↑ Up

SuperZenon---0.0.1.THM-Prf.s

View TPTP
Problem
Process solution in
SystemOnTSTP
Download .tgz
%------------------------------------------------------------------------------
% File     : SuperZenon---0.0.1
% Problem  : SCT171+7 : TPTP v8.1.0. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_super_zenon -p0 -itptp -om -max-time %d %s

% Computer : n015.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Mon Jul 18 22:16:35 EDT 2022

% Result   : Theorem 0.44s 0.61s
% Output   : Proof 0.44s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : SCT171+7 : TPTP v8.1.0. Released v5.3.0.
% 0.11/0.12  % Command  : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.12/0.33  % Computer : n015.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sat Jul  2 06:41:29 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.44/0.61  % SZS status Theorem
% 0.44/0.61  (* PROOF-FOUND *)
% 0.44/0.61  (* BEGIN-PROOF *)
% 0.44/0.61  % SZS output start Proof
% 0.44/0.61  1. (hBOOL (hAPP (fun (product_prod (arrow_2142409994le_alt) (arrow_2142409994le_alt)) (bool)) (bool) (hAPP (product_prod (arrow_2142409994le_alt) (arrow_2142409994le_alt)) (fun (fun (product_prod (arrow_2142409994le_alt) (arrow_2142409994le_alt)) (bool)) (bool)) (member (product_prod (arrow_2142409994le_alt) (arrow_2142409994le_alt))) (hAPP (arrow_2142409994le_alt) (product_prod (arrow_2142409994le_alt) (arrow_2142409994le_alt)) (hAPP (arrow_2142409994le_alt) (fun (arrow_2142409994le_alt) (product_prod (arrow_2142409994le_alt) (arrow_2142409994le_alt))) (product_Pair (arrow_2142409994le_alt) (arrow_2142409994le_alt)) (c)) (d))) (hAPP (fun (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))))))))   ### Axiom
% 0.44/0.62  2. (-. (hBOOL (hAPP (fun (product_prod (arrow_2142409994le_alt) (arrow_2142409994le_alt)) (bool)) (bool) (hAPP (product_prod (arrow_2142409994le_alt) (arrow_2142409994le_alt)) (fun (fun (product_prod (arrow_2142409994le_alt) (arrow_2142409994le_alt)) (bool)) (bool)) (member (product_prod (arrow_2142409994le_alt) (arrow_2142409994le_alt))) (hAPP (arrow_2142409994le_alt) (product_prod (arrow_2142409994le_alt) (arrow_2142409994le_alt)) (hAPP (arrow_2142409994le_alt) (fun (arrow_2142409994le_alt) (product_prod (arrow_2142409994le_alt) (arrow_2142409994le_alt))) (product_Pair (arrow_2142409994le_alt) (arrow_2142409994le_alt)) (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) (p))))   ### Axiom
% 0.44/0.62  3. ((hBOOL (hAPP (fun (product_prod (arrow_2142409994le_alt) (arrow_2142409994le_alt)) (bool)) (bool) (hAPP (product_prod (arrow_2142409994le_alt) (arrow_2142409994le_alt)) (fun (fun (product_prod (arrow_2142409994le_alt) (arrow_2142409994le_alt)) (bool)) (bool)) (member (product_prod (arrow_2142409994le_alt) (arrow_2142409994le_alt))) (hAPP (arrow_2142409994le_alt) (product_prod (arrow_2142409994le_alt) (arrow_2142409994le_alt)) (hAPP (arrow_2142409994le_alt) (fun (arrow_2142409994le_alt) (product_prod (arrow_2142409994le_alt) (arrow_2142409994le_alt))) (product_Pair (arrow_2142409994le_alt) (arrow_2142409994le_alt)) (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) (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)))))))   ### Equiv 1 2
% 0.44/0.62  % SZS output end Proof
% 0.44/0.62  (* END-PROOF *)
%------------------------------------------------------------------------------