,U_299),bool),bool,hAPP(product_prod(U_301,U_299),fun(fun(product_prod(U_301,U_299),bool),bool),member(product_prod(U_301,U_299)),hAPP(U_299,product_prod(U_301,U_299),hAPP(U_301,fun(U_299,product_prod(U_301,U_299)),product_Pair(U_301,U_299),sK26(U_301,U_299,U_297,U_295)),sK27(U_301,U_299,U_297,U_295))),U_297))
| ~ hBOOL(hAPP(fun(product_prod(U_301,U_299),bool),bool,hAPP(product_prod(U_301,U_299),fun(fun(product_prod(U_301,U_299),bool),bool),member(product_prod(U_301,U_299)),hAPP(U_299,product_prod(U_301,U_299),hAPP(U_301,fun(U_299,product_prod(U_301,U_299)),product_Pair(U_301,U_299),sK24(U_301,U_299,U_297,U_295)),sK25(U_301,U_299,U_297,U_295))),U_297))
| ti(fun(product_prod(U_301,U_299),bool),U_295) = ti(fun(product_prod(U_301,U_299),bool),U_297) ),
inference(clausify,[status(thm)],[f_98_7]) ).
cnf(f_98_11,plain,
( ~ hBOOL(hAPP(fun(product_prod(U_301,U_299),bool),bool,hAPP(product_prod(U_301,U_299),fun(fun(product_prod(U_301,U_299),bool),bool),member(product_prod(U_301,U_299)),hAPP(U_299,product_prod(U_301,U_299),hAPP(U_301,fun(U_299,product_prod(U_301,U_299)),product_Pair(U_301,U_299),sK26(U_301,U_299,U_297,U_295)),sK27(U_301,U_299,U_297,U_295))),U_295))
| ~ hBOOL(hAPP(fun(product_prod(U_301,U_299),bool),bool,hAPP(product_prod(U_301,U_299),fun(fun(product_prod(U_301,U_299),bool),bool),member(product_prod(U_301,U_299)),hAPP(U_299,product_prod(U_301,U_299),hAPP(U_301,fun(U_299,product_prod(U_301,U_299)),product_Pair(U_301,U_299),sK24(U_301,U_299,U_297,U_295)),sK25(U_301,U_299,U_297,U_295))),U_297))
| ti(fun(product_prod(U_301,U_299),bool),U_295) = ti(fun(product_prod(U_301,U_299),bool),U_297) ),
inference(clausify,[status(thm)],[f_98_7]) ).
cnf(f_98_12,plain,
( hBOOL(hAPP(fun(product_prod(U_302,U_300),bool),bool,hAPP(product_prod(U_302,U_300),fun(fun(product_prod(U_302,U_300),bool),bool),member(product_prod(U_302,U_300)),hAPP(U_300,product_prod(U_302,U_300),hAPP(U_302,fun(U_300,product_prod(U_302,U_300)),product_Pair(U_302,U_300),U_293),U_291)),U_298))
| ~ hBOOL(hAPP(fun(product_prod(U_302,U_300),bool),bool,hAPP(product_prod(U_302,U_300),fun(fun(product_prod(U_302,U_300),bool),bool),member(product_prod(U_302,U_300)),hAPP(U_300,product_prod(U_302,U_300),hAPP(U_302,fun(U_300,product_prod(U_302,U_300)),product_Pair(U_302,U_300),U_293),U_291)),U_296))
| ti(fun(product_prod(U_302,U_300),bool),U_296) != ti(fun(product_prod(U_302,U_300),bool),U_298) ),
inference(clausify,[status(thm)],[f_98_7]) ).
cnf(f_98_13,plain,
( hBOOL(hAPP(fun(product_prod(U_302,U_300),bool),bool,hAPP(product_prod(U_302,U_300),fun(fun(product_prod(U_302,U_300),bool),bool),member(product_prod(U_302,U_300)),hAPP(U_300,product_prod(U_302,U_300),hAPP(U_302,fun(U_300,product_prod(U_302,U_300)),product_Pair(U_302,U_300),U_294),U_292)),U_296))
| ~ hBOOL(hAPP(fun(product_prod(U_302,U_300),bool),bool,hAPP(product_prod(U_302,U_300),fun(fun(product_prod(U_302,U_300),bool),bool),member(product_prod(U_302,U_300)),hAPP(U_300,product_prod(U_302,U_300),hAPP(U_302,fun(U_300,product_prod(U_302,U_300)),product_Pair(U_302,U_300),U_294),U_292)),U_298))
| ti(fun(product_prod(U_302,U_300),bool),U_296) != ti(fun(product_prod(U_302,U_300),bool),U_298) ),
inference(clausify,[status(thm)],[f_98_7]) ).
fof(f_99_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_55_less__top]) ).
fof(f_99_2,plain,
! [U_304] :
( ! [U_303] :
( ( ti(U_304,U_303) != top_top(U_304)
| ~ hBOOL(hAPP(U_304,bool,hAPP(U_304,fun(U_304,bool),ord_less(U_304),U_303),top_top(U_304))) )
& ( hBOOL(hAPP(U_304,bool,hAPP(U_304,fun(U_304,bool),ord_less(U_304),U_303),top_top(U_304)))
| ti(U_304,U_303) = top_top(U_304) ) )
| ~ top(U_304) ),
inference(variable_rename,[status(thm)],[f_99_1]) ).
fof(f_99_3,plain,
! [U_304] :
( ( ! [U_306] :
( ti(U_304,U_306) != top_top(U_304)
| ~ hBOOL(hAPP(U_304,bool,hAPP(U_304,fun(U_304,bool),ord_less(U_304),U_306),top_top(U_304))) )
& ! [U_305] :
( hBOOL(hAPP(U_304,bool,hAPP(U_304,fun(U_304,bool),ord_less(U_304),U_305),top_top(U_304)))
| ti(U_304,U_305) = top_top(U_304) ) )
| ~ top(U_304) ),
inference(miniscope,[status(thm)],[f_99_2]) ).
cnf(f_99_4,plain,
( hBOOL(hAPP(U_304,bool,hAPP(U_304,fun(U_304,bool),ord_less(U_304),U_305),top_top(U_304)))
| ti(U_304,U_305) = top_top(U_304)
| ~ top(U_304) ),
inference(clausify,[status(thm)],[f_99_3]) ).
cnf(f_99_5,plain,
( ti(U_304,U_306) != top_top(U_304)
| ~ hBOOL(hAPP(U_304,bool,hAPP(U_304,fun(U_304,bool),ord_less(U_304),U_306),top_top(U_304)))
| ~ top(U_304) ),
inference(clausify,[status(thm)],[f_99_3]) ).
fof(f_100_1,plain,
! [X_a,X_b,X_2,Y_1,F] :
( hAPP(X_b,X_a,hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),top_top(fun(X_a,bool))),F),Y_1) = ti(X_a,X_2)
| hAPP(X_a,X_b,F,X_2) != ti(X_b,Y_1)
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool)))) ),
inference(fof_nnf,[status(thm)],[fact_56_inv__f__eq]) ).
fof(f_100_2,plain,
! [U_311,U_310,U_309,U_308,U_307] :
( hAPP(U_310,U_311,hAPP(fun(U_311,U_310),fun(U_310,U_311),hAPP(fun(U_311,bool),fun(fun(U_311,U_310),fun(U_310,U_311)),hilbert_inv_into(U_311,U_310),top_top(fun(U_311,bool))),U_307),U_308) = ti(U_311,U_309)
| hAPP(U_311,U_310,U_307,U_309) != ti(U_310,U_308)
| ~ hBOOL(hAPP(fun(U_311,bool),bool,hAPP(fun(U_311,U_310),fun(fun(U_311,bool),bool),inj_on(U_311,U_310),U_307),top_top(fun(U_311,bool)))) ),
inference(variable_rename,[status(thm)],[f_100_1]) ).
cnf(f_100_3,plain,
( hAPP(U_310,U_311,hAPP(fun(U_311,U_310),fun(U_310,U_311),hAPP(fun(U_311,bool),fun(fun(U_311,U_310),fun(U_310,U_311)),hilbert_inv_into(U_311,U_310),top_top(fun(U_311,bool))),U_307),U_308) = ti(U_311,U_309)
| hAPP(U_311,U_310,U_307,U_309) != ti(U_310,U_308)
| ~ hBOOL(hAPP(fun(U_311,bool),bool,hAPP(fun(U_311,U_310),fun(fun(U_311,bool),bool),inj_on(U_311,U_310),U_307),top_top(fun(U_311,bool)))) ),
inference(clausify,[status(thm)],[f_100_2]) ).
fof(f_101_1,plain,
! [X_a,X_b,X_2,F] :
( hAPP(X_b,X_a,hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),top_top(fun(X_a,bool))),F),hAPP(X_a,X_b,F,X_2)) = ti(X_a,X_2)
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool)))) ),
inference(fof_nnf,[status(thm)],[fact_57_inv__f__f]) ).
fof(f_101_2,plain,
! [U_315,U_314,U_313,U_312] :
( hAPP(U_314,U_315,hAPP(fun(U_315,U_314),fun(U_314,U_315),hAPP(fun(U_315,bool),fun(fun(U_315,U_314),fun(U_314,U_315)),hilbert_inv_into(U_315,U_314),top_top(fun(U_315,bool))),U_312),hAPP(U_315,U_314,U_312,U_313)) = ti(U_315,U_313)
| ~ hBOOL(hAPP(fun(U_315,bool),bool,hAPP(fun(U_315,U_314),fun(fun(U_315,bool),bool),inj_on(U_315,U_314),U_312),top_top(fun(U_315,bool)))) ),
inference(variable_rename,[status(thm)],[f_101_1]) ).
cnf(f_101_3,plain,
( hAPP(U_314,U_315,hAPP(fun(U_315,U_314),fun(U_314,U_315),hAPP(fun(U_315,bool),fun(fun(U_315,U_314),fun(U_314,U_315)),hilbert_inv_into(U_315,U_314),top_top(fun(U_315,bool))),U_312),hAPP(U_315,U_314,U_312,U_313)) = ti(U_315,U_313)
| ~ hBOOL(hAPP(fun(U_315,bool),bool,hAPP(fun(U_315,U_314),fun(fun(U_315,bool),bool),inj_on(U_315,U_314),U_312),top_top(fun(U_315,bool)))) ),
inference(clausify,[status(thm)],[f_101_2]) ).
fof(f_102_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_58_inj__fun]) ).
fof(f_102_2,plain,
! [U_319,U_318,U_317,U_316] :
( hBOOL(hAPP(fun(U_318,bool),bool,hAPP(fun(U_318,fun(U_319,U_317)),fun(fun(U_318,bool),bool),inj_on(U_318,fun(U_319,U_317)),hAPP(fun(U_318,U_317),fun(U_318,fun(U_319,U_317)),hAPP(fun(U_317,fun(U_319,U_317)),fun(fun(U_318,U_317),fun(U_318,fun(U_319,U_317))),combb(U_317,fun(U_319,U_317),U_318),combk(U_317,U_319)),U_316)),top_top(fun(U_318,bool))))
| ~ hBOOL(hAPP(fun(U_318,bool),bool,hAPP(fun(U_318,U_317),fun(fun(U_318,bool),bool),inj_on(U_318,U_317),U_316),top_top(fun(U_318,bool)))) ),
inference(variable_rename,[status(thm)],[f_102_1]) ).
cnf(f_102_3,plain,
( hBOOL(hAPP(fun(U_318,bool),bool,hAPP(fun(U_318,fun(U_319,U_317)),fun(fun(U_318,bool),bool),inj_on(U_318,fun(U_319,U_317)),hAPP(fun(U_318,U_317),fun(U_318,fun(U_319,U_317)),hAPP(fun(U_317,fun(U_319,U_317)),fun(fun(U_318,U_317),fun(U_318,fun(U_319,U_317))),combb(U_317,fun(U_319,U_317),U_318),combk(U_317,U_319)),U_316)),top_top(fun(U_318,bool))))
| ~ hBOOL(hAPP(fun(U_318,bool),bool,hAPP(fun(U_318,U_317),fun(fun(U_318,bool),bool),inj_on(U_318,U_317),U_316),top_top(fun(U_318,bool)))) ),
inference(clausify,[status(thm)],[f_102_2]) ).
fof(f_103_1,plain,
! [X_a,X_b,X_2,F,A_1] :
( hAPP(X_b,X_a,hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),A_1),F),hAPP(X_a,X_b,F,X_2)) = ti(X_a,X_2)
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) ),
inference(fof_nnf,[status(thm)],[fact_59_inv__into__f__f]) ).
fof(f_103_2,plain,
! [U_324,U_323,U_322,U_321,U_320] :
( hAPP(U_323,U_324,hAPP(fun(U_324,U_323),fun(U_323,U_324),hAPP(fun(U_324,bool),fun(fun(U_324,U_323),fun(U_323,U_324)),hilbert_inv_into(U_324,U_323),U_320),U_321),hAPP(U_324,U_323,U_321,U_322)) = ti(U_324,U_322)
| ~ hBOOL(hAPP(fun(U_324,bool),bool,hAPP(U_324,fun(fun(U_324,bool),bool),member(U_324),U_322),U_320))
| ~ hBOOL(hAPP(fun(U_324,bool),bool,hAPP(fun(U_324,U_323),fun(fun(U_324,bool),bool),inj_on(U_324,U_323),U_321),U_320)) ),
inference(variable_rename,[status(thm)],[f_103_1]) ).
cnf(f_103_3,plain,
( hAPP(U_323,U_324,hAPP(fun(U_324,U_323),fun(U_323,U_324),hAPP(fun(U_324,bool),fun(fun(U_324,U_323),fun(U_323,U_324)),hilbert_inv_into(U_324,U_323),U_320),U_321),hAPP(U_324,U_323,U_321,U_322)) = ti(U_324,U_322)
| ~ hBOOL(hAPP(fun(U_324,bool),bool,hAPP(U_324,fun(fun(U_324,bool),bool),member(U_324),U_322),U_320))
| ~ hBOOL(hAPP(fun(U_324,bool),bool,hAPP(fun(U_324,U_323),fun(fun(U_324,bool),bool),inj_on(U_324,U_323),U_321),U_320)) ),
inference(clausify,[status(thm)],[f_103_2]) ).
fof(f_104_1,plain,
! [X_a,X_b,Y_1,X_2,F,A_1] :
( hAPP(X_b,X_a,hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),A_1),F),Y_1) = ti(X_a,X_2)
| hAPP(X_a,X_b,F,X_2) != ti(X_b,Y_1)
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) ),
inference(fof_nnf,[status(thm)],[fact_60_inv__into__f__eq]) ).
fof(f_104_2,plain,
! [U_330,U_329,U_328,U_327,U_326,U_325] :
( hAPP(U_329,U_330,hAPP(fun(U_330,U_329),fun(U_329,U_330),hAPP(fun(U_330,bool),fun(fun(U_330,U_329),fun(U_329,U_330)),hilbert_inv_into(U_330,U_329),U_325),U_326),U_328) = ti(U_330,U_327)
| hAPP(U_330,U_329,U_326,U_327) != ti(U_329,U_328)
| ~ hBOOL(hAPP(fun(U_330,bool),bool,hAPP(U_330,fun(fun(U_330,bool),bool),member(U_330),U_327),U_325))
| ~ hBOOL(hAPP(fun(U_330,bool),bool,hAPP(fun(U_330,U_329),fun(fun(U_330,bool),bool),inj_on(U_330,U_329),U_326),U_325)) ),
inference(variable_rename,[status(thm)],[f_104_1]) ).
cnf(f_104_3,plain,
( hAPP(U_329,U_330,hAPP(fun(U_330,U_329),fun(U_329,U_330),hAPP(fun(U_330,bool),fun(fun(U_330,U_329),fun(U_329,U_330)),hilbert_inv_into(U_330,U_329),U_325),U_326),U_328) = ti(U_330,U_327)
| hAPP(U_330,U_329,U_326,U_327) != ti(U_329,U_328)
| ~ hBOOL(hAPP(fun(U_330,bool),bool,hAPP(U_330,fun(fun(U_330,bool),bool),member(U_330),U_327),U_325))
| ~ hBOOL(hAPP(fun(U_330,bool),bool,hAPP(fun(U_330,U_329),fun(fun(U_330,bool),bool),inj_on(U_330,U_329),U_326),U_325)) ),
inference(clausify,[status(thm)],[f_104_2]) ).
fof(f_105_1,plain,
! [X_a,X_b,X_2,Y_1,F] :
( ( ( hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,F,Y_1)
| ti(X_a,X_2) != ti(X_a,Y_1) )
& ( ti(X_a,X_2) = ti(X_a,Y_1)
| hAPP(X_a,X_b,F,X_2) != hAPP(X_a,X_b,F,Y_1) ) )
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool)))) ),
inference(fof_nnf,[status(thm)],[fact_61_inj__eq]) ).
fof(f_105_2,plain,
! [U_335,U_334,U_333,U_332,U_331] :
( ( ( hAPP(U_335,U_334,U_331,U_333) = hAPP(U_335,U_334,U_331,U_332)
| ti(U_335,U_333) != ti(U_335,U_332) )
& ( ti(U_335,U_333) = ti(U_335,U_332)
| hAPP(U_335,U_334,U_331,U_333) != hAPP(U_335,U_334,U_331,U_332) ) )
| ~ hBOOL(hAPP(fun(U_335,bool),bool,hAPP(fun(U_335,U_334),fun(fun(U_335,bool),bool),inj_on(U_335,U_334),U_331),top_top(fun(U_335,bool)))) ),
inference(variable_rename,[status(thm)],[f_105_1]) ).
cnf(f_105_3,plain,
( ti(U_335,U_333) = ti(U_335,U_332)
| hAPP(U_335,U_334,U_331,U_333) != hAPP(U_335,U_334,U_331,U_332)
| ~ hBOOL(hAPP(fun(U_335,bool),bool,hAPP(fun(U_335,U_334),fun(fun(U_335,bool),bool),inj_on(U_335,U_334),U_331),top_top(fun(U_335,bool)))) ),
inference(clausify,[status(thm)],[f_105_2]) ).
cnf(f_105_4,plain,
( hAPP(U_335,U_334,U_331,U_333) = hAPP(U_335,U_334,U_331,U_332)
| ti(U_335,U_333) != ti(U_335,U_332)
| ~ hBOOL(hAPP(fun(U_335,bool),bool,hAPP(fun(U_335,U_334),fun(fun(U_335,bool),bool),inj_on(U_335,U_334),U_331),top_top(fun(U_335,bool)))) ),
inference(clausify,[status(thm)],[f_105_2]) ).
fof(f_106_1,plain,
! [X_a,X_b,F,A_1] :
( ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))
| ? [X_1] :
( ? [Xa] :
( ti(X_a,X_1) != ti(X_a,Xa)
& hAPP(X_a,X_b,F,X_1) = hAPP(X_a,X_b,F,Xa)
& hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),A_1)) )
& hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) ) )
& ( ! [X_1] :
( ! [Xa] :
( ti(X_a,X_1) = ti(X_a,Xa)
| hAPP(X_a,X_b,F,X_1) != hAPP(X_a,X_b,F,Xa)
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),A_1)) )
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) )
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) ) ),
inference(fof_nnf,[status(thm)],[fact_62_inj__on__def]) ).
fof(f_106_2,plain,
! [U_343,U_342,U_341,U_340] :
( ( hBOOL(hAPP(fun(U_343,bool),bool,hAPP(fun(U_343,U_342),fun(fun(U_343,bool),bool),inj_on(U_343,U_342),U_341),U_340))
| ? [U_339] :
( ? [U_338] :
( ti(U_343,U_339) != ti(U_343,U_338)
& hAPP(U_343,U_342,U_341,U_339) = hAPP(U_343,U_342,U_341,U_338)
& hBOOL(hAPP(fun(U_343,bool),bool,hAPP(U_343,fun(fun(U_343,bool),bool),member(U_343),U_338),U_340)) )
& hBOOL(hAPP(fun(U_343,bool),bool,hAPP(U_343,fun(fun(U_343,bool),bool),member(U_343),U_339),U_340)) ) )
& ( ! [U_337] :
( ! [U_336] :
( ti(U_343,U_337) = ti(U_343,U_336)
| hAPP(U_343,U_342,U_341,U_337) != hAPP(U_343,U_342,U_341,U_336)
| ~ hBOOL(hAPP(fun(U_343,bool),bool,hAPP(U_343,fun(fun(U_343,bool),bool),member(U_343),U_336),U_340)) )
| ~ hBOOL(hAPP(fun(U_343,bool),bool,hAPP(U_343,fun(fun(U_343,bool),bool),member(U_343),U_337),U_340)) )
| ~ hBOOL(hAPP(fun(U_343,bool),bool,hAPP(fun(U_343,U_342),fun(fun(U_343,bool),bool),inj_on(U_343,U_342),U_341),U_340)) ) ),
inference(variable_rename,[status(thm)],[f_106_1]) ).
fof(f_106_3,plain,
( ! [U_351,U_349,U_347,U_345] :
( hBOOL(hAPP(fun(U_351,bool),bool,hAPP(fun(U_351,U_349),fun(fun(U_351,bool),bool),inj_on(U_351,U_349),U_347),U_345))
| ? [U_339] :
( ? [U_338] :
( ti(U_351,U_339) != ti(U_351,U_338)
& hAPP(U_351,U_349,U_347,U_339) = hAPP(U_351,U_349,U_347,U_338)
& hBOOL(hAPP(fun(U_351,bool),bool,hAPP(U_351,fun(fun(U_351,bool),bool),member(U_351),U_338),U_345)) )
& hBOOL(hAPP(fun(U_351,bool),bool,hAPP(U_351,fun(fun(U_351,bool),bool),member(U_351),U_339),U_345)) ) )
& ! [U_350,U_348,U_346,U_344] :
( ! [U_337] :
( ! [U_336] :
( ti(U_350,U_337) = ti(U_350,U_336)
| hAPP(U_350,U_348,U_346,U_337) != hAPP(U_350,U_348,U_346,U_336)
| ~ hBOOL(hAPP(fun(U_350,bool),bool,hAPP(U_350,fun(fun(U_350,bool),bool),member(U_350),U_336),U_344)) )
| ~ hBOOL(hAPP(fun(U_350,bool),bool,hAPP(U_350,fun(fun(U_350,bool),bool),member(U_350),U_337),U_344)) )
| ~ hBOOL(hAPP(fun(U_350,bool),bool,hAPP(fun(U_350,U_348),fun(fun(U_350,bool),bool),inj_on(U_350,U_348),U_346),U_344)) ) ),
inference(miniscope,[status(thm)],[f_106_2]) ).
fof(f_106_4,plain,
( ! [U_351,U_349,U_347,U_345] :
( hBOOL(hAPP(fun(U_351,bool),bool,hAPP(fun(U_351,U_349),fun(fun(U_351,bool),bool),inj_on(U_351,U_349),U_347),U_345))
| ( ? [U_338] :
( ti(U_351,sK28(U_351,U_349,U_347,U_345)) != ti(U_351,U_338)
& hAPP(U_351,U_349,U_347,sK28(U_351,U_349,U_347,U_345)) = hAPP(U_351,U_349,U_347,U_338)
& hBOOL(hAPP(fun(U_351,bool),bool,hAPP(U_351,fun(fun(U_351,bool),bool),member(U_351),U_338),U_345)) )
& hBOOL(hAPP(fun(U_351,bool),bool,hAPP(U_351,fun(fun(U_351,bool),bool),member(U_351),sK28(U_351,U_349,U_347,U_345)),U_345)) ) )
& ! [U_350,U_348,U_346,U_344] :
( ! [U_337] :
( ! [U_336] :
( ti(U_350,U_337) = ti(U_350,U_336)
| hAPP(U_350,U_348,U_346,U_337) != hAPP(U_350,U_348,U_346,U_336)
| ~ hBOOL(hAPP(fun(U_350,bool),bool,hAPP(U_350,fun(fun(U_350,bool),bool),member(U_350),U_336),U_344)) )
| ~ hBOOL(hAPP(fun(U_350,bool),bool,hAPP(U_350,fun(fun(U_350,bool),bool),member(U_350),U_337),U_344)) )
| ~ hBOOL(hAPP(fun(U_350,bool),bool,hAPP(fun(U_350,U_348),fun(fun(U_350,bool),bool),inj_on(U_350,U_348),U_346),U_344)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_339,sK28(U_351,U_349,U_347,U_345))],[f_106_3]) ).
fof(f_106_5,plain,
( ! [U_351,U_349,U_347,U_345] :
( hBOOL(hAPP(fun(U_351,bool),bool,hAPP(fun(U_351,U_349),fun(fun(U_351,bool),bool),inj_on(U_351,U_349),U_347),U_345))
| ( ti(U_351,sK28(U_351,U_349,U_347,U_345)) != ti(U_351,sK29(U_351,U_349,U_347,U_345))
& hAPP(U_351,U_349,U_347,sK28(U_351,U_349,U_347,U_345)) = hAPP(U_351,U_349,U_347,sK29(U_351,U_349,U_347,U_345))
& hBOOL(hAPP(fun(U_351,bool),bool,hAPP(U_351,fun(fun(U_351,bool),bool),member(U_351),sK29(U_351,U_349,U_347,U_345)),U_345))
& hBOOL(hAPP(fun(U_351,bool),bool,hAPP(U_351,fun(fun(U_351,bool),bool),member(U_351),sK28(U_351,U_349,U_347,U_345)),U_345)) ) )
& ! [U_350,U_348,U_346,U_344] :
( ! [U_337] :
( ! [U_336] :
( ti(U_350,U_337) = ti(U_350,U_336)
| hAPP(U_350,U_348,U_346,U_337) != hAPP(U_350,U_348,U_346,U_336)
| ~ hBOOL(hAPP(fun(U_350,bool),bool,hAPP(U_350,fun(fun(U_350,bool),bool),member(U_350),U_336),U_344)) )
| ~ hBOOL(hAPP(fun(U_350,bool),bool,hAPP(U_350,fun(fun(U_350,bool),bool),member(U_350),U_337),U_344)) )
| ~ hBOOL(hAPP(fun(U_350,bool),bool,hAPP(fun(U_350,U_348),fun(fun(U_350,bool),bool),inj_on(U_350,U_348),U_346),U_344)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_338,sK29(U_351,U_349,U_347,U_345))],[f_106_4]) ).
cnf(f_106_6,plain,
( ti(U_350,U_337) = ti(U_350,U_336)
| hAPP(U_350,U_348,U_346,U_337) != hAPP(U_350,U_348,U_346,U_336)
| ~ hBOOL(hAPP(fun(U_350,bool),bool,hAPP(U_350,fun(fun(U_350,bool),bool),member(U_350),U_336),U_344))
| ~ hBOOL(hAPP(fun(U_350,bool),bool,hAPP(U_350,fun(fun(U_350,bool),bool),member(U_350),U_337),U_344))
| ~ hBOOL(hAPP(fun(U_350,bool),bool,hAPP(fun(U_350,U_348),fun(fun(U_350,bool),bool),inj_on(U_350,U_348),U_346),U_344)) ),
inference(clausify,[status(thm)],[f_106_5]) ).
cnf(f_106_7,plain,
( hBOOL(hAPP(fun(U_351,bool),bool,hAPP(U_351,fun(fun(U_351,bool),bool),member(U_351),sK28(U_351,U_349,U_347,U_345)),U_345))
| hBOOL(hAPP(fun(U_351,bool),bool,hAPP(fun(U_351,U_349),fun(fun(U_351,bool),bool),inj_on(U_351,U_349),U_347),U_345)) ),
inference(clausify,[status(thm)],[f_106_5]) ).
cnf(f_106_8,plain,
( hBOOL(hAPP(fun(U_351,bool),bool,hAPP(U_351,fun(fun(U_351,bool),bool),member(U_351),sK29(U_351,U_349,U_347,U_345)),U_345))
| hBOOL(hAPP(fun(U_351,bool),bool,hAPP(fun(U_351,U_349),fun(fun(U_351,bool),bool),inj_on(U_351,U_349),U_347),U_345)) ),
inference(clausify,[status(thm)],[f_106_5]) ).
cnf(f_106_9,plain,
( hAPP(U_351,U_349,U_347,sK28(U_351,U_349,U_347,U_345)) = hAPP(U_351,U_349,U_347,sK29(U_351,U_349,U_347,U_345))
| hBOOL(hAPP(fun(U_351,bool),bool,hAPP(fun(U_351,U_349),fun(fun(U_351,bool),bool),inj_on(U_351,U_349),U_347),U_345)) ),
inference(clausify,[status(thm)],[f_106_5]) ).
cnf(f_106_10,plain,
( ti(U_351,sK28(U_351,U_349,U_347,U_345)) != ti(U_351,sK29(U_351,U_349,U_347,U_345))
| hBOOL(hAPP(fun(U_351,bool),bool,hAPP(fun(U_351,U_349),fun(fun(U_351,bool),bool),inj_on(U_351,U_349),U_347),U_345)) ),
inference(clausify,[status(thm)],[f_106_5]) ).
fof(f_107_1,plain,
! [X_a,X_b,X_2,Y_1,F,A_1] :
( hAPP(X_a,X_b,F,X_2) != hAPP(X_a,X_b,F,Y_1)
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_1),A_1))
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
| ti(X_a,X_2) = ti(X_a,Y_1)
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) ),
inference(fof_nnf,[status(thm)],[fact_63_inj__on__contraD]) ).
fof(f_107_2,plain,
! [U_357,U_356,U_355,U_354,U_353,U_352] :
( hAPP(U_357,U_356,U_353,U_355) != hAPP(U_357,U_356,U_353,U_354)
| ~ hBOOL(hAPP(fun(U_357,bool),bool,hAPP(U_357,fun(fun(U_357,bool),bool),member(U_357),U_354),U_352))
| ~ hBOOL(hAPP(fun(U_357,bool),bool,hAPP(U_357,fun(fun(U_357,bool),bool),member(U_357),U_355),U_352))
| ti(U_357,U_355) = ti(U_357,U_354)
| ~ hBOOL(hAPP(fun(U_357,bool),bool,hAPP(fun(U_357,U_356),fun(fun(U_357,bool),bool),inj_on(U_357,U_356),U_353),U_352)) ),
inference(variable_rename,[status(thm)],[f_107_1]) ).
cnf(f_107_3,plain,
( hAPP(U_357,U_356,U_353,U_355) != hAPP(U_357,U_356,U_353,U_354)
| ~ hBOOL(hAPP(fun(U_357,bool),bool,hAPP(U_357,fun(fun(U_357,bool),bool),member(U_357),U_354),U_352))
| ~ hBOOL(hAPP(fun(U_357,bool),bool,hAPP(U_357,fun(fun(U_357,bool),bool),member(U_357),U_355),U_352))
| ti(U_357,U_355) = ti(U_357,U_354)
| ~ hBOOL(hAPP(fun(U_357,bool),bool,hAPP(fun(U_357,U_356),fun(fun(U_357,bool),bool),inj_on(U_357,U_356),U_353),U_352)) ),
inference(clausify,[status(thm)],[f_107_2]) ).
fof(f_108_1,plain,
! [X_a,X_b,Y_1,X_2,F,A_1] :
( ( ( hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,F,Y_1)
| ti(X_a,X_2) != ti(X_a,Y_1) )
& ( ti(X_a,X_2) = ti(X_a,Y_1)
| hAPP(X_a,X_b,F,X_2) != hAPP(X_a,X_b,F,Y_1) ) )
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_1),A_1))
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) ),
inference(fof_nnf,[status(thm)],[fact_64_inj__on__iff]) ).
fof(f_108_2,plain,
! [U_363,U_362,U_361,U_360,U_359,U_358] :
( ( ( hAPP(U_363,U_362,U_359,U_360) = hAPP(U_363,U_362,U_359,U_361)
| ti(U_363,U_360) != ti(U_363,U_361) )
& ( ti(U_363,U_360) = ti(U_363,U_361)
| hAPP(U_363,U_362,U_359,U_360) != hAPP(U_363,U_362,U_359,U_361) ) )
| ~ hBOOL(hAPP(fun(U_363,bool),bool,hAPP(U_363,fun(fun(U_363,bool),bool),member(U_363),U_361),U_358))
| ~ hBOOL(hAPP(fun(U_363,bool),bool,hAPP(U_363,fun(fun(U_363,bool),bool),member(U_363),U_360),U_358))
| ~ hBOOL(hAPP(fun(U_363,bool),bool,hAPP(fun(U_363,U_362),fun(fun(U_363,bool),bool),inj_on(U_363,U_362),U_359),U_358)) ),
inference(variable_rename,[status(thm)],[f_108_1]) ).
cnf(f_108_3,plain,
( ti(U_363,U_360) = ti(U_363,U_361)
| hAPP(U_363,U_362,U_359,U_360) != hAPP(U_363,U_362,U_359,U_361)
| ~ hBOOL(hAPP(fun(U_363,bool),bool,hAPP(U_363,fun(fun(U_363,bool),bool),member(U_363),U_361),U_358))
| ~ hBOOL(hAPP(fun(U_363,bool),bool,hAPP(U_363,fun(fun(U_363,bool),bool),member(U_363),U_360),U_358))
| ~ hBOOL(hAPP(fun(U_363,bool),bool,hAPP(fun(U_363,U_362),fun(fun(U_363,bool),bool),inj_on(U_363,U_362),U_359),U_358)) ),
inference(clausify,[status(thm)],[f_108_2]) ).
cnf(f_108_4,plain,
( hAPP(U_363,U_362,U_359,U_360) = hAPP(U_363,U_362,U_359,U_361)
| ti(U_363,U_360) != ti(U_363,U_361)
| ~ hBOOL(hAPP(fun(U_363,bool),bool,hAPP(U_363,fun(fun(U_363,bool),bool),member(U_363),U_361),U_358))
| ~ hBOOL(hAPP(fun(U_363,bool),bool,hAPP(U_363,fun(fun(U_363,bool),bool),member(U_363),U_360),U_358))
| ~ hBOOL(hAPP(fun(U_363,bool),bool,hAPP(fun(U_363,U_362),fun(fun(U_363,bool),bool),inj_on(U_363,U_362),U_359),U_358)) ),
inference(clausify,[status(thm)],[f_108_2]) ).
fof(f_109_1,plain,
! [X_a,X_b,X_2,Y_1,F,A_1] :
( ti(X_a,X_2) = ti(X_a,Y_1)
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_1),A_1))
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
| hAPP(X_a,X_b,F,X_2) != hAPP(X_a,X_b,F,Y_1)
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) ),
inference(fof_nnf,[status(thm)],[fact_65_inj__onD]) ).
fof(f_109_2,plain,
! [U_369,U_368,U_367,U_366,U_365,U_364] :
( ti(U_369,U_367) = ti(U_369,U_366)
| ~ hBOOL(hAPP(fun(U_369,bool),bool,hAPP(U_369,fun(fun(U_369,bool),bool),member(U_369),U_366),U_364))
| ~ hBOOL(hAPP(fun(U_369,bool),bool,hAPP(U_369,fun(fun(U_369,bool),bool),member(U_369),U_367),U_364))
| hAPP(U_369,U_368,U_365,U_367) != hAPP(U_369,U_368,U_365,U_366)
| ~ hBOOL(hAPP(fun(U_369,bool),bool,hAPP(fun(U_369,U_368),fun(fun(U_369,bool),bool),inj_on(U_369,U_368),U_365),U_364)) ),
inference(variable_rename,[status(thm)],[f_109_1]) ).
cnf(f_109_3,plain,
( ti(U_369,U_367) = ti(U_369,U_366)
| ~ hBOOL(hAPP(fun(U_369,bool),bool,hAPP(U_369,fun(fun(U_369,bool),bool),member(U_369),U_366),U_364))
| ~ hBOOL(hAPP(fun(U_369,bool),bool,hAPP(U_369,fun(fun(U_369,bool),bool),member(U_369),U_367),U_364))
| hAPP(U_369,U_368,U_365,U_367) != hAPP(U_369,U_368,U_365,U_366)
| ~ hBOOL(hAPP(fun(U_369,bool),bool,hAPP(fun(U_369,U_368),fun(fun(U_369,bool),bool),inj_on(U_369,U_368),U_365),U_364)) ),
inference(clausify,[status(thm)],[f_109_2]) ).
fof(f_110_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_66_inj__on__id2]) ).
fof(f_110_2,plain,
! [U_371,U_370] : hBOOL(hAPP(fun(U_371,bool),bool,hAPP(fun(U_371,U_371),fun(fun(U_371,bool),bool),inj_on(U_371,U_371),combi(U_371)),U_370)),
inference(variable_rename,[status(thm)],[f_110_1]) ).
cnf(f_110_3,plain,
hBOOL(hAPP(fun(U_371,bool),bool,hAPP(fun(U_371,U_371),fun(fun(U_371,bool),bool),inj_on(U_371,U_371),combi(U_371)),U_370)),
inference(clausify,[status(thm)],[f_110_2]) ).
fof(f_111_1,plain,
! [X_a,X_b,X_2,Y_1,F] :
( ti(X_a,X_2) = ti(X_a,Y_1)
| hAPP(X_a,X_b,F,X_2) != hAPP(X_a,X_b,F,Y_1)
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool)))) ),
inference(fof_nnf,[status(thm)],[fact_67_injD]) ).
fof(f_111_2,plain,
! [U_376,U_375,U_374,U_373,U_372] :
( ti(U_376,U_374) = ti(U_376,U_373)
| hAPP(U_376,U_375,U_372,U_374) != hAPP(U_376,U_375,U_372,U_373)
| ~ hBOOL(hAPP(fun(U_376,bool),bool,hAPP(fun(U_376,U_375),fun(fun(U_376,bool),bool),inj_on(U_376,U_375),U_372),top_top(fun(U_376,bool)))) ),
inference(variable_rename,[status(thm)],[f_111_1]) ).
cnf(f_111_3,plain,
( ti(U_376,U_374) = ti(U_376,U_373)
| hAPP(U_376,U_375,U_372,U_374) != hAPP(U_376,U_375,U_372,U_373)
| ~ hBOOL(hAPP(fun(U_376,bool),bool,hAPP(fun(U_376,U_375),fun(fun(U_376,bool),bool),inj_on(U_376,U_375),U_372),top_top(fun(U_376,bool)))) ),
inference(clausify,[status(thm)],[f_111_2]) ).
fof(f_112_1,plain,
! [X_a,X_b,G,F] :
( hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),top_top(fun(X_a,bool))),F) = ti(fun(X_b,X_a),G)
| ? [X_1] : hAPP(X_a,X_b,F,hAPP(X_b,X_a,G,X_1)) != ti(X_b,X_1)
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool)))) ),
inference(fof_nnf,[status(thm)],[fact_68_inj__imp__inv__eq]) ).
fof(f_112_2,plain,
! [U_381,U_380,U_379,U_378] :
( hAPP(fun(U_381,U_380),fun(U_380,U_381),hAPP(fun(U_381,bool),fun(fun(U_381,U_380),fun(U_380,U_381)),hilbert_inv_into(U_381,U_380),top_top(fun(U_381,bool))),U_378) = ti(fun(U_380,U_381),U_379)
| ? [U_377] : hAPP(U_381,U_380,U_378,hAPP(U_380,U_381,U_379,U_377)) != ti(U_380,U_377)
| ~ hBOOL(hAPP(fun(U_381,bool),bool,hAPP(fun(U_381,U_380),fun(fun(U_381,bool),bool),inj_on(U_381,U_380),U_378),top_top(fun(U_381,bool)))) ),
inference(variable_rename,[status(thm)],[f_112_1]) ).
fof(f_112_3,plain,
! [U_381,U_380,U_379,U_378] :
( hAPP(fun(U_381,U_380),fun(U_380,U_381),hAPP(fun(U_381,bool),fun(fun(U_381,U_380),fun(U_380,U_381)),hilbert_inv_into(U_381,U_380),top_top(fun(U_381,bool))),U_378) = ti(fun(U_380,U_381),U_379)
| hAPP(U_381,U_380,U_378,hAPP(U_380,U_381,U_379,sK30(U_381,U_380,U_379,U_378))) != ti(U_380,sK30(U_381,U_380,U_379,U_378))
| ~ hBOOL(hAPP(fun(U_381,bool),bool,hAPP(fun(U_381,U_380),fun(fun(U_381,bool),bool),inj_on(U_381,U_380),U_378),top_top(fun(U_381,bool)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_377,sK30(U_381,U_380,U_379,U_378))],[f_112_2]) ).
cnf(f_112_4,plain,
( hAPP(fun(U_381,U_380),fun(U_380,U_381),hAPP(fun(U_381,bool),fun(fun(U_381,U_380),fun(U_380,U_381)),hilbert_inv_into(U_381,U_380),top_top(fun(U_381,bool))),U_378) = ti(fun(U_380,U_381),U_379)
| hAPP(U_381,U_380,U_378,hAPP(U_380,U_381,U_379,sK30(U_381,U_380,U_379,U_378))) != ti(U_380,sK30(U_381,U_380,U_379,U_378))
| ~ hBOOL(hAPP(fun(U_381,bool),bool,hAPP(fun(U_381,U_380),fun(fun(U_381,bool),bool),inj_on(U_381,U_380),U_378),top_top(fun(U_381,bool)))) ),
inference(clausify,[status(thm)],[f_112_3]) ).
fof(f_113_1,plain,
! [X_a,X_b,F] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool))))
| ? [X_1,Y_2] :
( ti(X_a,X_1) != ti(X_a,Y_2)
& hAPP(X_a,X_b,F,X_1) = hAPP(X_a,X_b,F,Y_2) ) ),
inference(fof_nnf,[status(thm)],[fact_69_injI]) ).
fof(f_113_2,plain,
! [U_386,U_385,U_384] :
( hBOOL(hAPP(fun(U_386,bool),bool,hAPP(fun(U_386,U_385),fun(fun(U_386,bool),bool),inj_on(U_386,U_385),U_384),top_top(fun(U_386,bool))))
| ? [U_383,U_382] :
( ti(U_386,U_383) != ti(U_386,U_382)
& hAPP(U_386,U_385,U_384,U_383) = hAPP(U_386,U_385,U_384,U_382) ) ),
inference(variable_rename,[status(thm)],[f_113_1]) ).
fof(f_113_3,plain,
! [U_386,U_385,U_384] :
( hBOOL(hAPP(fun(U_386,bool),bool,hAPP(fun(U_386,U_385),fun(fun(U_386,bool),bool),inj_on(U_386,U_385),U_384),top_top(fun(U_386,bool))))
| ? [U_382] :
( ti(U_386,sK31(U_386,U_385,U_384)) != ti(U_386,U_382)
& hAPP(U_386,U_385,U_384,sK31(U_386,U_385,U_384)) = hAPP(U_386,U_385,U_384,U_382) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_383,sK31(U_386,U_385,U_384))],[f_113_2]) ).
fof(f_113_4,plain,
! [U_386,U_385,U_384] :
( hBOOL(hAPP(fun(U_386,bool),bool,hAPP(fun(U_386,U_385),fun(fun(U_386,bool),bool),inj_on(U_386,U_385),U_384),top_top(fun(U_386,bool))))
| ( ti(U_386,sK31(U_386,U_385,U_384)) != ti(U_386,sK32(U_386,U_385,U_384))
& hAPP(U_386,U_385,U_384,sK31(U_386,U_385,U_384)) = hAPP(U_386,U_385,U_384,sK32(U_386,U_385,U_384)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_382,sK32(U_386,U_385,U_384))],[f_113_3]) ).
cnf(f_113_5,plain,
( hAPP(U_386,U_385,U_384,sK31(U_386,U_385,U_384)) = hAPP(U_386,U_385,U_384,sK32(U_386,U_385,U_384))
| hBOOL(hAPP(fun(U_386,bool),bool,hAPP(fun(U_386,U_385),fun(fun(U_386,bool),bool),inj_on(U_386,U_385),U_384),top_top(fun(U_386,bool)))) ),
inference(clausify,[status(thm)],[f_113_4]) ).
cnf(f_113_6,plain,
( ti(U_386,sK31(U_386,U_385,U_384)) != ti(U_386,sK32(U_386,U_385,U_384))
| hBOOL(hAPP(fun(U_386,bool),bool,hAPP(fun(U_386,U_385),fun(fun(U_386,bool),bool),inj_on(U_386,U_385),U_384),top_top(fun(U_386,bool)))) ),
inference(clausify,[status(thm)],[f_113_4]) ).
fof(f_114_1,plain,
hBOOL(hAPP(fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),f),hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool)),pi(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1834574746e_Prof),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_638930832le_Lin)))),
inference(fof_nnf,[status(thm)],[fact_70_assms_I1_J]) ).
cnf(f_114_2,plain,
hBOOL(hAPP(fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),f),hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool)),pi(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1834574746e_Prof),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_638930832le_Lin)))),
inference(clausify,[status(thm)],[f_114_1]) ).
fof(f_115_1,plain,
hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),lba),arrow_638930832le_Lin)),
inference(fof_nnf,[status(thm)],[fact_71__096Lba_A_058_ALin_096]) ).
cnf(f_115_2,plain,
hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),lba),arrow_638930832le_Lin)),
inference(clausify,[status(thm)],[f_115_1]) ).
fof(f_116_1,plain,
hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),lab),arrow_638930832le_Lin)),
inference(fof_nnf,[status(thm)],[fact_72__096Lab_A_058_ALin_096]) ).
cnf(f_116_2,plain,
hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),lab),arrow_638930832le_Lin)),
inference(clausify,[status(thm)],[f_116_1]) ).
fof(f_117_1,plain,
! [Aa,Ba,L] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Ba),Aa)),L))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Ba)),L))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),L),arrow_638930832le_Lin)) ),
inference(fof_nnf,[status(thm)],[fact_73_Lin__irrefl]) ).
fof(f_117_2,plain,
! [U_389,U_388,U_387] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_388),U_389)),U_387))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_389),U_388)),U_387))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),U_387),arrow_638930832le_Lin)) ),
inference(variable_rename,[status(thm)],[f_117_1]) ).
cnf(f_117_3,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_388),U_389)),U_387))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_389),U_388)),U_387))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),U_387),arrow_638930832le_Lin)) ),
inference(clausify,[status(thm)],[f_117_2]) ).
fof(f_118_1,plain,
! [X_2,Y_1,L] :
( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),X_2),Y_1)),L))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Y_1),X_2)),L)) )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Y_1),X_2)),L))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),X_2),Y_1)),L)) ) )
| ti(arrow_1212486748le_alt,X_2) = ti(arrow_1212486748le_alt,Y_1)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),L),arrow_638930832le_Lin)) ),
inference(fof_nnf,[status(thm)],[fact_74_notin__Lin__iff]) ).
fof(f_118_2,plain,
! [U_392,U_391,U_390] :
( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_392),U_391)),U_390))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_391),U_392)),U_390)) )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_391),U_392)),U_390))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_392),U_391)),U_390)) ) )
| ti(arrow_1212486748le_alt,U_392) = ti(arrow_1212486748le_alt,U_391)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),U_390),arrow_638930832le_Lin)) ),
inference(variable_rename,[status(thm)],[f_118_1]) ).
cnf(f_118_3,plain,
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_391),U_392)),U_390))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_392),U_391)),U_390))
| ti(arrow_1212486748le_alt,U_392) = ti(arrow_1212486748le_alt,U_391)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),U_390),arrow_638930832le_Lin)) ),
inference(clausify,[status(thm)],[f_118_2]) ).
cnf(f_118_4,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_392),U_391)),U_390))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_391),U_392)),U_390))
| ti(arrow_1212486748le_alt,U_392) = ti(arrow_1212486748le_alt,U_391)
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),U_390),arrow_638930832le_Lin)) ),
inference(clausify,[status(thm)],[f_118_2]) ).
fof(f_119_1,plain,
! [X_a,X_b,F,G] :
( ti(fun(X_a,X_b),F) = ti(fun(X_a,X_b),G)
| ? [X_1] : hAPP(X_a,X_b,F,X_1) != hAPP(X_a,X_b,G,X_1) ),
inference(fof_nnf,[status(thm)],[fact_75_ext]) ).
fof(f_119_2,plain,
! [U_397,U_396,U_395,U_394] :
( ti(fun(U_397,U_396),U_395) = ti(fun(U_397,U_396),U_394)
| ? [U_393] : hAPP(U_397,U_396,U_395,U_393) != hAPP(U_397,U_396,U_394,U_393) ),
inference(variable_rename,[status(thm)],[f_119_1]) ).
fof(f_119_3,plain,
! [U_397,U_396,U_395,U_394] :
( ti(fun(U_397,U_396),U_395) = ti(fun(U_397,U_396),U_394)
| hAPP(U_397,U_396,U_395,sK33(U_397,U_396,U_395,U_394)) != hAPP(U_397,U_396,U_394,sK33(U_397,U_396,U_395,U_394)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_393,sK33(U_397,U_396,U_395,U_394))],[f_119_2]) ).
cnf(f_119_4,plain,
( ti(fun(U_397,U_396),U_395) = ti(fun(U_397,U_396),U_394)
| hAPP(U_397,U_396,U_395,sK33(U_397,U_396,U_395,U_394)) != hAPP(U_397,U_396,U_394,sK33(U_397,U_396,U_395,U_394)) ),
inference(clausify,[status(thm)],[f_119_3]) ).
fof(f_120_1,plain,
! [X_a,X_2,A_1] :
( ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
| ~ hBOOL(hAPP(X_a,bool,A_1,X_2)) )
& ( hBOOL(hAPP(X_a,bool,A_1,X_2))
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) ) ),
inference(fof_nnf,[status(thm)],[fact_76_mem__def]) ).
fof(f_120_2,plain,
! [U_400,U_399,U_398] :
( ( hBOOL(hAPP(fun(U_400,bool),bool,hAPP(U_400,fun(fun(U_400,bool),bool),member(U_400),U_399),U_398))
| ~ hBOOL(hAPP(U_400,bool,U_398,U_399)) )
& ( hBOOL(hAPP(U_400,bool,U_398,U_399))
| ~ hBOOL(hAPP(fun(U_400,bool),bool,hAPP(U_400,fun(fun(U_400,bool),bool),member(U_400),U_399),U_398)) ) ),
inference(variable_rename,[status(thm)],[f_120_1]) ).
fof(f_120_3,plain,
( ! [U_406,U_404,U_402] :
( hBOOL(hAPP(fun(U_406,bool),bool,hAPP(U_406,fun(fun(U_406,bool),bool),member(U_406),U_404),U_402))
| ~ hBOOL(hAPP(U_406,bool,U_402,U_404)) )
& ! [U_405,U_403,U_401] :
( hBOOL(hAPP(U_405,bool,U_401,U_403))
| ~ hBOOL(hAPP(fun(U_405,bool),bool,hAPP(U_405,fun(fun(U_405,bool),bool),member(U_405),U_403),U_401)) ) ),
inference(miniscope,[status(thm)],[f_120_2]) ).
cnf(f_120_4,plain,
( hBOOL(hAPP(U_405,bool,U_401,U_403))
| ~ hBOOL(hAPP(fun(U_405,bool),bool,hAPP(U_405,fun(fun(U_405,bool),bool),member(U_405),U_403),U_401)) ),
inference(clausify,[status(thm)],[f_120_3]) ).
cnf(f_120_5,plain,
( hBOOL(hAPP(fun(U_406,bool),bool,hAPP(U_406,fun(fun(U_406,bool),bool),member(U_406),U_404),U_402))
| ~ hBOOL(hAPP(U_406,bool,U_402,U_404)) ),
inference(clausify,[status(thm)],[f_120_3]) ).
fof(f_121_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_121_2,plain,
! [U_408,U_407] : hAPP(fun(U_408,bool),fun(U_408,bool),collect(U_408),U_407) = ti(fun(U_408,bool),U_407),
inference(variable_rename,[status(thm)],[f_121_1]) ).
cnf(f_121_3,plain,
hAPP(fun(U_408,bool),fun(U_408,bool),collect(U_408),U_407) = ti(fun(U_408,bool),U_407),
inference(clausify,[status(thm)],[f_121_2]) ).
fof(f_122_1,plain,
! [X_2,L] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,L),X_2)),arrow_638930832le_Lin))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),L),arrow_638930832le_Lin)) ),
inference(fof_nnf,[status(thm)],[fact_78_mktop__Lin]) ).
fof(f_122_2,plain,
! [U_410,U_409] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,U_409),U_410)),arrow_638930832le_Lin))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),U_409),arrow_638930832le_Lin)) ),
inference(variable_rename,[status(thm)],[f_122_1]) ).
cnf(f_122_3,plain,
( hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,U_409),U_410)),arrow_638930832le_Lin))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),U_409),arrow_638930832le_Lin)) ),
inference(clausify,[status(thm)],[f_122_2]) ).
fof(f_123_1,plain,
! [X_2,L] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,L),X_2)),arrow_638930832le_Lin))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),L),arrow_638930832le_Lin)) ),
inference(fof_nnf,[status(thm)],[fact_79_mkbot__Lin]) ).
fof(f_123_2,plain,
! [U_412,U_411] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,U_411),U_412)),arrow_638930832le_Lin))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),U_411),arrow_638930832le_Lin)) ),
inference(variable_rename,[status(thm)],[f_123_1]) ).
cnf(f_123_3,plain,
( hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,U_411),U_412)),arrow_638930832le_Lin))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),U_411),arrow_638930832le_Lin)) ),
inference(clausify,[status(thm)],[f_123_2]) ).
fof(f_124_1,plain,
! [L,X_2,Y_1] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,L),X_2),Y_1)),arrow_638930832le_Lin))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),L),arrow_638930832le_Lin))
| ti(arrow_1212486748le_alt,X_2) = ti(arrow_1212486748le_alt,Y_1) ),
inference(fof_nnf,[status(thm)],[fact_80_above__Lin]) ).
fof(f_124_2,plain,
! [U_415,U_414,U_413] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,U_415),U_414),U_413)),arrow_638930832le_Lin))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),U_415),arrow_638930832le_Lin))
| ti(arrow_1212486748le_alt,U_414) = ti(arrow_1212486748le_alt,U_413) ),
inference(variable_rename,[status(thm)],[f_124_1]) ).
cnf(f_124_3,plain,
( hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,U_415),U_414),U_413)),arrow_638930832le_Lin))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),U_415),arrow_638930832le_Lin))
| ti(arrow_1212486748le_alt,U_414) = ti(arrow_1212486748le_alt,U_413) ),
inference(clausify,[status(thm)],[f_124_2]) ).
fof(f_125_1,plain,
! [L] :
( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),combk(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),arrow_1384031255e_indi),L)),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),L),arrow_638930832le_Lin)) ),
inference(fof_nnf,[status(thm)],[fact_81_const__Lin__Prof]) ).
fof(f_125_2,plain,
! [U_416] :
( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),combk(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),arrow_1384031255e_indi),U_416)),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),U_416),arrow_638930832le_Lin)) ),
inference(variable_rename,[status(thm)],[f_125_1]) ).
cnf(f_125_3,plain,
( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),combk(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),arrow_1384031255e_indi),U_416)),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),U_416),arrow_638930832le_Lin)) ),
inference(clausify,[status(thm)],[f_125_2]) ).
fof(f_126_1,plain,
! [X_2,Y_1,L,Aa,Ba] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),X_2),Y_1)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,L),Aa),Ba)))
| ( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),X_2),Y_1)),L))
& ti(arrow_1212486748le_alt,Y_1) != ti(arrow_1212486748le_alt,Ba) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),X_2),Aa)),L))
& ti(arrow_1212486748le_alt,X_2) != ti(arrow_1212486748le_alt,Aa)
& ti(arrow_1212486748le_alt,Y_1) = ti(arrow_1212486748le_alt,Ba) ) )
& ti(arrow_1212486748le_alt,X_2) != ti(arrow_1212486748le_alt,Ba) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Y_1)),L))
& ti(arrow_1212486748le_alt,X_2) = ti(arrow_1212486748le_alt,Ba) )
| ti(arrow_1212486748le_alt,X_2) = ti(arrow_1212486748le_alt,Y_1) )
& ( ( ( ( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),X_2),Y_1)),L))
| ti(arrow_1212486748le_alt,Y_1) = ti(arrow_1212486748le_alt,Ba) )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),X_2),Aa)),L))
| ti(arrow_1212486748le_alt,X_2) = ti(arrow_1212486748le_alt,Aa)
| ti(arrow_1212486748le_alt,Y_1) != ti(arrow_1212486748le_alt,Ba) ) )
| ti(arrow_1212486748le_alt,X_2) = ti(arrow_1212486748le_alt,Ba) )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Y_1)),L))
| ti(arrow_1212486748le_alt,X_2) != ti(arrow_1212486748le_alt,Ba) )
& ti(arrow_1212486748le_alt,X_2) != ti(arrow_1212486748le_alt,Y_1) )
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),X_2),Y_1)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,L),Aa),Ba))) ) )
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),L),arrow_638930832le_Lin))
| ti(arrow_1212486748le_alt,Aa) = ti(arrow_1212486748le_alt,Ba) ),
inference(fof_nnf,[status(thm)],[fact_82_in__above]) ).
fof(f_126_2,plain,
! [U_421,U_420,U_419,U_418,U_417] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_421),U_420)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,U_419),U_418),U_417)))
| ( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_421),U_420)),U_419))
& ti(arrow_1212486748le_alt,U_420) != ti(arrow_1212486748le_alt,U_417) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_421),U_418)),U_419))
& ti(arrow_1212486748le_alt,U_421) != ti(arrow_1212486748le_alt,U_418)
& ti(arrow_1212486748le_alt,U_420) = ti(arrow_1212486748le_alt,U_417) ) )
& ti(arrow_1212486748le_alt,U_421) != ti(arrow_1212486748le_alt,U_417) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_418),U_420)),U_419))
& ti(arrow_1212486748le_alt,U_421) = ti(arrow_1212486748le_alt,U_417) )
| ti(arrow_1212486748le_alt,U_421) = ti(arrow_1212486748le_alt,U_420) )
& ( ( ( ( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_421),U_420)),U_419))
| ti(arrow_1212486748le_alt,U_420) = ti(arrow_1212486748le_alt,U_417) )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_421),U_418)),U_419))
| ti(arrow_1212486748le_alt,U_421) = ti(arrow_1212486748le_alt,U_418)
| ti(arrow_1212486748le_alt,U_420) != ti(arrow_1212486748le_alt,U_417) ) )
| ti(arrow_1212486748le_alt,U_421) = ti(arrow_1212486748le_alt,U_417) )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_418),U_420)),U_419))
| ti(arrow_1212486748le_alt,U_421) != ti(arrow_1212486748le_alt,U_417) )
& ti(arrow_1212486748le_alt,U_421) != ti(arrow_1212486748le_alt,U_420) )
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_421),U_420)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,U_419),U_418),U_417))) ) )
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),U_419),arrow_638930832le_Lin))
| ti(arrow_1212486748le_alt,U_418) = ti(arrow_1212486748le_alt,U_417) ),
inference(variable_rename,[status(thm)],[f_126_1]) ).
cnf(f_126_3,plain,
( ti(arrow_1212486748le_alt,U_421) != ti(arrow_1212486748le_alt,U_420)
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_421),U_420)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,U_419),U_418),U_417)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),U_419),arrow_638930832le_Lin))
| ti(arrow_1212486748le_alt,U_418) = ti(arrow_1212486748le_alt,U_417) ),
inference(clausify,[status(thm)],[f_126_2]) ).
cnf(f_126_4,plain,
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_418),U_420)),U_419))
| ti(arrow_1212486748le_alt,U_421) != ti(arrow_1212486748le_alt,U_417)
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_421),U_420)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,U_419),U_418),U_417)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),U_419),arrow_638930832le_Lin))
| ti(arrow_1212486748le_alt,U_418) = ti(arrow_1212486748le_alt,U_417) ),
inference(clausify,[status(thm)],[f_126_2]) ).
cnf(f_126_5,plain,
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_421),U_418)),U_419))
| ti(arrow_1212486748le_alt,U_421) = ti(arrow_1212486748le_alt,U_418)
| ti(arrow_1212486748le_alt,U_420) != ti(arrow_1212486748le_alt,U_417)
| ti(arrow_1212486748le_alt,U_421) = ti(arrow_1212486748le_alt,U_417)
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_421),U_420)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,U_419),U_418),U_417)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),U_419),arrow_638930832le_Lin))
| ti(arrow_1212486748le_alt,U_418) = ti(arrow_1212486748le_alt,U_417) ),
inference(clausify,[status(thm)],[f_126_2]) ).
cnf(f_126_6,plain,
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_421),U_420)),U_419))
| ti(arrow_1212486748le_alt,U_420) = ti(arrow_1212486748le_alt,U_417)
| ti(arrow_1212486748le_alt,U_421) = ti(arrow_1212486748le_alt,U_417)
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_421),U_420)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,U_419),U_418),U_417)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),U_419),arrow_638930832le_Lin))
| ti(arrow_1212486748le_alt,U_418) = ti(arrow_1212486748le_alt,U_417) ),
inference(clausify,[status(thm)],[f_126_2]) ).
cnf(f_126_7,plain,
( ti(arrow_1212486748le_alt,U_421) != ti(arrow_1212486748le_alt,U_417)
| ti(arrow_1212486748le_alt,U_421) = ti(arrow_1212486748le_alt,U_417)
| ti(arrow_1212486748le_alt,U_421) = ti(arrow_1212486748le_alt,U_420)
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_421),U_420)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,U_419),U_418),U_417)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),U_419),arrow_638930832le_Lin))
| ti(arrow_1212486748le_alt,U_418) = ti(arrow_1212486748le_alt,U_417) ),
inference(clausify,[status(thm)],[f_126_2]) ).
cnf(f_126_8,plain,
( ti(arrow_1212486748le_alt,U_420) != ti(arrow_1212486748le_alt,U_417)
| ti(arrow_1212486748le_alt,U_420) = ti(arrow_1212486748le_alt,U_417)
| ti(arrow_1212486748le_alt,U_421) = ti(arrow_1212486748le_alt,U_417)
| ti(arrow_1212486748le_alt,U_421) = ti(arrow_1212486748le_alt,U_420)
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_421),U_420)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,U_419),U_418),U_417)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),U_419),arrow_638930832le_Lin))
| ti(arrow_1212486748le_alt,U_418) = ti(arrow_1212486748le_alt,U_417) ),
inference(clausify,[status(thm)],[f_126_2]) ).
cnf(f_126_9,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_421),U_420)),U_419))
| ti(arrow_1212486748le_alt,U_420) = ti(arrow_1212486748le_alt,U_417)
| ti(arrow_1212486748le_alt,U_421) = ti(arrow_1212486748le_alt,U_417)
| ti(arrow_1212486748le_alt,U_421) = ti(arrow_1212486748le_alt,U_420)
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_421),U_420)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,U_419),U_418),U_417)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),U_419),arrow_638930832le_Lin))
| ti(arrow_1212486748le_alt,U_418) = ti(arrow_1212486748le_alt,U_417) ),
inference(clausify,[status(thm)],[f_126_2]) ).
cnf(f_126_10,plain,
( ti(arrow_1212486748le_alt,U_421) != ti(arrow_1212486748le_alt,U_418)
| ti(arrow_1212486748le_alt,U_420) != ti(arrow_1212486748le_alt,U_417)
| ti(arrow_1212486748le_alt,U_421) = ti(arrow_1212486748le_alt,U_417)
| ti(arrow_1212486748le_alt,U_421) = ti(arrow_1212486748le_alt,U_420)
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_421),U_420)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,U_419),U_418),U_417)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),U_419),arrow_638930832le_Lin))
| ti(arrow_1212486748le_alt,U_418) = ti(arrow_1212486748le_alt,U_417) ),
inference(clausify,[status(thm)],[f_126_2]) ).
cnf(f_126_11,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_421),U_418)),U_419))
| ti(arrow_1212486748le_alt,U_420) != ti(arrow_1212486748le_alt,U_417)
| ti(arrow_1212486748le_alt,U_421) = ti(arrow_1212486748le_alt,U_417)
| ti(arrow_1212486748le_alt,U_421) = ti(arrow_1212486748le_alt,U_420)
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_421),U_420)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,U_419),U_418),U_417)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),U_419),arrow_638930832le_Lin))
| ti(arrow_1212486748le_alt,U_418) = ti(arrow_1212486748le_alt,U_417) ),
inference(clausify,[status(thm)],[f_126_2]) ).
cnf(f_126_12,plain,
( ti(arrow_1212486748le_alt,U_421) != ti(arrow_1212486748le_alt,U_418)
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_421),U_420)),U_419))
| ti(arrow_1212486748le_alt,U_421) = ti(arrow_1212486748le_alt,U_417)
| ti(arrow_1212486748le_alt,U_421) = ti(arrow_1212486748le_alt,U_420)
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_421),U_420)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,U_419),U_418),U_417)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),U_419),arrow_638930832le_Lin))
| ti(arrow_1212486748le_alt,U_418) = ti(arrow_1212486748le_alt,U_417) ),
inference(clausify,[status(thm)],[f_126_2]) ).
cnf(f_126_13,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_421),U_418)),U_419))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_421),U_420)),U_419))
| ti(arrow_1212486748le_alt,U_421) = ti(arrow_1212486748le_alt,U_417)
| ti(arrow_1212486748le_alt,U_421) = ti(arrow_1212486748le_alt,U_420)
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_421),U_420)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,U_419),U_418),U_417)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),U_419),arrow_638930832le_Lin))
| ti(arrow_1212486748le_alt,U_418) = ti(arrow_1212486748le_alt,U_417) ),
inference(clausify,[status(thm)],[f_126_2]) ).
cnf(f_126_14,plain,
( ti(arrow_1212486748le_alt,U_421) != ti(arrow_1212486748le_alt,U_417)
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_418),U_420)),U_419))
| ti(arrow_1212486748le_alt,U_421) = ti(arrow_1212486748le_alt,U_420)
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_421),U_420)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,U_419),U_418),U_417)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),U_419),arrow_638930832le_Lin))
| ti(arrow_1212486748le_alt,U_418) = ti(arrow_1212486748le_alt,U_417) ),
inference(clausify,[status(thm)],[f_126_2]) ).
cnf(f_126_15,plain,
( ti(arrow_1212486748le_alt,U_420) != ti(arrow_1212486748le_alt,U_417)
| ti(arrow_1212486748le_alt,U_420) = ti(arrow_1212486748le_alt,U_417)
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_418),U_420)),U_419))
| ti(arrow_1212486748le_alt,U_421) = ti(arrow_1212486748le_alt,U_420)
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_421),U_420)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,U_419),U_418),U_417)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),U_419),arrow_638930832le_Lin))
| ti(arrow_1212486748le_alt,U_418) = ti(arrow_1212486748le_alt,U_417) ),
inference(clausify,[status(thm)],[f_126_2]) ).
cnf(f_126_16,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_421),U_420)),U_419))
| ti(arrow_1212486748le_alt,U_420) = ti(arrow_1212486748le_alt,U_417)
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_418),U_420)),U_419))
| ti(arrow_1212486748le_alt,U_421) = ti(arrow_1212486748le_alt,U_420)
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_421),U_420)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,U_419),U_418),U_417)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),U_419),arrow_638930832le_Lin))
| ti(arrow_1212486748le_alt,U_418) = ti(arrow_1212486748le_alt,U_417) ),
inference(clausify,[status(thm)],[f_126_2]) ).
cnf(f_126_17,plain,
( ti(arrow_1212486748le_alt,U_421) != ti(arrow_1212486748le_alt,U_418)
| ti(arrow_1212486748le_alt,U_420) != ti(arrow_1212486748le_alt,U_417)
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_418),U_420)),U_419))
| ti(arrow_1212486748le_alt,U_421) = ti(arrow_1212486748le_alt,U_420)
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_421),U_420)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,U_419),U_418),U_417)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),U_419),arrow_638930832le_Lin))
| ti(arrow_1212486748le_alt,U_418) = ti(arrow_1212486748le_alt,U_417) ),
inference(clausify,[status(thm)],[f_126_2]) ).
cnf(f_126_18,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_421),U_418)),U_419))
| ti(arrow_1212486748le_alt,U_420) != ti(arrow_1212486748le_alt,U_417)
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_418),U_420)),U_419))
| ti(arrow_1212486748le_alt,U_421) = ti(arrow_1212486748le_alt,U_420)
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_421),U_420)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,U_419),U_418),U_417)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),U_419),arrow_638930832le_Lin))
| ti(arrow_1212486748le_alt,U_418) = ti(arrow_1212486748le_alt,U_417) ),
inference(clausify,[status(thm)],[f_126_2]) ).
cnf(f_126_19,plain,
( ti(arrow_1212486748le_alt,U_421) != ti(arrow_1212486748le_alt,U_418)
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_421),U_420)),U_419))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_418),U_420)),U_419))
| ti(arrow_1212486748le_alt,U_421) = ti(arrow_1212486748le_alt,U_420)
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_421),U_420)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,U_419),U_418),U_417)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),U_419),arrow_638930832le_Lin))
| ti(arrow_1212486748le_alt,U_418) = ti(arrow_1212486748le_alt,U_417) ),
inference(clausify,[status(thm)],[f_126_2]) ).
cnf(f_126_20,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_421),U_418)),U_419))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_421),U_420)),U_419))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_418),U_420)),U_419))
| ti(arrow_1212486748le_alt,U_421) = ti(arrow_1212486748le_alt,U_420)
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_421),U_420)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,U_419),U_418),U_417)))
| ~ hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),U_419),arrow_638930832le_Lin))
| ti(arrow_1212486748le_alt,U_418) = ti(arrow_1212486748le_alt,U_417) ),
inference(clausify,[status(thm)],[f_126_2]) ).
fof(f_127_1,plain,
! [I_1,Fa] :
( hBOOL(hAPP(arrow_1384031255e_indi,bool,hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,bool),arrow_1990387629ctator,Fa),I_1))
| ? [X_1] :
( ? [A_2,B_1] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_2),B_1)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Fa,X_1)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_2),B_1)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),X_1,I_1)))
& ti(arrow_1212486748le_alt,A_2) != ti(arrow_1212486748le_alt,B_1) )
& hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),X_1),arrow_1834574746e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),Fa),hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool)),pi(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1834574746e_Prof),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_638930832le_Lin)))) ),
inference(fof_nnf,[status(thm)],[fact_83_dictatorI]) ).
fof(f_127_2,plain,
! [U_426,U_425] :
( hBOOL(hAPP(arrow_1384031255e_indi,bool,hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,bool),arrow_1990387629ctator,U_425),U_426))
| ? [U_424] :
( ? [U_423,U_422] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_423),U_422)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_425,U_424)))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_423),U_422)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_424,U_426)))
& ti(arrow_1212486748le_alt,U_423) != ti(arrow_1212486748le_alt,U_422) )
& hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_424),arrow_1834574746e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_425),hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool)),pi(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1834574746e_Prof),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_638930832le_Lin)))) ),
inference(variable_rename,[status(thm)],[f_127_1]) ).
fof(f_127_3,plain,
! [U_426,U_425] :
( hBOOL(hAPP(arrow_1384031255e_indi,bool,hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,bool),arrow_1990387629ctator,U_425),U_426))
| ( ? [U_423,U_422] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_423),U_422)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_425,sK34(U_426,U_425))))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_423),U_422)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),sK34(U_426,U_425),U_426)))
& ti(arrow_1212486748le_alt,U_423) != ti(arrow_1212486748le_alt,U_422) )
& hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),sK34(U_426,U_425)),arrow_1834574746e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_425),hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool)),pi(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1834574746e_Prof),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_638930832le_Lin)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_424,sK34(U_426,U_425))],[f_127_2]) ).
fof(f_127_4,plain,
! [U_426,U_425] :
( hBOOL(hAPP(arrow_1384031255e_indi,bool,hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,bool),arrow_1990387629ctator,U_425),U_426))
| ( ? [U_422] :
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),sK35(U_426,U_425)),U_422)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_425,sK34(U_426,U_425))))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),sK35(U_426,U_425)),U_422)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),sK34(U_426,U_425),U_426)))
& ti(arrow_1212486748le_alt,sK35(U_426,U_425)) != ti(arrow_1212486748le_alt,U_422) )
& hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),sK34(U_426,U_425)),arrow_1834574746e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_425),hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool)),pi(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1834574746e_Prof),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_638930832le_Lin)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_423,sK35(U_426,U_425))],[f_127_3]) ).
fof(f_127_5,plain,
! [U_426,U_425] :
( hBOOL(hAPP(arrow_1384031255e_indi,bool,hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,bool),arrow_1990387629ctator,U_425),U_426))
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),sK35(U_426,U_425)),sK36(U_426,U_425))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_425,sK34(U_426,U_425))))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),sK35(U_426,U_425)),sK36(U_426,U_425))),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),sK34(U_426,U_425),U_426)))
& ti(arrow_1212486748le_alt,sK35(U_426,U_425)) != ti(arrow_1212486748le_alt,sK36(U_426,U_425))
& hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),sK34(U_426,U_425)),arrow_1834574746e_Prof)) )
| ~ hBOOL(hAPP(fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_425),hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool)),pi(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1834574746e_Prof),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_638930832le_Lin)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_422,sK36(U_426,U_425))],[f_127_4]) ).
cnf(f_127_6,plain,
( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),sK34(U_426,U_425)),arrow_1834574746e_Prof))
| hBOOL(hAPP(arrow_1384031255e_indi,bool,hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,bool),arrow_1990387629ctator,U_425),U_426))
| ~ hBOOL(hAPP(fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_425),hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool)),pi(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1834574746e_Prof),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_638930832le_Lin)))) ),
inference(clausify,[status(thm)],[f_127_5]) ).
cnf(f_127_7,plain,
( ti(arrow_1212486748le_alt,sK35(U_426,U_425)) != ti(arrow_1212486748le_alt,sK36(U_426,U_425))
| hBOOL(hAPP(arrow_1384031255e_indi,bool,hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,bool),arrow_1990387629ctator,U_425),U_426))
| ~ hBOOL(hAPP(fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_425),hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool)),pi(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1834574746e_Prof),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_638930832le_Lin)))) ),
inference(clausify,[status(thm)],[f_127_5]) ).
cnf(f_127_8,plain,
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),sK35(U_426,U_425)),sK36(U_426,U_425))),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),sK34(U_426,U_425),U_426)))
| hBOOL(hAPP(arrow_1384031255e_indi,bool,hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,bool),arrow_1990387629ctator,U_425),U_426))
| ~ hBOOL(hAPP(fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_425),hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool)),pi(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1834574746e_Prof),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_638930832le_Lin)))) ),
inference(clausify,[status(thm)],[f_127_5]) ).
cnf(f_127_9,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),sK35(U_426,U_425)),sK36(U_426,U_425))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_425,sK34(U_426,U_425))))
| hBOOL(hAPP(arrow_1384031255e_indi,bool,hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,bool),arrow_1990387629ctator,U_425),U_426))
| ~ hBOOL(hAPP(fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_425),hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool)),pi(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1834574746e_Prof),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_638930832le_Lin)))) ),
inference(clausify,[status(thm)],[f_127_5]) ).
fof(f_128_1,plain,
! [X_a,X_b,X_2,F,A_1,B] :
( ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
| hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,fun(X_b,bool),B,X_2)))
| ~ hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B))) ),
inference(fof_nnf,[status(thm)],[fact_84_PiE]) ).
fof(f_128_2,plain,
! [U_432,U_431,U_430,U_429,U_428,U_427] :
( ~ hBOOL(hAPP(fun(U_432,bool),bool,hAPP(U_432,fun(fun(U_432,bool),bool),member(U_432),U_430),U_428))
| hBOOL(hAPP(fun(U_431,bool),bool,hAPP(U_431,fun(fun(U_431,bool),bool),member(U_431),hAPP(U_432,U_431,U_429,U_430)),hAPP(U_432,fun(U_431,bool),U_427,U_430)))
| ~ hBOOL(hAPP(fun(fun(U_432,U_431),bool),bool,hAPP(fun(U_432,U_431),fun(fun(fun(U_432,U_431),bool),bool),member(fun(U_432,U_431)),U_429),hAPP(fun(U_432,fun(U_431,bool)),fun(fun(U_432,U_431),bool),hAPP(fun(U_432,bool),fun(fun(U_432,fun(U_431,bool)),fun(fun(U_432,U_431),bool)),pi(U_432,U_431),U_428),U_427))) ),
inference(variable_rename,[status(thm)],[f_128_1]) ).
cnf(f_128_3,plain,
( ~ hBOOL(hAPP(fun(U_432,bool),bool,hAPP(U_432,fun(fun(U_432,bool),bool),member(U_432),U_430),U_428))
| hBOOL(hAPP(fun(U_431,bool),bool,hAPP(U_431,fun(fun(U_431,bool),bool),member(U_431),hAPP(U_432,U_431,U_429,U_430)),hAPP(U_432,fun(U_431,bool),U_427,U_430)))
| ~ hBOOL(hAPP(fun(fun(U_432,U_431),bool),bool,hAPP(fun(U_432,U_431),fun(fun(fun(U_432,U_431),bool),bool),member(fun(U_432,U_431)),U_429),hAPP(fun(U_432,fun(U_431,bool)),fun(fun(U_432,U_431),bool),hAPP(fun(U_432,bool),fun(fun(U_432,fun(U_431,bool)),fun(fun(U_432,U_431),bool)),pi(U_432,U_431),U_428),U_427))) ),
inference(clausify,[status(thm)],[f_128_2]) ).
fof(f_129_1,plain,
! [Aa,Ba] :
( ? [X_1] :
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Ba)),X_1))
& hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),X_1),arrow_638930832le_Lin)) )
| ti(arrow_1212486748le_alt,Aa) = ti(arrow_1212486748le_alt,Ba) ),
inference(fof_nnf,[status(thm)],[fact_85_complete__Lin]) ).
fof(f_129_2,plain,
! [U_435,U_434] :
( ? [U_433] :
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_435),U_434)),U_433))
& hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),U_433),arrow_638930832le_Lin)) )
| ti(arrow_1212486748le_alt,U_435) = ti(arrow_1212486748le_alt,U_434) ),
inference(variable_rename,[status(thm)],[f_129_1]) ).
fof(f_129_3,plain,
! [U_435,U_434] :
( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_435),U_434)),sK37(U_435,U_434)))
& hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),sK37(U_435,U_434)),arrow_638930832le_Lin)) )
| ti(arrow_1212486748le_alt,U_435) = ti(arrow_1212486748le_alt,U_434) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_433,sK37(U_435,U_434))],[f_129_2]) ).
cnf(f_129_4,plain,
( hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),sK37(U_435,U_434)),arrow_638930832le_Lin))
| ti(arrow_1212486748le_alt,U_435) = ti(arrow_1212486748le_alt,U_434) ),
inference(clausify,[status(thm)],[f_129_3]) ).
cnf(f_129_5,plain,
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),U_435),U_434)),sK37(U_435,U_434)))
| ti(arrow_1212486748le_alt,U_435) = ti(arrow_1212486748le_alt,U_434) ),
inference(clausify,[status(thm)],[f_129_3]) ).
fof(f_130_1,plain,
! [Na] : hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combc(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),ord_less(nat)),h)),Na))),lab)),lba)),arrow_1834574746e_Prof)),
inference(fof_nnf,[status(thm)],[fact_86_PiProf]) ).
fof(f_130_2,plain,
! [U_436] : hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combc(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),ord_less(nat)),h)),U_436))),lab)),lba)),arrow_1834574746e_Prof)),
inference(variable_rename,[status(thm)],[f_130_1]) ).
cnf(f_130_3,plain,
hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combc(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),ord_less(nat)),h)),U_436))),lab)),lba)),arrow_1834574746e_Prof)),
inference(clausify,[status(thm)],[f_130_2]) ).
fof(f_131_1,plain,
! [X_a,X_b,X_2,F,A_1,B] :
( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,fun(X_b,bool),B,X_2)))
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
| ~ hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B))) ),
inference(fof_nnf,[status(thm)],[fact_87_Pi__mem]) ).
fof(f_131_2,plain,
! [U_442,U_441,U_440,U_439,U_438,U_437] :
( hBOOL(hAPP(fun(U_441,bool),bool,hAPP(U_441,fun(fun(U_441,bool),bool),member(U_441),hAPP(U_442,U_441,U_439,U_440)),hAPP(U_442,fun(U_441,bool),U_437,U_440)))
| ~ hBOOL(hAPP(fun(U_442,bool),bool,hAPP(U_442,fun(fun(U_442,bool),bool),member(U_442),U_440),U_438))
| ~ hBOOL(hAPP(fun(fun(U_442,U_441),bool),bool,hAPP(fun(U_442,U_441),fun(fun(fun(U_442,U_441),bool),bool),member(fun(U_442,U_441)),U_439),hAPP(fun(U_442,fun(U_441,bool)),fun(fun(U_442,U_441),bool),hAPP(fun(U_442,bool),fun(fun(U_442,fun(U_441,bool)),fun(fun(U_442,U_441),bool)),pi(U_442,U_441),U_438),U_437))) ),
inference(variable_rename,[status(thm)],[f_131_1]) ).
cnf(f_131_3,plain,
( hBOOL(hAPP(fun(U_441,bool),bool,hAPP(U_441,fun(fun(U_441,bool),bool),member(U_441),hAPP(U_442,U_441,U_439,U_440)),hAPP(U_442,fun(U_441,bool),U_437,U_440)))
| ~ hBOOL(hAPP(fun(U_442,bool),bool,hAPP(U_442,fun(fun(U_442,bool),bool),member(U_442),U_440),U_438))
| ~ hBOOL(hAPP(fun(fun(U_442,U_441),bool),bool,hAPP(fun(U_442,U_441),fun(fun(fun(U_442,U_441),bool),bool),member(fun(U_442,U_441)),U_439),hAPP(fun(U_442,fun(U_441,bool)),fun(fun(U_442,U_441),bool),hAPP(fun(U_442,bool),fun(fun(U_442,fun(U_441,bool)),fun(fun(U_442,U_441),bool)),pi(U_442,U_441),U_438),U_437))) ),
inference(clausify,[status(thm)],[f_131_2]) ).
fof(f_132_1,plain,
arrow_1834574746e_Prof = hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),hAPP(fun(arrow_1384031255e_indi,bool),fun(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool)),pi(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),top_top(fun(arrow_1384031255e_indi,bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),arrow_1384031255e_indi),arrow_638930832le_Lin)),
inference(fof_nnf,[status(thm)],[fact_88_Prof__def]) ).
cnf(f_132_2,plain,
arrow_1834574746e_Prof = hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),hAPP(fun(arrow_1384031255e_indi,bool),fun(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool)),pi(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),top_top(fun(arrow_1384031255e_indi,bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),arrow_1384031255e_indi),arrow_638930832le_Lin)),
inference(clausify,[status(thm)],[f_132_1]) ).
fof(f_133_1,plain,
! [X_a,X_b,X_2,F,A_1,B] :
( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_2)),B))
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
| ~ hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),combk(fun(X_b,bool),X_a),B)))) ),
inference(fof_nnf,[status(thm)],[fact_89_funcset__mem]) ).
fof(f_133_2,plain,
! [U_448,U_447,U_446,U_445,U_444,U_443] :
( hBOOL(hAPP(fun(U_447,bool),bool,hAPP(U_447,fun(fun(U_447,bool),bool),member(U_447),hAPP(U_448,U_447,U_445,U_446)),U_443))
| ~ hBOOL(hAPP(fun(U_448,bool),bool,hAPP(U_448,fun(fun(U_448,bool),bool),member(U_448),U_446),U_444))
| ~ hBOOL(hAPP(fun(fun(U_448,U_447),bool),bool,hAPP(fun(U_448,U_447),fun(fun(fun(U_448,U_447),bool),bool),member(fun(U_448,U_447)),U_445),hAPP(fun(U_448,fun(U_447,bool)),fun(fun(U_448,U_447),bool),hAPP(fun(U_448,bool),fun(fun(U_448,fun(U_447,bool)),fun(fun(U_448,U_447),bool)),pi(U_448,U_447),U_444),hAPP(fun(U_447,bool),fun(U_448,fun(U_447,bool)),combk(fun(U_447,bool),U_448),U_443)))) ),
inference(variable_rename,[status(thm)],[f_133_1]) ).
cnf(f_133_3,plain,
( hBOOL(hAPP(fun(U_447,bool),bool,hAPP(U_447,fun(fun(U_447,bool),bool),member(U_447),hAPP(U_448,U_447,U_445,U_446)),U_443))
| ~ hBOOL(hAPP(fun(U_448,bool),bool,hAPP(U_448,fun(fun(U_448,bool),bool),member(U_448),U_446),U_444))
| ~ hBOOL(hAPP(fun(fun(U_448,U_447),bool),bool,hAPP(fun(U_448,U_447),fun(fun(fun(U_448,U_447),bool),bool),member(fun(U_448,U_447)),U_445),hAPP(fun(U_448,fun(U_447,bool)),fun(fun(U_448,U_447),bool),hAPP(fun(U_448,bool),fun(fun(U_448,fun(U_447,bool)),fun(fun(U_448,U_447),bool)),pi(U_448,U_447),U_444),hAPP(fun(U_447,bool),fun(U_448,fun(U_447,bool)),combk(fun(U_447,bool),U_448),U_443)))) ),
inference(clausify,[status(thm)],[f_133_2]) ).
fof(f_134_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_90_funcset__id]) ).
fof(f_134_2,plain,
! [U_450,U_449] : hBOOL(hAPP(fun(fun(U_450,U_450),bool),bool,hAPP(fun(U_450,U_450),fun(fun(fun(U_450,U_450),bool),bool),member(fun(U_450,U_450)),combi(U_450)),hAPP(fun(U_450,fun(U_450,bool)),fun(fun(U_450,U_450),bool),hAPP(fun(U_450,bool),fun(fun(U_450,fun(U_450,bool)),fun(fun(U_450,U_450),bool)),pi(U_450,U_450),U_449),hAPP(fun(U_450,bool),fun(U_450,fun(U_450,bool)),combk(fun(U_450,bool),U_450),U_449)))),
inference(variable_rename,[status(thm)],[f_134_1]) ).
cnf(f_134_3,plain,
hBOOL(hAPP(fun(fun(U_450,U_450),bool),bool,hAPP(fun(U_450,U_450),fun(fun(fun(U_450,U_450),bool),bool),member(fun(U_450,U_450)),combi(U_450)),hAPP(fun(U_450,fun(U_450,bool)),fun(fun(U_450,U_450),bool),hAPP(fun(U_450,bool),fun(fun(U_450,fun(U_450,bool)),fun(fun(U_450,U_450),bool)),pi(U_450,U_450),U_449),hAPP(fun(U_450,bool),fun(U_450,fun(U_450,bool)),combk(fun(U_450,bool),U_450),U_449)))),
inference(clausify,[status(thm)],[f_134_2]) ).
fof(f_135_1,plain,
! [Fa,I_1] :
( ( hBOOL(hAPP(arrow_1384031255e_indi,bool,hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,bool),arrow_1990387629ctator,Fa),I_1))
| ? [X_1] :
( hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Fa,X_1) != hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),X_1,I_1)
& hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),X_1),arrow_1834574746e_Prof)) ) )
& ( ! [X_1] :
( hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Fa,X_1) = hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),X_1,I_1)
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),X_1),arrow_1834574746e_Prof)) )
| ~ hBOOL(hAPP(arrow_1384031255e_indi,bool,hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,bool),arrow_1990387629ctator,Fa),I_1)) ) ),
inference(fof_nnf,[status(thm)],[fact_91_dictator__def]) ).
fof(f_135_2,plain,
! [U_454,U_453] :
( ( hBOOL(hAPP(arrow_1384031255e_indi,bool,hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,bool),arrow_1990387629ctator,U_454),U_453))
| ? [U_452] :
( hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_454,U_452) != hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_452,U_453)
& hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_452),arrow_1834574746e_Prof)) ) )
& ( ! [U_451] :
( hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_454,U_451) = hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_451,U_453)
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_451),arrow_1834574746e_Prof)) )
| ~ hBOOL(hAPP(arrow_1384031255e_indi,bool,hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,bool),arrow_1990387629ctator,U_454),U_453)) ) ),
inference(variable_rename,[status(thm)],[f_135_1]) ).
fof(f_135_3,plain,
( ! [U_458,U_456] :
( hBOOL(hAPP(arrow_1384031255e_indi,bool,hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,bool),arrow_1990387629ctator,U_458),U_456))
| ? [U_452] :
( hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_458,U_452) != hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_452,U_456)
& hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_452),arrow_1834574746e_Prof)) ) )
& ! [U_457,U_455] :
( ! [U_451] :
( hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_457,U_451) = hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_451,U_455)
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_451),arrow_1834574746e_Prof)) )
| ~ hBOOL(hAPP(arrow_1384031255e_indi,bool,hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,bool),arrow_1990387629ctator,U_457),U_455)) ) ),
inference(miniscope,[status(thm)],[f_135_2]) ).
fof(f_135_4,plain,
( ! [U_458,U_456] :
( hBOOL(hAPP(arrow_1384031255e_indi,bool,hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,bool),arrow_1990387629ctator,U_458),U_456))
| ( hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_458,sK38(U_458,U_456)) != hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),sK38(U_458,U_456),U_456)
& hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),sK38(U_458,U_456)),arrow_1834574746e_Prof)) ) )
& ! [U_457,U_455] :
( ! [U_451] :
( hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_457,U_451) = hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_451,U_455)
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_451),arrow_1834574746e_Prof)) )
| ~ hBOOL(hAPP(arrow_1384031255e_indi,bool,hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,bool),arrow_1990387629ctator,U_457),U_455)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_452,sK38(U_458,U_456))],[f_135_3]) ).
cnf(f_135_5,plain,
( hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_457,U_451) = hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_451,U_455)
| ~ hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),U_451),arrow_1834574746e_Prof))
| ~ hBOOL(hAPP(arrow_1384031255e_indi,bool,hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,bool),arrow_1990387629ctator,U_457),U_455)) ),
inference(clausify,[status(thm)],[f_135_4]) ).
cnf(f_135_6,plain,
( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),sK38(U_458,U_456)),arrow_1834574746e_Prof))
| hBOOL(hAPP(arrow_1384031255e_indi,bool,hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,bool),arrow_1990387629ctator,U_458),U_456)) ),
inference(clausify,[status(thm)],[f_135_4]) ).
cnf(f_135_7,plain,
( hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),U_458,sK38(U_458,U_456)) != hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),sK38(U_458,U_456),U_456)
| hBOOL(hAPP(arrow_1384031255e_indi,bool,hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,bool),arrow_1990387629ctator,U_458),U_456)) ),
inference(clausify,[status(thm)],[f_135_4]) ).
fof(f_136_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_92_Pi__UNIV]) ).
fof(f_136_2,plain,
! [U_461,U_460,U_459] : hAPP(fun(U_461,fun(U_460,bool)),fun(fun(U_461,U_460),bool),hAPP(fun(U_461,bool),fun(fun(U_461,fun(U_460,bool)),fun(fun(U_461,U_460),bool)),pi(U_461,U_460),U_459),hAPP(fun(U_460,bool),fun(U_461,fun(U_460,bool)),combk(fun(U_460,bool),U_461),top_top(fun(U_460,bool)))) = top_top(fun(fun(U_461,U_460),bool)),
inference(variable_rename,[status(thm)],[f_136_1]) ).
cnf(f_136_3,plain,
hAPP(fun(U_461,fun(U_460,bool)),fun(fun(U_461,U_460),bool),hAPP(fun(U_461,bool),fun(fun(U_461,fun(U_460,bool)),fun(fun(U_461,U_460),bool)),pi(U_461,U_460),U_459),hAPP(fun(U_460,bool),fun(U_461,fun(U_460,bool)),combk(fun(U_460,bool),U_461),top_top(fun(U_460,bool)))) = top_top(fun(fun(U_461,U_460),bool)),
inference(clausify,[status(thm)],[f_136_2]) ).
fof(f_137_1,plain,
( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),ord_less(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1384031255e_indi),arrow_992993526_mktop),p)),e))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),fequal(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),arrow_1726925404_above),p)),c)),e))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1384031255e_indi),arrow_844286440_mkbot),p)),e))))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combc(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),ord_less(nat)),h)),n))),lab)),lba)))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combc(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),ord_less(nat)),h)),n))),lab)),lba))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),ord_less(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1384031255e_indi),arrow_992993526_mktop),p)),e))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),fequal(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),arrow_1726925404_above),p)),c)),e))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1384031255e_indi),arrow_844286440_mkbot),p)),e)))))) ) ),
inference(fof_nnf,[status(thm)],[fact_93__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amk]) ).
cnf(f_137_2,plain,
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combc(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),ord_less(nat)),h)),n))),lab)),lba))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),ord_less(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1384031255e_indi),arrow_992993526_mktop),p)),e))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),fequal(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),arrow_1726925404_above),p)),c)),e))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1384031255e_indi),arrow_844286440_mkbot),p)),e)))))) ),
inference(clausify,[status(thm)],[f_137_1]) ).
cnf(f_137_3,plain,
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),ord_less(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1384031255e_indi),arrow_992993526_mktop),p)),e))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),fequal(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),arrow_1726925404_above),p)),c)),e))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1384031255e_indi),arrow_844286440_mkbot),p)),e))))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combc(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),ord_less(nat)),h)),n))),lab)),lba)))) ),
inference(clausify,[status(thm)],[f_137_1]) ).
fof(f_138_1,plain,
! [I] :
( ( ( ( ( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,I)),e)))
| hAPP(arrow_1384031255e_indi,nat,h,I) = n )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,I)),c),e)))
| hAPP(arrow_1384031255e_indi,nat,h,I) != n ) )
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,I)),n)) )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,I)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,I)),n)) ) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lba))
& ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,I)),n)) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lab))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,I)),n)) ) )
& ( ( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,I)),n)) )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,I)),n)) ) )
| ( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,I)),e)))
& hAPP(arrow_1384031255e_indi,nat,h,I) != n )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,I)),c),e)))
& hAPP(arrow_1384031255e_indi,nat,h,I) = n ) )
& ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,I)),n)) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,I)),e)))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,I)),n)) ) ) ),
inference(fof_nnf,[status(thm)],[fact_94__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk]) ).
fof(f_138_2,plain,
! [U_462] :
( ( ( ( ( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_462)),e)))
| hAPP(arrow_1384031255e_indi,nat,h,U_462) = n )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_462)),c),e)))
| hAPP(arrow_1384031255e_indi,nat,h,U_462) != n ) )
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_462)),n)) )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_462)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_462)),n)) ) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lba))
& ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_462)),n)) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lab))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_462)),n)) ) )
& ( ( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_462)),n)) )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_462)),n)) ) )
| ( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_462)),e)))
& hAPP(arrow_1384031255e_indi,nat,h,U_462) != n )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_462)),c),e)))
& hAPP(arrow_1384031255e_indi,nat,h,U_462) = n ) )
& ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_462)),n)) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_462)),e)))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_462)),n)) ) ) ),
inference(variable_rename,[status(thm)],[f_138_1]) ).
fof(f_138_3,plain,
( ! [U_464] :
( ( ( ( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_464)),e)))
| hAPP(arrow_1384031255e_indi,nat,h,U_464) = n )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_464)),c),e)))
| hAPP(arrow_1384031255e_indi,nat,h,U_464) != n ) )
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_464)),n)) )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_464)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_464)),n)) ) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lba))
& ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_464)),n)) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lab))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_464)),n)) ) )
& ! [U_463] :
( ( ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_463)),n)) )
& ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_463)),n)) ) )
| ( ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_463)),e)))
& hAPP(arrow_1384031255e_indi,nat,h,U_463) != n )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_463)),c),e)))
& hAPP(arrow_1384031255e_indi,nat,h,U_463) = n ) )
& ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_463)),n)) )
| ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_463)),e)))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_463)),n)) ) ) ),
inference(miniscope,[status(thm)],[f_138_2]) ).
cnf(f_138_4,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_463)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_463)),n))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_463)),n)) ),
inference(clausify,[status(thm)],[f_138_3]) ).
cnf(f_138_5,plain,
( hAPP(arrow_1384031255e_indi,nat,h,U_463) != n
| hAPP(arrow_1384031255e_indi,nat,h,U_463) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_463)),n))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_463)),n)) ),
inference(clausify,[status(thm)],[f_138_3]) ).
cnf(f_138_6,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_463)),e)))
| hAPP(arrow_1384031255e_indi,nat,h,U_463) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_463)),n))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_463)),n)) ),
inference(clausify,[status(thm)],[f_138_3]) ).
cnf(f_138_7,plain,
( hAPP(arrow_1384031255e_indi,nat,h,U_463) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_463)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_463)),n))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_463)),n)) ),
inference(clausify,[status(thm)],[f_138_3]) ).
cnf(f_138_8,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_463)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_463)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_463)),n))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_463)),n)) ),
inference(clausify,[status(thm)],[f_138_3]) ).
cnf(f_138_9,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_463)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_463)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_463)),n)) ),
inference(clausify,[status(thm)],[f_138_3]) ).
cnf(f_138_10,plain,
( hAPP(arrow_1384031255e_indi,nat,h,U_463) != n
| hAPP(arrow_1384031255e_indi,nat,h,U_463) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_463)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_463)),n)) ),
inference(clausify,[status(thm)],[f_138_3]) ).
cnf(f_138_11,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_463)),e)))
| hAPP(arrow_1384031255e_indi,nat,h,U_463) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_463)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_463)),n)) ),
inference(clausify,[status(thm)],[f_138_3]) ).
cnf(f_138_12,plain,
( hAPP(arrow_1384031255e_indi,nat,h,U_463) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_463)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_463)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_463)),n)) ),
inference(clausify,[status(thm)],[f_138_3]) ).
cnf(f_138_13,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_463)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_463)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_463)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lab))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_463)),n)) ),
inference(clausify,[status(thm)],[f_138_3]) ).
cnf(f_138_14,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_463)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_463)),n))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_463)),n)) ),
inference(clausify,[status(thm)],[f_138_3]) ).
cnf(f_138_15,plain,
( hAPP(arrow_1384031255e_indi,nat,h,U_463) != n
| hAPP(arrow_1384031255e_indi,nat,h,U_463) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_463)),n))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_463)),n)) ),
inference(clausify,[status(thm)],[f_138_3]) ).
cnf(f_138_16,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_463)),e)))
| hAPP(arrow_1384031255e_indi,nat,h,U_463) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_463)),n))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_463)),n)) ),
inference(clausify,[status(thm)],[f_138_3]) ).
cnf(f_138_17,plain,
( hAPP(arrow_1384031255e_indi,nat,h,U_463) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_463)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_463)),n))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_463)),n)) ),
inference(clausify,[status(thm)],[f_138_3]) ).
cnf(f_138_18,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_463)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_463)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_463)),n))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_463)),n)) ),
inference(clausify,[status(thm)],[f_138_3]) ).
cnf(f_138_19,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_463)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_463)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_463)),n)) ),
inference(clausify,[status(thm)],[f_138_3]) ).
cnf(f_138_20,plain,
( hAPP(arrow_1384031255e_indi,nat,h,U_463) != n
| hAPP(arrow_1384031255e_indi,nat,h,U_463) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_463)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_463)),n)) ),
inference(clausify,[status(thm)],[f_138_3]) ).
cnf(f_138_21,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_463)),e)))
| hAPP(arrow_1384031255e_indi,nat,h,U_463) = n
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_463)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_463)),n)) ),
inference(clausify,[status(thm)],[f_138_3]) ).
cnf(f_138_22,plain,
( hAPP(arrow_1384031255e_indi,nat,h,U_463) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_463)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_463)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_463)),n)) ),
inference(clausify,[status(thm)],[f_138_3]) ).
cnf(f_138_23,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_463)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_463)),c),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_463)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_463)),n)) ),
inference(clausify,[status(thm)],[f_138_3]) ).
cnf(f_138_24,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_464)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_464)),n))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_464)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_464)),n)) ),
inference(clausify,[status(thm)],[f_138_3]) ).
cnf(f_138_25,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_464)),n))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_464)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_464)),n)) ),
inference(clausify,[status(thm)],[f_138_3]) ).
cnf(f_138_26,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_464)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lab))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_464)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_464)),n)) ),
inference(clausify,[status(thm)],[f_138_3]) ).
cnf(f_138_27,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lba))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lab))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_464)),e)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_464)),n)) ),
inference(clausify,[status(thm)],[f_138_3]) ).
cnf(f_138_28,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_464)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_464)),n))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_464)),c),e)))
| hAPP(arrow_1384031255e_indi,nat,h,U_464) != n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_464)),n)) ),
inference(clausify,[status(thm)],[f_138_3]) ).
cnf(f_138_29,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_464)),n))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_464)),c),e)))
| hAPP(arrow_1384031255e_indi,nat,h,U_464) != n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_464)),n)) ),
inference(clausify,[status(thm)],[f_138_3]) ).
cnf(f_138_30,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_464)),n))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_464)),n))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_464)),e)))
| hAPP(arrow_1384031255e_indi,nat,h,U_464) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_464)),n)) ),
inference(clausify,[status(thm)],[f_138_3]) ).
cnf(f_138_31,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_464)),n))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_464)),e)))
| hAPP(arrow_1384031255e_indi,nat,h,U_464) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_464)),n)) ),
inference(clausify,[status(thm)],[f_138_3]) ).
cnf(f_138_32,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_464)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lab))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_464)),c),e)))
| hAPP(arrow_1384031255e_indi,nat,h,U_464) != n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_464)),n)) ),
inference(clausify,[status(thm)],[f_138_3]) ).
cnf(f_138_33,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lba))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lab))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_464)),c),e)))
| hAPP(arrow_1384031255e_indi,nat,h,U_464) != n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_464)),n)) ),
inference(clausify,[status(thm)],[f_138_3]) ).
cnf(f_138_34,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_464)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lab))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_464)),e)))
| hAPP(arrow_1384031255e_indi,nat,h,U_464) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_464)),n)) ),
inference(clausify,[status(thm)],[f_138_3]) ).
cnf(f_138_35,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lba))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lab))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_464)),e)))
| hAPP(arrow_1384031255e_indi,nat,h,U_464) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_464)),n)) ),
inference(clausify,[status(thm)],[f_138_3]) ).
fof(f_139_1,plain,
a != b,
inference(fof_nnf,[status(thm)],[fact_95__096a_A_126_061_Ab_096]) ).
cnf(f_139_2,plain,
a != b,
inference(clausify,[status(thm)],[f_139_1]) ).
fof(f_140_1,plain,
hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lba)),
inference(fof_nnf,[status(thm)],[fact_96__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096]) ).
cnf(f_140_2,plain,
hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lba)),
inference(clausify,[status(thm)],[f_140_1]) ).
fof(f_141_1,plain,
hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),a),b)),lab)),
inference(fof_nnf,[status(thm)],[fact_97__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096]) ).
cnf(f_141_2,plain,
hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),a),b)),lab)),
inference(clausify,[status(thm)],[f_141_1]) ).
fof(f_142_1,plain,
~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),a),b)),lba)),
inference(fof_nnf,[status(thm)],[fact_98__096_Ia_M_Ab_J_A_126_058_ALba_096]) ).
cnf(f_142_2,plain,
~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),a),b)),lba)),
inference(clausify,[status(thm)],[f_142_1]) ).
fof(f_143_1,plain,
~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lab)),
inference(fof_nnf,[status(thm)],[fact_99__096_Ib_M_Aa_J_A_126_058_ALab_096]) ).
cnf(f_143_2,plain,
~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lab)),
inference(clausify,[status(thm)],[f_143_1]) ).
fof(f_144_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_144_2,plain,
! [U_466,U_465] :
( preorder(fun(U_466,U_465))
| ~ preorder(U_465) ),
inference(variable_rename,[status(thm)],[f_144_1]) ).
cnf(f_144_3,plain,
( preorder(fun(U_466,U_465))
| ~ preorder(U_465) ),
inference(clausify,[status(thm)],[f_144_2]) ).
fof(f_145_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_145_2,plain,
! [U_468,U_467] :
( order(fun(U_468,U_467))
| ~ order(U_467) ),
inference(variable_rename,[status(thm)],[f_145_1]) ).
cnf(f_145_3,plain,
( order(fun(U_468,U_467))
| ~ order(U_467) ),
inference(clausify,[status(thm)],[f_145_2]) ).
fof(f_146_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_146_2,plain,
! [U_470,U_469] :
( top(fun(U_470,U_469))
| ~ top(U_469) ),
inference(variable_rename,[status(thm)],[f_146_1]) ).
cnf(f_146_3,plain,
( top(fun(U_470,U_469))
| ~ top(U_469) ),
inference(clausify,[status(thm)],[f_146_2]) ).
fof(f_147_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_147_2,plain,
! [U_472,U_471] :
( ord(fun(U_472,U_471))
| ~ ord(U_471) ),
inference(variable_rename,[status(thm)],[f_147_1]) ).
cnf(f_147_3,plain,
( ord(fun(U_472,U_471))
| ~ ord(U_471) ),
inference(clausify,[status(thm)],[f_147_2]) ).
fof(f_148_1,plain,
preorder(nat),
inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Orderings_Opreorder]) ).
cnf(f_148_2,plain,
preorder(nat),
inference(clausify,[status(thm)],[f_148_1]) ).
fof(f_149_1,plain,
linorder(nat),
inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Orderings_Olinorder]) ).
cnf(f_149_2,plain,
linorder(nat),
inference(clausify,[status(thm)],[f_149_1]) ).
fof(f_150_1,plain,
order(nat),
inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Orderings_Oorder]) ).
cnf(f_150_2,plain,
order(nat),
inference(clausify,[status(thm)],[f_150_1]) ).
fof(f_151_1,plain,
ord(nat),
inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Orderings_Oord]) ).
cnf(f_151_2,plain,
ord(nat),
inference(clausify,[status(thm)],[f_151_1]) ).
fof(f_152_1,plain,
preorder(bool),
inference(fof_nnf,[status(thm)],[arity_HOL_Obool___Orderings_Opreorder]) ).
cnf(f_152_2,plain,
preorder(bool),
inference(clausify,[status(thm)],[f_152_1]) ).
fof(f_153_1,plain,
order(bool),
inference(fof_nnf,[status(thm)],[arity_HOL_Obool___Orderings_Oorder]) ).
cnf(f_153_2,plain,
order(bool),
inference(clausify,[status(thm)],[f_153_1]) ).
fof(f_154_1,plain,
top(bool),
inference(fof_nnf,[status(thm)],[arity_HOL_Obool___Orderings_Otop]) ).
cnf(f_154_2,plain,
top(bool),
inference(clausify,[status(thm)],[f_154_1]) ).
fof(f_155_1,plain,
ord(bool),
inference(fof_nnf,[status(thm)],[arity_HOL_Obool___Orderings_Oord]) ).
cnf(f_155_2,plain,
ord(bool),
inference(clausify,[status(thm)],[f_155_1]) ).
fof(f_156_1,plain,
! [T,A] : ti(T,ti(T,A)) = ti(T,A),
inference(fof_nnf,[status(thm)],[help_ti_idem]) ).
fof(f_156_2,plain,
! [U_474,U_473] : ti(U_474,ti(U_474,U_473)) = ti(U_474,U_473),
inference(variable_rename,[status(thm)],[f_156_1]) ).
cnf(f_156_3,plain,
ti(U_474,ti(U_474,U_473)) = ti(U_474,U_473),
inference(clausify,[status(thm)],[f_156_2]) ).
fof(f_157_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_157_2,plain,
! [U_477,U_476,U_475] : hAPP(U_477,U_477,hAPP(U_477,fun(U_477,U_477),hAPP(bool,fun(U_477,fun(U_477,U_477)),if(U_477),fTrue),U_476),U_475) = ti(U_477,U_476),
inference(variable_rename,[status(thm)],[f_157_1]) ).
cnf(f_157_3,plain,
hAPP(U_477,U_477,hAPP(U_477,fun(U_477,U_477),hAPP(bool,fun(U_477,fun(U_477,U_477)),if(U_477),fTrue),U_476),U_475) = ti(U_477,U_476),
inference(clausify,[status(thm)],[f_157_2]) ).
fof(f_158_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_158_2,plain,
! [U_480,U_479,U_478] : hAPP(U_480,U_480,hAPP(U_480,fun(U_480,U_480),hAPP(bool,fun(U_480,fun(U_480,U_480)),if(U_480),fFalse),U_479),U_478) = ti(U_480,U_478),
inference(variable_rename,[status(thm)],[f_158_1]) ).
cnf(f_158_3,plain,
hAPP(U_480,U_480,hAPP(U_480,fun(U_480,U_480),hAPP(bool,fun(U_480,fun(U_480,U_480)),if(U_480),fFalse),U_479),U_478) = ti(U_480,U_478),
inference(clausify,[status(thm)],[f_158_2]) ).
fof(f_159_1,plain,
! [P] :
( ti(bool,P) = fFalse
| ti(bool,P) = fTrue ),
inference(fof_nnf,[status(thm)],[help_If_3_1_T]) ).
fof(f_159_2,plain,
! [U_481] :
( ti(bool,U_481) = fFalse
| ti(bool,U_481) = fTrue ),
inference(variable_rename,[status(thm)],[f_159_1]) ).
cnf(f_159_3,plain,
( ti(bool,U_481) = fFalse
| ti(bool,U_481) = fTrue ),
inference(clausify,[status(thm)],[f_159_2]) ).
fof(f_160_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_160_2,plain,
! [U_487,U_486,U_485,U_484,U_483,U_482] : hAPP(U_487,U_486,hAPP(fun(U_487,U_485),fun(U_487,U_486),hAPP(fun(U_485,U_486),fun(fun(U_487,U_485),fun(U_487,U_486)),combb(U_485,U_486,U_487),U_484),U_483),U_482) = hAPP(U_485,U_486,U_484,hAPP(U_487,U_485,U_483,U_482)),
inference(variable_rename,[status(thm)],[f_160_1]) ).
cnf(f_160_3,plain,
hAPP(U_487,U_486,hAPP(fun(U_487,U_485),fun(U_487,U_486),hAPP(fun(U_485,U_486),fun(fun(U_487,U_485),fun(U_487,U_486)),combb(U_485,U_486,U_487),U_484),U_483),U_482) = hAPP(U_485,U_486,U_484,hAPP(U_487,U_485,U_483,U_482)),
inference(clausify,[status(thm)],[f_160_2]) ).
fof(f_161_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_161_2,plain,
! [U_493,U_492,U_491,U_490,U_489,U_488] : hAPP(U_493,U_492,hAPP(U_491,fun(U_493,U_492),hAPP(fun(U_493,fun(U_491,U_492)),fun(U_491,fun(U_493,U_492)),combc(U_493,U_491,U_492),U_490),U_489),U_488) = hAPP(U_491,U_492,hAPP(U_493,fun(U_491,U_492),U_490,U_488),U_489),
inference(variable_rename,[status(thm)],[f_161_1]) ).
cnf(f_161_3,plain,
hAPP(U_493,U_492,hAPP(U_491,fun(U_493,U_492),hAPP(fun(U_493,fun(U_491,U_492)),fun(U_491,fun(U_493,U_492)),combc(U_493,U_491,U_492),U_490),U_489),U_488) = hAPP(U_491,U_492,hAPP(U_493,fun(U_491,U_492),U_490,U_488),U_489),
inference(clausify,[status(thm)],[f_161_2]) ).
fof(f_162_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_162_2,plain,
! [U_495,U_494] : hAPP(U_495,U_495,combi(U_495),U_494) = ti(U_495,U_494),
inference(variable_rename,[status(thm)],[f_162_1]) ).
cnf(f_162_3,plain,
hAPP(U_495,U_495,combi(U_495),U_494) = ti(U_495,U_494),
inference(clausify,[status(thm)],[f_162_2]) ).
fof(f_163_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_163_2,plain,
! [U_499,U_498,U_497,U_496] : hAPP(U_499,U_498,hAPP(U_498,fun(U_499,U_498),combk(U_498,U_499),U_497),U_496) = ti(U_498,U_497),
inference(variable_rename,[status(thm)],[f_163_1]) ).
cnf(f_163_3,plain,
hAPP(U_499,U_498,hAPP(U_498,fun(U_499,U_498),combk(U_498,U_499),U_497),U_496) = ti(U_498,U_497),
inference(clausify,[status(thm)],[f_163_2]) ).
fof(f_164_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_164_2,plain,
! [U_505,U_504,U_503,U_502,U_501,U_500] : hAPP(U_505,U_504,hAPP(fun(U_505,U_503),fun(U_505,U_504),hAPP(fun(U_505,fun(U_503,U_504)),fun(fun(U_505,U_503),fun(U_505,U_504)),combs(U_505,U_503,U_504),U_502),U_501),U_500) = hAPP(U_503,U_504,hAPP(U_505,fun(U_503,U_504),U_502,U_500),hAPP(U_505,U_503,U_501,U_500)),
inference(variable_rename,[status(thm)],[f_164_1]) ).
cnf(f_164_3,plain,
hAPP(U_505,U_504,hAPP(fun(U_505,U_503),fun(U_505,U_504),hAPP(fun(U_505,fun(U_503,U_504)),fun(fun(U_505,U_503),fun(U_505,U_504)),combs(U_505,U_503,U_504),U_502),U_501),U_500) = hAPP(U_503,U_504,hAPP(U_505,fun(U_503,U_504),U_502,U_500),hAPP(U_505,U_503,U_501,U_500)),
inference(clausify,[status(thm)],[f_164_2]) ).
fof(f_165_1,plain,
hBOOL(fTrue),
inference(fof_nnf,[status(thm)],[help_fTrue_1_1_U]) ).
cnf(f_165_2,plain,
hBOOL(fTrue),
inference(clausify,[status(thm)],[f_165_1]) ).
fof(f_166_1,plain,
! [P] :
( ti(bool,P) = fFalse
| ti(bool,P) = fTrue ),
inference(fof_nnf,[status(thm)],[help_fTrue_1_1_T]) ).
fof(f_166_2,plain,
! [U_506] :
( ti(bool,U_506) = fFalse
| ti(bool,U_506) = fTrue ),
inference(variable_rename,[status(thm)],[f_166_1]) ).
cnf(f_166_3,plain,
( ti(bool,U_506) = fFalse
| ti(bool,U_506) = fTrue ),
inference(clausify,[status(thm)],[f_166_2]) ).
fof(f_167_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_167_2,plain,
! [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),fequal(U_509),U_508),U_507)) ),
inference(variable_rename,[status(thm)],[f_167_1]) ).
cnf(f_167_3,plain,
( ti(U_509,U_508) = ti(U_509,U_507)
| ~ hBOOL(hAPP(U_509,bool,hAPP(U_509,fun(U_509,bool),fequal(U_509),U_508),U_507)) ),
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),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_168_2,plain,
! [U_512,U_511,U_510] :
( hBOOL(hAPP(U_512,bool,hAPP(U_512,fun(U_512,bool),fequal(U_512),U_511),U_510))
| ti(U_512,U_511) != ti(U_512,U_510) ),
inference(variable_rename,[status(thm)],[f_168_1]) ).
cnf(f_168_3,plain,
( hBOOL(hAPP(U_512,bool,hAPP(U_512,fun(U_512,bool),fequal(U_512),U_511),U_510))
| ti(U_512,U_511) != ti(U_512,U_510) ),
inference(clausify,[status(thm)],[f_168_2]) ).
fof(f_169_1,negated_conjecture,
~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,p))),
inference(negate,[status(cth)],[conj_0]) ).
fof(f_169_2,negated_conjecture,
~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,p))),
inference(definitional_conversion,[status(esa)],[f_169_1]) ).
cnf(f_169_3,negated_conjecture,
~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),c),d)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,p))),
inference(clausify,[status(thm)],[f_169_2]) ).
cnf(f_48_7_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_48_7]) ).
cnf(f_49_7_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_49_7]) ).
cnf(f_55_7_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_55_7]) ).
cnf(f_55_8_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_55_8]) ).
cnf(f_55_13_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_55_13]) ).
cnf(f_67_23_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_67_23]) ).
cnf(f_67_24_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_67_24]) ).
cnf(f_126_7_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_126_7]) ).
cnf(f_126_8_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_126_8]) ).
cnf(f_126_15_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_126_15]) ).
cnf(f_138_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_138_4]) ).
cnf(f_138_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_138_5]) ).
cnf(f_138_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_138_6]) ).
cnf(f_138_7_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_138_7]) ).
cnf(f_138_8_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_138_8]) ).
cnf(f_138_9_simplified,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_463)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_463)),e)))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lab)) ),
inference(simplify_clause,[status(thm)],[f_138_9]) ).
cnf(f_138_10_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_138_10]) ).
cnf(f_138_14_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_138_14]) ).
cnf(f_138_15_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_138_15]) ).
cnf(f_138_16_simplified,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_463)),e)))
| hAPP(arrow_1384031255e_indi,nat,h,U_463) = n
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_463)),n))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lba)) ),
inference(simplify_clause,[status(thm)],[f_138_16]) ).
cnf(f_138_17_simplified,plain,
( hAPP(arrow_1384031255e_indi,nat,h,U_463) != n
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_463)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_463)),n))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lba)) ),
inference(simplify_clause,[status(thm)],[f_138_17]) ).
cnf(f_138_18_simplified,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_463)),e)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_463)),c),e)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_463)),n))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lba)) ),
inference(simplify_clause,[status(thm)],[f_138_18]) ).
cnf(f_138_19_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_138_19]) ).
cnf(f_138_20_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_138_20]) ).
cnf(f_138_24_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_138_24]) ).
cnf(f_138_25_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_138_25]) ).
cnf(f_138_26_simplified,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_464)),n))
| ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lab))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_464)),e))) ),
inference(simplify_clause,[status(thm)],[f_138_26]) ).
cnf(f_138_28_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_138_28]) ).
cnf(f_138_29_simplified,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_464)),n))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_464)),c),e)))
| hAPP(arrow_1384031255e_indi,nat,h,U_464) != n ),
inference(simplify_clause,[status(thm)],[f_138_29]) ).
cnf(f_138_30_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_138_30]) ).
cnf(f_138_31_simplified,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),lba))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,U_464)),n))
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),e),d)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,U_464)),e)))
| hAPP(arrow_1384031255e_indi,nat,h,U_464) = n ),
inference(simplify_clause,[status(thm)],[f_138_31]) ).
cnf(f_138_32_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_138_32]) ).
cnf(f_138_34_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_138_34]) ).
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,
( 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_14,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_15,axiom,
( undefined(Eq_x_0) = undefined(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,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_17,axiom,
( if(Eq_x_0) = if(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( ord_less(Eq_x_0) = ord_less(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,axiom,
( top_top(Eq_x_0) = top_top(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,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_21,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_22,axiom,
( collect(Eq_x_0) = collect(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_23,axiom,
( fequal(Eq_x_0) = fequal(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_24,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_25,axiom,
( member(Eq_x_0) = member(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_26,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_27,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_28,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_29,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_30,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_31,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_32,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_33,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_34,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_35,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_36,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_37,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_38,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_39,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_40,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_41,axiom,
( sK16(Eq_x_0) = sK16(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_42,axiom,
( sK17(Eq_x_0) = sK17(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_43,axiom,
( sK18(Eq_x_0) = sK18(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_44,axiom,
( sK19(Eq_x_0) = sK19(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_45,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_46,axiom,
( sK21(Eq_x_0) = sK21(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_47,axiom,
( sK22(Eq_x_0) = sK22(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_48,axiom,
( sK23(Eq_x_0) = sK23(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_49,axiom,
( sK24(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK24(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| 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,
( sK25(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK25(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| 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,
( 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_52,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_53,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_54,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_55,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_56,axiom,
( sK31(Eq_x_0,Eq_x_1,Eq_x_2) = sK31(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_57,axiom,
( sK32(Eq_x_0,Eq_x_1,Eq_x_2) = sK32(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_58,axiom,
( sK33(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK33(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_59,axiom,
( 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_60,axiom,
( sK35(Eq_x_0,Eq_x_1) = sK35(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_61,axiom,
( sK36(Eq_x_0,Eq_x_1) = sK36(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_62,axiom,
( sK37(Eq_x_0,Eq_x_1) = sK37(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_63,axiom,
( sK38(Eq_x_0,Eq_x_1) = sK38(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_64,axiom,
( ord(Eq_y_0)
| ~ ord(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_65,axiom,
( top(Eq_y_0)
| ~ top(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_66,axiom,
( hBOOL(Eq_y_0)
| ~ hBOOL(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_67,axiom,
( linorder(Eq_y_0)
| ~ linorder(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_68,axiom,
( preorder(Eq_y_0)
| ~ preorder(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_69,axiom,
( order(Eq_y_0)
| ~ order(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT171+5 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n020.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 19 21:25:16 UTC 2026
% 0.09/0.35 % CPUTime :
% 1.15/1.45 % SZS status Theorem for theBenchmark
% 1.15/1.45 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------