%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SCT171+7 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 02:08:03 PM UTC 2026
% Result : Theorem 6.97s 1.50s
% Output : CNFRefutation 6.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 9 unt; 0 def)
% Number of atoms : 17 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 13 ( 8 ~; 3 |; 1 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 19 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 25 ( 25 usr; 14 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conj_0,conjecture,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,p))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(fact_14_PW,axiom,
( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,p)))
<=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_PW) ).
fof(fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,axiom,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) ).
fof(c_0_3,negated_conjecture,
~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,p))),
inference(assume_negation,[status(cth)],[conj_0]) ).
fof(c_0_4,negated_conjecture,
~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,p))),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_5,plain,
( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,p)))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))))) )
& ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e))))))
| ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,p))) ) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_14_PW])]) ).
fof(c_0_6,negated_conjecture,
~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,p))),
inference(fof_nnf,[status(thm)],[c_0_4]) ).
cnf(c_0_7,plain,
( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e))))))
| hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,p))) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,negated_conjecture,
~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,p))),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))))),
inference(split_conjunct,[status(thm)],[fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto]) ).
cnf(c_0_10,plain,
~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))))),
inference(sr,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,plain,
$false,
inference(sr,[status(thm)],[c_0_9,c_0_10]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT171+7 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n001.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 04:43:44 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.97/1.50 % Version: 3.5.1
% 6.97/1.50 % Preprocessing class: FMLMSMSMSSSNFFN.
% 6.97/1.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.97/1.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 6.97/1.50 % Starting new_bool_3 with 300s (1) cores
% 6.97/1.50 % Starting new_bool_1 with 300s (1) cores
% 6.97/1.50 % Starting sh5l with 300s (1) cores
% 6.97/1.50 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2203677 completed with status 0
% 6.97/1.50 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 6.97/1.50 % Preprocessing class: FMLMSMSMSSSNFFN.
% 6.97/1.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.97/1.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 6.97/1.50 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 6.97/1.50 % No SInE strategy applied
% 6.97/1.50 % Search class: FGHSM-SMLM33-DFFFFFNN
% 6.97/1.50 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 6.97/1.50 % Starting SubtermCWHack with 136s (1) cores
% 6.97/1.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 6.97/1.50 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 6.97/1.50 % Starting SAT001_CA_MinMin_p005000_rr with 136s (1) cores
% 6.97/1.50 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 136s (1) cores
% 6.97/1.50 % SAT001_CA_MinMin_p005000_rr with pid 2203687 completed with status 0
% 6.97/1.50 % Result found by SAT001_CA_MinMin_p005000_rr
% 6.97/1.50 % Preprocessing class: FMLMSMSMSSSNFFN.
% 6.97/1.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.97/1.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 6.97/1.50 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 6.97/1.50 % No SInE strategy applied
% 6.97/1.50 % Search class: FGHSM-SMLM33-DFFFFFNN
% 6.97/1.50 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 6.97/1.50 % Starting SubtermCWHack with 136s (1) cores
% 6.97/1.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 6.97/1.50 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 6.97/1.50 % Starting SAT001_CA_MinMin_p005000_rr with 136s (1) cores
% 6.97/1.50 % Preprocessing time : 0.065 s
% 6.97/1.50 % Presaturation interreduction done
% 6.97/1.50
% 6.97/1.50 % Proof found!
% 6.97/1.50 % SZS status Theorem
% 6.97/1.50 % SZS output start CNFRefutation
% See solution above
% 6.97/1.50 % Parsed axioms : 1173
% 6.97/1.50 % Removed by relevancy pruning/SinE : 0
% 6.97/1.50 % Initial clauses : 1769
% 6.97/1.50 % Removed in clause preprocessing : 60
% 6.97/1.50 % Initial clauses in saturation : 1709
% 6.97/1.50 % Processed clauses : 1710
% 6.97/1.50 % ...of these trivial : 30
% 6.97/1.50 % ...subsumed : 263
% 6.97/1.50 % ...remaining for further processing : 1416
% 6.97/1.50 % Other redundant clauses eliminated : 43
% 6.97/1.50 % Clauses deleted for lack of memory : 0
% 6.97/1.50 % Backward-subsumed : 4
% 6.97/1.50 % Backward-rewritten : 3
% 6.97/1.50 % Generated clauses : 35
% 6.97/1.50 % ...of the previous two non-redundant : 11
% 6.97/1.50 % ...aggressively subsumed : 0
% 6.97/1.50 % Contextual simplify-reflections : 13
% 6.97/1.50 % Paramodulations : 0
% 6.97/1.50 % Factorizations : 0
% 6.97/1.50 % NegExts : 0
% 6.97/1.50 % Equation resolutions : 43
% 6.97/1.50 % Disequality decompositions : 0
% 6.97/1.50 % Total rewrite steps : 574
% 6.97/1.50 % ...of those cached : 438
% 6.97/1.50 % Propositional unsat checks : 0
% 6.97/1.50 % Propositional check models : 0
% 6.97/1.50 % Propositional check unsatisfiable : 0
% 6.97/1.50 % Propositional clauses : 0
% 6.97/1.50 % Propositional clauses after purity: 0
% 6.97/1.50 % Propositional unsat core size : 0
% 6.97/1.50 % Propositional preprocessing time : 0.000
% 6.97/1.50 % Propositional encoding time : 0.000
% 6.97/1.50 % Propositional solver time : 0.000
% 6.97/1.50 % Success case prop preproc time : 0.000
% 6.97/1.50 % Success case prop encoding time : 0.000
% 6.97/1.50 % Success case prop solver time : 0.000
% 6.97/1.50 % Current number of processed clauses : 1374
% 6.97/1.50 % Positive orientable unit clauses : 245
% 6.97/1.50 % Positive unorientable unit clauses: 16
% 6.97/1.50 % Negative unit clauses : 15
% 6.97/1.50 % Non-unit-clauses : 1098
% 6.97/1.50 % Current number of unprocessed clauses: 10
% 6.97/1.50 % ...number of literals in the above : 20
% 6.97/1.50 % Current number of archived formulas : 0
% 6.97/1.50 % Current number of archived clauses : 8
% 6.97/1.50 % Clause-clause subsumption calls (NU) : 390621
% 6.97/1.50 % Rec. Clause-clause subsumption calls : 119219
% 6.97/1.50 % Non-unit clause-clause subsumptions : 254
% 6.97/1.50 % Unit Clause-clause subsumption calls : 351
% 6.97/1.50 % Rewrite failures with RHS unbound : 0
% 6.97/1.50 % BW rewrite match attempts : 16951
% 6.97/1.50 % BW rewrite match successes : 79
% 6.97/1.50 % Condensation attempts : 1751
% 6.97/1.50 % Condensation successes : 3
% 6.97/1.50 % Termbank termtop insertions : 637696
% 6.97/1.50 % Search garbage collected termcells : 28166
% 6.97/1.50
% 6.97/1.50 % -------------------------------------------------
% 6.97/1.50 % User time : 0.881 s
% 6.97/1.50 % System time : 0.049 s
% 6.97/1.50 % Total time : 0.930 s
% 6.97/1.50 % Maximum resident set size: 13404 pages
% 6.97/1.50
% 6.97/1.50 % -------------------------------------------------
% 6.97/1.50 % User time : 3.752 s
% 6.97/1.50 % System time : 0.205 s
% 6.97/1.50 % Total time : 3.957 s
% 6.97/1.50 % Maximum resident set size: 6400 pages
% 6.97/1.50 % E exiting
%------------------------------------------------------------------------------