CSE_E---1.7.THM-CRf.s

%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : SCT167+1 : TPTP v9.2.1. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d

% Computer : n029.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  : 300s
% DateTime : Tue May  5 05:06:13 PM UTC 2026

% Result   : Theorem 6.16s 5.77s
% Output   : CNFRefutation 15.42s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named 1140)

% Comments : 
%------------------------------------------------------------------------------
fof(fact__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ad_J_A_061_A_Ib_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_096,axiom,
    ! [X4] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X4)),v_n____))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X4)),v_e____))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X4)),v_n____))
         => ( ( hAPP(v_h____,X4) = v_n____
             => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X4)),v_c____),v_e____))) )
            & ( hAPP(v_h____,X4) != v_n____
             => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X4)),v_e____))) ) ) ) )
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X4)),v_n____))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X4)),v_n____))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ad_J_A_061_A_Ib_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_096) ).

fof(fact__096_091_124_Ae_A_126_061_Ad_059_Ab_A_126_061_Aa_059_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_A_058_AProf_059_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_ALab_Aelse_ALba_J_A_058_AProf_059_AALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ad_J_A_061_A_Ib_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_A_124_093_061_061_062_A_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ad_J_A_061_A_Ib_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_096,axiom,
    ( v_e____ != v_d____
   => ( v_b____ != v_a____
     => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____)))),c_Arrow__Order__Mirabelle_OProf))
       => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____)),c_Arrow__Order__Mirabelle_OProf))
         => ( ! [X4] :
                ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X4)),v_n____))
                   => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X4)),v_e____))) )
                  & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X4)),v_n____))
                   => ( ( hAPP(v_h____,X4) = v_n____
                       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X4)),v_c____),v_e____))) )
                      & ( hAPP(v_h____,X4) != v_n____
                       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X4)),v_e____))) ) ) ) )
              <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X4)),v_n____))
                   => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____)) )
                  & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X4)),v_n____))
                   => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____)) ) ) )
           => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
            <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____)))) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_091_124_Ae_A_126_061_Ad_059_Ab_A_126_061_Aa_059_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_A_058_AProf_059_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_ALab_Aelse_ALba_J_A_058_AProf_059_AALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ad_J_A_061_A_Ib_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_A_124_093_061_061_062_A_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ad_J_A_061_A_Ib_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_096) ).

fof(conj_0,conjecture,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
  <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

fof(fact__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_Am_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_059_Aa_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
    ~ ! [X28] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))))
       => ( ! [X5] :
              ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5),X28))
             => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),X5))),v_Lab____)),v_Lba____)))) )
         => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X28),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_Am_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_059_Aa_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).

fof(fact_folding__image__simple_Oinsert,axiom,
    ! [X9,X14,X40,X1,X6,X2,X17,X12] :
      ( c_Finite__Set_Ofolding__image__simple(X12,X17,X2,X6,X1,X40)
     => ( c_Finite__Set_Ofinite(X17,X14)
       => ( ~ hBOOL(hAPP(hAPP(c_member(X17),X9),X14))
         => hAPP(X40,c_Set_Oinsert(X17,X9,X14)) = hAPP(hAPP(X2,hAPP(X1,X9)),hAPP(X40,X14)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple_Oinsert) ).

fof(fact__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ae_J_A_061_A_Ia_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_J_096,axiom,
    ! [X4] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X4)),v_n____))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X4)),v_e____))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X4)),v_n____))
         => ( ( hAPP(v_h____,X4) = v_n____
             => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X4)),v_c____),v_e____))) )
            & ( hAPP(v_h____,X4) != v_n____
             => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X4)),v_e____))) ) ) ) )
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lab____)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lba____)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ae_J_A_061_A_Ia_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_J_096) ).

fof(fact__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J_A_061_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ad_J_096,axiom,
    ! [X4] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,X4)))
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X4)),v_n____))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X4)),v_e____))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X4)),v_n____))
         => ( ( hAPP(v_h____,X4) = v_n____
             => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X4)),v_c____),v_e____))) )
            & ( hAPP(v_h____,X4) != v_n____
             => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X4)),v_e____))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J_A_061_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ad_J_096) ).

fof(fact_pigeonhole,axiom,
    ! [X14,X2,X17,X12] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X12,c_Set_Oimage(X17,X12,X2,X14))),c_Finite__Set_Ocard(X17,X14)))
     => ~ c_Fun_Oinj__on(X17,X12,X2,X14) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pigeonhole) ).

fof(fact_card__def,axiom,
    ! [X14,X12] :
      ( ( c_Finite__Set_Ofinite(X12,X14)
       => c_Finite__Set_Ocard(X12,X14) = c_Finite__Set_Ofold__image(tc_Nat_Onat,X12,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X12),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X14) )
      & ( ~ c_Finite__Set_Ofinite(X12,X14)
       => c_Finite__Set_Ocard(X12,X14) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__def) ).

fof(fact_notin__Lin__iff,axiom,
    ! [X8,X9,X7] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X7),c_Arrow__Order__Mirabelle_OLin))
     => ( X9 != X8
       => ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X9),X8)),X7))
        <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8),X9)),X7)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_notin__Lin__iff) ).

fof(fact_Lin__irrefl,axiom,
    ! [X23,X24,X7] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X7),c_Arrow__Order__Mirabelle_OLin))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X24),X23)),X7))
       => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X23),X24)),X7)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Lin__irrefl) ).

fof(fact_PiE,axiom,
    ! [X9,X13,X14,X2,X17,X12] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(X12,X17)),X2),c_FuncSet_OPi(X12,X17,X14,X13)))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X17),hAPP(X2,X9)),hAPP(X13,X9)))
       => ~ hBOOL(hAPP(hAPP(c_member(X12),X9),X14)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_PiE) ).

fof(fact_subset__insert,axiom,
    ! [X13,X14,X9,X12] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X12),X9),X14))
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X14),c_Set_Oinsert(X12,X9,X13)))
      <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X14),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__insert) ).

fof(fact__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_059_ALba_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
    ~ ! [X34] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),X34))
       => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X34),c_Arrow__Order__Mirabelle_OLin)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_059_ALba_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).

fof(fact__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_059_ALab_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
    ~ ! [X33] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),X33))
       => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X33),c_Arrow__Order__Mirabelle_OLin)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_059_ALab_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).

fof(fact_less__fun__def,axiom,
    ! [X1,X2,X12,X17] :
      ( class_Orderings_Oord(X17)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12,X17)),X2),X1))
      <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,X17),X2),X1))
          & ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,X17),X1),X2)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__fun__def) ).

fof(fact_add__leE,axiom,
    ! [X44,X45,X46] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X46),X45)),X44))
     => ~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X46),X44))
         => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X45),X44)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leE) ).

fof(fact_not__add__less1,axiom,
    ! [X48,X49] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X49),X48)),X49)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less1) ).

fof(fact_not__add__less2,axiom,
    ! [X49,X48] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X48),X49)),X49)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less2) ).

fof(fact_ex__least__nat__less,axiom,
    ! [X10,X19] :
      ( ~ hBOOL(hAPP(X19,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
     => ( hBOOL(hAPP(X19,X10))
       => ? [X55] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X55),X10))
            & ! [X4] :
                ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),X55))
               => ~ hBOOL(hAPP(X19,X4)) )
            & hBOOL(hAPP(X19,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X55),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ex__least__nat__less) ).

fof(fact_insertCI,axiom,
    ! [X23,X13,X24,X12] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X12),X24),X13))
       => X24 = X23 )
     => hBOOL(hAPP(hAPP(c_member(X12),X24),c_Set_Oinsert(X12,X23,X13))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertCI) ).

fof(fact_insert__ident,axiom,
    ! [X13,X14,X9,X12] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X12),X9),X14))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X12),X9),X13))
       => ( c_Set_Oinsert(X12,X9,X14) = c_Set_Oinsert(X12,X9,X13)
        <=> X14 = X13 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__ident) ).

fof(fact_not__less__eq__eq,axiom,
    ! [X10,X50] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X50),X10))
    <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X10)),X50)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).

fof(fact_not__less__eq,axiom,
    ! [X10,X50] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X50),X10))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10),hAPP(c_Nat_OSuc,X50))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq) ).

fof(fact_xt1_I9_J,axiom,
    ! [X29,X32,X12] :
      ( class_Orderings_Oorder(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X32),X29))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X29),X32)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I9_J) ).

fof(fact_not__less__iff__gr__or__eq,axiom,
    ! [X8,X9,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X9),X8))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X8),X9))
          | X9 = X8 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).

fof(fact_order__less__asym,axiom,
    ! [X21,X22,X12] :
      ( class_Orderings_Opreorder(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X22),X21))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X21),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym) ).

fof(fact_order__less__asym_H,axiom,
    ! [X32,X29,X12] :
      ( class_Orderings_Opreorder(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X29),X32))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X32),X29)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym_H) ).

fof(fact_order__less__imp__not__less,axiom,
    ! [X21,X22,X12] :
      ( class_Orderings_Opreorder(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X22),X21))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X21),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__less) ).

fof(fact_order__less__not__sym,axiom,
    ! [X21,X22,X12] :
      ( class_Orderings_Opreorder(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X22),X21))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X21),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__not__sym) ).

fof(fact_card_Oinsert,axiom,
    ! [X9,X14,X12] :
      ( c_Finite__Set_Ofinite(X12,X14)
     => ( ~ hBOOL(hAPP(hAPP(c_member(X12),X9),X14))
       => c_Finite__Set_Ocard(X12,c_Set_Oinsert(X12,X9,X14)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Finite__Set_Ocard(X12,X14)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card_Oinsert) ).

fof(fact_less__le__not__le,axiom,
    ! [X8,X9,X12] :
      ( class_Orderings_Opreorder(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X9),X8))
      <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X9),X8))
          & ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X8),X9)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__le__not__le) ).

fof(fact_card__insert__if,axiom,
    ! [X9,X14,X12] :
      ( c_Finite__Set_Ofinite(X12,X14)
     => ( ( hBOOL(hAPP(hAPP(c_member(X12),X9),X14))
         => c_Finite__Set_Ocard(X12,c_Set_Oinsert(X12,X9,X14)) = c_Finite__Set_Ocard(X12,X14) )
        & ( ~ hBOOL(hAPP(hAPP(c_member(X12),X9),X14))
         => c_Finite__Set_Ocard(X12,c_Set_Oinsert(X12,X9,X14)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X12,X14)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__insert__if) ).

fof(fact_not__less__less__Suc__eq,axiom,
    ! [X50,X10] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10),X50))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10),hAPP(c_Nat_OSuc,X50)))
      <=> X10 = X50 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).

fof(fact_less__antisym,axiom,
    ! [X46,X44] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X46))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),hAPP(c_Nat_OSuc,X46)))
       => X46 = X44 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__antisym) ).

fof(fact_less__SucE,axiom,
    ! [X44,X46] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),hAPP(c_Nat_OSuc,X44)))
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),X44))
       => X46 = X44 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__SucE) ).

fof(fact_linorder__antisym__conv2,axiom,
    ! [X8,X9,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X9),X8))
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X9),X8))
        <=> X9 = X8 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv2) ).

fof(fact_leD,axiom,
    ! [X22,X21,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X21),X22))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X22),X21)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leD) ).

fof(fact_linorder__not__less,axiom,
    ! [X8,X9,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X9),X8))
      <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X8),X9)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__less) ).

fof(fact_linorder__not__le,axiom,
    ! [X8,X9,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X9),X8))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X8),X9)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__le) ).

fof(fact_card__insert__disjoint,axiom,
    ! [X9,X14,X12] :
      ( c_Finite__Set_Ofinite(X12,X14)
     => ( ~ hBOOL(hAPP(hAPP(c_member(X12),X9),X14))
       => c_Finite__Set_Ocard(X12,c_Set_Oinsert(X12,X9,X14)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X12,X14)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__insert__disjoint) ).

fof(fact_le__SucE,axiom,
    ! [X44,X46] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X46),hAPP(c_Nat_OSuc,X44)))
     => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X46),X44))
       => X46 = hAPP(c_Nat_OSuc,X44) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__SucE) ).

fof(fact_Suc__n__not__le__n,axiom,
    ! [X44] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X44)),X44)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).

fof(fact_linorder__antisym__conv1,axiom,
    ! [X8,X9,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X9),X8))
       => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X9),X8))
        <=> X9 = X8 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv1) ).

fof(fact_not__one__less__zero,axiom,
    ! [X12] :
      ( class_Rings_Olinordered__semidom(X12)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),c_Groups_Oone__class_Oone(X12)),c_Groups_Ozero__class_Ozero(X12))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__less__zero) ).

fof(fact_linorder__neqE__linordered__idom,axiom,
    ! [X21,X22,X12] :
      ( class_Rings_Olinordered__idom(X12)
     => ( X22 != X21
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X22),X21))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X21),X22)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).

fof(fact_linorder__cases,axiom,
    ! [X21,X22,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X22),X21))
       => ( X22 != X21
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X21),X22)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__cases) ).

fof(fact_linorder__neqE,axiom,
    ! [X21,X22,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( X22 != X21
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X22),X21))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X21),X22)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE) ).

fof(fact_linorder__antisym__conv3,axiom,
    ! [X9,X8,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X8),X9))
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X9),X8))
        <=> X9 = X8 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv3) ).

fof(fact_not__leE,axiom,
    ! [X22,X21,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X21),X22))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X22),X21)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__leE) ).

fof(fact_leI,axiom,
    ! [X21,X22,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X22),X21))
       => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X21),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leI) ).

fof(fact_not__one__le__zero,axiom,
    ! [X12] :
      ( class_Rings_Olinordered__semidom(X12)
     => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,c_Groups_Oone__class_Oone(X12)),c_Groups_Ozero__class_Ozero(X12))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__le__zero) ).

fof(fact_linorder__neqE__nat,axiom,
    ! [X21,X22] :
      ( X22 != X21
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22),X21))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).

fof(fact_equalityE,axiom,
    ! [X12,X13,X14] :
      ( X14 = X13
     => ~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X14),X13))
         => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X13),X14)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityE) ).

fof(fact_order__less__irrefl,axiom,
    ! [X22,X12] :
      ( class_Orderings_Opreorder(X12)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X22),X22)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__irrefl) ).

fof(fact_linorder__le__cases,axiom,
    ! [X21,X22,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X22),X21))
       => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X21),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__cases) ).

fof(fact_not__less0,axiom,
    ! [X44] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less0) ).

fof(fact_less__nat__zero__code,axiom,
    ! [X44] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__nat__zero__code) ).

fof(fact_less__zeroE,axiom,
    ! [X44] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__zeroE) ).

fof(fact_less__not__refl,axiom,
    ! [X44] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X44)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl) ).

fof(fact_less__irrefl__nat,axiom,
    ! [X44] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X44)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).

fof(help_c__fequal__1,axiom,
    ! [X8,X9] :
      ( ~ hBOOL(hAPP(hAPP(c_fequal,X9),X8))
      | X9 = X8 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__1) ).

fof(fact_card__infinite,axiom,
    ! [X14,X12] :
      ( ~ c_Finite__Set_Ofinite(X12,X14)
     => c_Finite__Set_Ocard(X12,X14) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__infinite) ).

fof(fact__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ae_J_A_061_Ia_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_J_096,axiom,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
  <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ae_J_A_061_Ia_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_J_096) ).

fof(fact_PW,axiom,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_F,v_P____)))
  <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____)))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_PW) ).

fof(fact__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_Am_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_A_G_Aa_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_096,axiom,
    ? [X28] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))))
      & ! [X5] :
          ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5),X28))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),X5))),v_Lab____)),v_Lba____)))) )
      & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X28),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_Am_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_A_G_Aa_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_096) ).

fof(fact_PiProf,axiom,
    ! [X10] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),X10))),v_Lab____)),v_Lba____)),c_Arrow__Order__Mirabelle_OProf)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_PiProf) ).

fof(fact_n_I2_J,axiom,
    ! [X5] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5),v_n____))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),X5))),v_Lab____)),v_Lba____)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n_I2_J) ).

fof(fact_pred__subset__eq2,axiom,
    ! [X15,X16,X17,X12] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_fun(X17,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X12,tc_fun(tc_prod(X12,X17),tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X17,tc_fun(tc_fun(tc_prod(X12,X17),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X12,X17),tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),X12,c_COMBC(X17,tc_fun(tc_prod(X12,X17),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X17,tc_prod(X12,X17)),tc_fun(X17,tc_fun(tc_fun(tc_prod(X12,X17),tc_HOL_Obool),tc_HOL_Obool)),X12,c_COMBB(tc_prod(X12,X17),tc_fun(tc_fun(tc_prod(X12,X17),tc_HOL_Obool),tc_HOL_Obool),X17,c_member(tc_prod(X12,X17)))),c_Product__Type_OPair(X12,X17)))),X16)),hAPP(hAPP(c_COMBC(X12,tc_fun(tc_prod(X12,X17),tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X17,tc_fun(tc_fun(tc_prod(X12,X17),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X12,X17),tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),X12,c_COMBC(X17,tc_fun(tc_prod(X12,X17),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X17,tc_prod(X12,X17)),tc_fun(X17,tc_fun(tc_fun(tc_prod(X12,X17),tc_HOL_Obool),tc_HOL_Obool)),X12,c_COMBB(tc_prod(X12,X17),tc_fun(tc_fun(tc_prod(X12,X17),tc_HOL_Obool),tc_HOL_Obool),X17,c_member(tc_prod(X12,X17)))),c_Product__Type_OPair(X12,X17)))),X15)))
    <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X12,X17),tc_HOL_Obool),X16),X15)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__subset__eq2) ).

fof(fact__C2_C,axiom,
    ! [X25,X19,X26,X27,X23,X24] :
      ( X24 != X23
     => ( X27 != X26
       => ( X24 != X26
         => ( X23 != X27
           => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X19),c_Arrow__Order__Mirabelle_OProf))
             => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X25),c_Arrow__Order__Mirabelle_OProf))
               => ( ! [X4] :
                      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X24),X23)),hAPP(X19,X4)))
                    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X27),X26)),hAPP(X25,X4))) )
                 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X24),X23)),hAPP(v_F,X19)))
                  <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X27),X26)),hAPP(v_F,X25))) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__C2_C) ).

fof(fact__C1_C,axiom,
    ! [X25,X19,X26,X27,X23,X24] :
      ( X24 != X23
     => ( X27 != X26
       => ( X24 != X26
         => ( X23 != X27
           => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X19),c_Arrow__Order__Mirabelle_OProf))
             => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X25),c_Arrow__Order__Mirabelle_OProf))
               => ( ! [X4] :
                      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X24),X23)),hAPP(X19,X4)))
                    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X27),X26)),hAPP(X25,X4))) )
                 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X24),X23)),hAPP(v_F,X19)))
                   => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X27),X26)),hAPP(v_F,X25))) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__C1_C) ).

fof(fact_pairwise__neutrality,axiom,
    ! [X25,X19,X26,X27,X23,X24] :
      ( X24 != X23
     => ( X27 != X26
       => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X19),c_Arrow__Order__Mirabelle_OProf))
         => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X25),c_Arrow__Order__Mirabelle_OProf))
           => ( ! [X4] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X24),X23)),hAPP(X19,X4)))
                <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X27),X26)),hAPP(X25,X4))) )
             => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X24),X23)),hAPP(v_F,X19)))
              <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X27),X26)),hAPP(v_F,X25))) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pairwise__neutrality) ).

fof(fact_pred__equals__eq2,axiom,
    ! [X15,X16,X17,X12] :
      ( hAPP(hAPP(c_COMBC(X12,tc_fun(tc_prod(X12,X17),tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X17,tc_fun(tc_fun(tc_prod(X12,X17),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X12,X17),tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),X12,c_COMBC(X17,tc_fun(tc_prod(X12,X17),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X17,tc_prod(X12,X17)),tc_fun(X17,tc_fun(tc_fun(tc_prod(X12,X17),tc_HOL_Obool),tc_HOL_Obool)),X12,c_COMBB(tc_prod(X12,X17),tc_fun(tc_fun(tc_prod(X12,X17),tc_HOL_Obool),tc_HOL_Obool),X17,c_member(tc_prod(X12,X17)))),c_Product__Type_OPair(X12,X17)))),X16) = hAPP(hAPP(c_COMBC(X12,tc_fun(tc_prod(X12,X17),tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X17,tc_fun(tc_fun(tc_prod(X12,X17),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X12,X17),tc_HOL_Obool),tc_fun(X17,tc_HOL_Obool)),X12,c_COMBC(X17,tc_fun(tc_prod(X12,X17),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X17,tc_prod(X12,X17)),tc_fun(X17,tc_fun(tc_fun(tc_prod(X12,X17),tc_HOL_Obool),tc_HOL_Obool)),X12,c_COMBB(tc_prod(X12,X17),tc_fun(tc_fun(tc_prod(X12,X17),tc_HOL_Obool),tc_HOL_Obool),X17,c_member(tc_prod(X12,X17)))),c_Product__Type_OPair(X12,X17)))),X15)
    <=> X16 = X15 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__equals__eq2) ).

fof(fact_Pi__mono,axiom,
    ! [X37,X13,X17,X14,X12] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X12),X3),X14))
         => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17,tc_HOL_Obool),hAPP(X13,X3)),hAPP(X37,X3))) )
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X12,X17),tc_HOL_Obool),c_FuncSet_OPi(X12,X17,X14,X13)),c_FuncSet_OPi(X12,X17,X14,X37))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__mono) ).

fof(fact_Pi__I,axiom,
    ! [X13,X2,X17,X14,X12] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X12),X3),X14))
         => hBOOL(hAPP(hAPP(c_member(X17),hAPP(X2,X3)),hAPP(X13,X3))) )
     => hBOOL(hAPP(hAPP(c_member(tc_fun(X12,X17)),X2),c_FuncSet_OPi(X12,X17,X14,X13))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__I) ).

fof(fact_IIA__def,axiom,
    ! [X40] :
      ( c_Arrow__Order__Mirabelle_OIIA(X40)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf))
         => ! [X38] :
              ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X38),c_Arrow__Order__Mirabelle_OProf))
             => ! [X41,X42] :
                  ( ! [X4] :
                      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X41),X42)),hAPP(X3,X4)))
                    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X41),X42)),hAPP(X38,X4))) )
                 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X41),X42)),hAPP(X40,X3)))
                  <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X41),X42)),hAPP(X40,X38))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IIA__def) ).

fof(fact__C4_C,axiom,
    ! [X25,X19,X11,X23,X24] :
      ( X24 != X23
     => ( X23 != X11
       => ( X24 != X11
         => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X19),c_Arrow__Order__Mirabelle_OProf))
           => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X25),c_Arrow__Order__Mirabelle_OProf))
             => ( ! [X4] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X24),X23)),hAPP(X19,X4)))
                  <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X23),X11)),hAPP(X25,X4))) )
               => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X24),X23)),hAPP(v_F,X19)))
                <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X23),X11)),hAPP(v_F,X25))) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__C4_C) ).

fof(fact_dictatorI,axiom,
    ! [X39,X40] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X40),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin))))
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf))
           => ! [X41,X42] :
                ( X41 != X42
               => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X41),X42)),hAPP(X3,X39)))
                 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X41),X42)),hAPP(X40,X3))) ) ) )
       => c_Arrow__Order__Mirabelle_Odictator(X40,X39) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dictatorI) ).

fof(fact_in__lex__prod,axiom,
    ! [X56,X57,X26,X27,X23,X24,X17,X12] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X12,X17),tc_prod(X12,X17))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X12,X17),tc_prod(X12,X17)),hAPP(hAPP(c_Product__Type_OPair(X12,X17),X24),X23)),hAPP(hAPP(c_Product__Type_OPair(X12,X17),X27),X26))),c_Wellfounded_Olex__prod(X12,X17,X57,X56)))
    <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X12,X12)),hAPP(hAPP(c_Product__Type_OPair(X12,X12),X24),X27)),X57))
        | ( X24 = X27
          & hBOOL(hAPP(hAPP(c_member(tc_prod(X17,X17)),hAPP(hAPP(c_Product__Type_OPair(X17,X17),X23),X26)),X56)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__lex__prod) ).

fof(fact__C3_C,axiom,
    ! [X25,X19,X23,X24] :
      ( X24 != X23
     => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X19),c_Arrow__Order__Mirabelle_OProf))
       => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X25),c_Arrow__Order__Mirabelle_OProf))
         => ( ! [X4] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X24),X23)),hAPP(X19,X4)))
              <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X23),X24)),hAPP(X25,X4))) )
           => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X24),X23)),hAPP(v_F,X19)))
            <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X23),X24)),hAPP(v_F,X25))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__C3_C) ).

fof(fact_folding__image__simple_Oeq__fold__g,axiom,
    ! [X14,X40,X1,X6,X2,X17,X12] :
      ( c_Finite__Set_Ofolding__image__simple(X12,X17,X2,X6,X1,X40)
     => ( c_Finite__Set_Ofinite(X17,X14)
       => hAPP(X40,X14) = c_Finite__Set_Ofold__image(X12,X17,X2,X1,X6,X14) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple_Oeq__fold__g) ).

fof(fact_subset__image__iff,axiom,
    ! [X14,X2,X17,X13,X12] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X13),c_Set_Oimage(X17,X12,X2,X14)))
    <=> ? [X70] :
          ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17,tc_HOL_Obool),X70),X14))
          & X13 = c_Set_Oimage(X17,X12,X2,X70) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__image__iff) ).

fof(fact_same__fstI,axiom,
    ! [X12,X16,X8,X18,X17,X9,X19] :
      ( hBOOL(hAPP(X19,X9))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X17,X17)),hAPP(hAPP(c_Product__Type_OPair(X17,X17),X18),X8)),hAPP(X16,X9)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X12,X17),tc_prod(X12,X17))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X12,X17),tc_prod(X12,X17)),hAPP(hAPP(c_Product__Type_OPair(X12,X17),X9),X18)),hAPP(hAPP(c_Product__Type_OPair(X12,X17),X9),X8))),c_Recdef_Osame__fst(X12,X17,X19,X16))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_same__fstI) ).

fof(fact_le__fun__def,axiom,
    ! [X1,X2,X12,X17] :
      ( class_Orderings_Oord(X17)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,X17),X2),X1))
      <=> ! [X3] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X17,hAPP(X2,X3)),hAPP(X1,X3))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__fun__def) ).

fof(fact_card__bij__eq,axiom,
    ! [X1,X13,X14,X2,X17,X12] :
      ( c_Fun_Oinj__on(X12,X17,X2,X14)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17,tc_HOL_Obool),c_Set_Oimage(X12,X17,X2,X14)),X13))
       => ( c_Fun_Oinj__on(X17,X12,X1,X13)
         => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),c_Set_Oimage(X17,X12,X1,X13)),X14))
           => ( c_Finite__Set_Ofinite(X12,X14)
             => ( c_Finite__Set_Ofinite(X17,X13)
               => c_Finite__Set_Ocard(X12,X14) = c_Finite__Set_Ocard(X17,X13) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__bij__eq) ).

fof(fact_unanimity__def,axiom,
    ! [X40] :
      ( c_Arrow__Order__Mirabelle_Ounanimity(X40)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf))
         => ! [X41,X42] :
              ( ! [X4] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X41),X42)),hAPP(X3,X4)))
             => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X41),X42)),hAPP(X40,X3))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unanimity__def) ).

fof(fact_card__bij,axiom,
    ! [X1,X13,X14,X2,X17,X12] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(X12,X17)),X2),c_FuncSet_OPi(X12,X17,X14,hAPP(c_COMBK(tc_fun(X17,tc_HOL_Obool),X12),X13))))
     => ( c_Fun_Oinj__on(X12,X17,X2,X14)
       => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X17,X12)),X1),c_FuncSet_OPi(X17,X12,X13,hAPP(c_COMBK(tc_fun(X12,tc_HOL_Obool),X17),X14))))
         => ( c_Fun_Oinj__on(X17,X12,X1,X13)
           => ( c_Finite__Set_Ofinite(X12,X14)
             => ( c_Finite__Set_Ofinite(X17,X13)
               => c_Finite__Set_Ocard(X12,X14) = c_Finite__Set_Ocard(X17,X13) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__bij) ).

fof(fact_pred__subset__eq,axiom,
    ! [X15,X16,X12] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X12,tc_fun(X12,tc_HOL_Obool),tc_HOL_Obool),c_member(X12)),X16)),hAPP(hAPP(c_COMBC(X12,tc_fun(X12,tc_HOL_Obool),tc_HOL_Obool),c_member(X12)),X15)))
    <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X16),X15)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__subset__eq) ).

fof(fact_inj__on__iff__card__le,axiom,
    ! [X13,X17,X14,X12] :
      ( c_Finite__Set_Ofinite(X12,X14)
     => ( c_Finite__Set_Ofinite(X17,X13)
       => ( ? [X74] :
              ( c_Fun_Oinj__on(X12,X17,X74,X14)
              & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17,tc_HOL_Obool),c_Set_Oimage(X12,X17,X74,X14)),X13)) )
        <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X12,X14)),c_Finite__Set_Ocard(X17,X13))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__iff__card__le) ).

fof(fact_in__above,axiom,
    ! [X8,X9,X7,X23,X24] :
      ( X24 != X23
     => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X7),c_Arrow__Order__Mirabelle_OLin))
       => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X9),X8)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X7),X24),X23)))
        <=> ( X9 != X8
            & ( X9 = X23
             => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X24),X8)),X7)) )
            & ( X9 != X23
             => ( ( X8 = X23
                 => ( X9 = X24
                    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X9),X24)),X7)) ) )
                & ( X8 != X23
                 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X9),X8)),X7)) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__above) ).

fof(fact_in__below,axiom,
    ! [X8,X9,X7,X23,X24] :
      ( X24 != X23
     => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X7),c_Arrow__Order__Mirabelle_OLin))
       => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X9),X8)),c_Arrow__Order__Mirabelle_Obelow(X7,X24,X23)))
        <=> ( X9 != X8
            & ( X8 = X24
             => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X9),X23)),X7)) )
            & ( X8 != X24
             => ( ( X9 = X24
                 => ( X8 = X23
                    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X23),X8)),X7)) ) )
                & ( X9 != X24
                 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X9),X8)),X7)) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__below) ).

fof(fact_card_Oeq__fold__g,axiom,
    ! [X14,X12] :
      ( c_Finite__Set_Ofinite(X12,X14)
     => c_Finite__Set_Ocard(X12,X14) = c_Finite__Set_Ofold__image(tc_Nat_Onat,X12,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X12),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X14) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card_Oeq__fold__g) ).

fof(fact_inv__into__into,axiom,
    ! [X14,X2,X17,X9,X12] :
      ( hBOOL(hAPP(hAPP(c_member(X12),X9),c_Set_Oimage(X17,X12,X2,X14)))
     => hBOOL(hAPP(hAPP(c_member(X17),hAPP(c_Hilbert__Choice_Oinv__into(X17,X12,X14,X2),X9)),X14)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__into) ).

fof(fact_inj__image__subset__iff,axiom,
    ! [X13,X14,X2,X17,X12] :
      ( c_Fun_Oinj__on(X12,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17,tc_HOL_Obool),c_Set_Oimage(X12,X17,X2,X14)),c_Set_Oimage(X12,X17,X2,X13)))
      <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X14),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__image__subset__iff) ).

fof(fact_in__finite__psubset,axiom,
    ! [X13,X14,X12] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),X14),X13)),c_Wellfounded_Ofinite__psubset(X12)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12,tc_HOL_Obool)),X14),X13))
        & c_Finite__Set_Ofinite(X12,X13) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__finite__psubset) ).

fof(fact_funcset__image,axiom,
    ! [X13,X14,X2,X17,X12] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(X12,X17)),X2),c_FuncSet_OPi(X12,X17,X14,hAPP(c_COMBK(tc_fun(X17,tc_HOL_Obool),X12),X13))))
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17,tc_HOL_Obool),c_Set_Oimage(X12,X17,X2,X14)),X13)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funcset__image) ).

fof(fact_inv__into__injective,axiom,
    ! [X8,X9,X2,X14,X17,X12] :
      ( hAPP(c_Hilbert__Choice_Oinv__into(X12,X17,X14,X2),X9) = hAPP(c_Hilbert__Choice_Oinv__into(X12,X17,X14,X2),X8)
     => ( hBOOL(hAPP(hAPP(c_member(X17),X9),c_Set_Oimage(X12,X17,X2,X14)))
       => ( hBOOL(hAPP(hAPP(c_member(X17),X8),c_Set_Oimage(X12,X17,X2,X14)))
         => X9 = X8 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__injective) ).

fof(fact_Ints__odd__less__0,axiom,
    ! [X24,X12] :
      ( class_Rings_Olinordered__idom(X12)
     => ( hBOOL(hAPP(hAPP(c_member(X12),X24),c_Int_Oring__1__class_OInts(X12)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),c_Groups_Oone__class_Oone(X12)),X24)),X24)),c_Groups_Ozero__class_Ozero(X12)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X24),c_Groups_Ozero__class_Ozero(X12))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__odd__less__0) ).

fof(fact_range__ex1__eq,axiom,
    ! [X23,X2,X17,X12] :
      ( c_Fun_Oinj__on(X12,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))
     => ( hBOOL(hAPP(hAPP(c_member(X17),X23),c_Set_Oimage(X12,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))))
      <=> ? [X3] :
            ( X23 = hAPP(X2,X3)
            & ! [X66] :
                ( X23 = hAPP(X2,X66)
               => X66 = X3 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_range__ex1__eq) ).

fof(fact_card__image__le,axiom,
    ! [X2,X17,X14,X12] :
      ( c_Finite__Set_Ofinite(X12,X14)
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X17,c_Set_Oimage(X12,X17,X2,X14))),c_Finite__Set_Ocard(X12,X14))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__image__le) ).

fof(fact_inj__on__strict__subset,axiom,
    ! [X14,X13,X2,X17,X12] :
      ( c_Fun_Oinj__on(X12,X17,X2,X13)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12,tc_HOL_Obool)),X14),X13))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X17,tc_HOL_Obool)),c_Set_Oimage(X12,X17,X2,X14)),c_Set_Oimage(X12,X17,X2,X13))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__strict__subset) ).

fof(fact_endo__inj__surj,axiom,
    ! [X2,X14,X12] :
      ( c_Finite__Set_Ofinite(X12,X14)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),c_Set_Oimage(X12,X12,X2,X14)),X14))
       => ( c_Fun_Oinj__on(X12,X12,X2,X14)
         => c_Set_Oimage(X12,X12,X2,X14) = X14 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_endo__inj__surj) ).

fof(fact_card__inj__on__le,axiom,
    ! [X13,X14,X2,X17,X12] :
      ( c_Fun_Oinj__on(X12,X17,X2,X14)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17,tc_HOL_Obool),c_Set_Oimage(X12,X17,X2,X14)),X13))
       => ( c_Finite__Set_Ofinite(X17,X13)
         => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X12,X14)),c_Finite__Set_Ocard(X17,X13))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__inj__on__le) ).

fof(fact_image__iff,axiom,
    ! [X14,X2,X17,X6,X12] :
      ( hBOOL(hAPP(hAPP(c_member(X12),X6),c_Set_Oimage(X17,X12,X2,X14)))
    <=> ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X17),X3),X14))
          & X6 = hAPP(X2,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__iff) ).

fof(fact_card__inj,axiom,
    ! [X13,X14,X2,X17,X12] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(X12,X17)),X2),c_FuncSet_OPi(X12,X17,X14,hAPP(c_COMBK(tc_fun(X17,tc_HOL_Obool),X12),X13))))
     => ( c_Fun_Oinj__on(X12,X17,X2,X14)
       => ( c_Finite__Set_Ofinite(X17,X13)
         => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X12,X14)),c_Finite__Set_Ocard(X17,X13))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__inj) ).

fof(fact_Pi__anti__mono,axiom,
    ! [X13,X17,X14,X43,X12] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X43),X14))
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X12,X17),tc_HOL_Obool),c_FuncSet_OPi(X12,X17,X14,X13)),c_FuncSet_OPi(X12,X17,X43,X13))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__anti__mono) ).

fof(fact_finite__range__imageI,axiom,
    ! [X2,X35,X1,X17,X12] :
      ( c_Finite__Set_Ofinite(X12,c_Set_Oimage(X17,X12,X1,c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool))))
     => c_Finite__Set_Ofinite(X35,c_Set_Oimage(X17,X35,hAPP(c_COMBB(X12,X35,X17,X2),X1),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__range__imageI) ).

fof(fact_const__Lin__Prof,axiom,
    ! [X7] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X7),c_Arrow__Order__Mirabelle_OLin))
     => hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi),X7)),c_Arrow__Order__Mirabelle_OProf)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_const__Lin__Prof) ).

fof(fact_funcset__mem,axiom,
    ! [X9,X13,X14,X2,X17,X12] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(X12,X17)),X2),c_FuncSet_OPi(X12,X17,X14,hAPP(c_COMBK(tc_fun(X17,tc_HOL_Obool),X12),X13))))
     => ( hBOOL(hAPP(hAPP(c_member(X12),X9),X14))
       => hBOOL(hAPP(hAPP(c_member(X17),hAPP(X2,X9)),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funcset__mem) ).

fof(fact_image__mono,axiom,
    ! [X2,X17,X13,X14,X12] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X14),X13))
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17,tc_HOL_Obool),c_Set_Oimage(X12,X17,X2,X14)),c_Set_Oimage(X12,X17,X2,X13))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__mono) ).

fof(fact_mlex__leq,axiom,
    ! [X16,X12,X8,X9,X2] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X2,X9)),hAPP(X2,X8)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X12,X12)),hAPP(hAPP(c_Product__Type_OPair(X12,X12),X9),X8)),X16))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X12,X12)),hAPP(hAPP(c_Product__Type_OPair(X12,X12),X9),X8)),c_Wellfounded_Omlex__prod(X12,X2,X16))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mlex__leq) ).

fof(fact_in__rel__def,axiom,
    ! [X8,X9,X16,X17,X12] :
      ( c_FunDef_Oin__rel(X12,X17,X16,X9,X8)
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X12,X17)),hAPP(hAPP(c_Product__Type_OPair(X12,X17),X9),X8)),X16)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__rel__def) ).

fof(fact_f__inv__into__f,axiom,
    ! [X14,X2,X17,X8,X12] :
      ( hBOOL(hAPP(hAPP(c_member(X12),X8),c_Set_Oimage(X17,X12,X2,X14)))
     => hAPP(X2,hAPP(c_Hilbert__Choice_Oinv__into(X17,X12,X14,X2),X8)) = X8 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_f__inv__into__f) ).

fof(fact_surj__iff__all,axiom,
    ! [X2,X12,X17] :
      ( c_Set_Oimage(X17,X12,X2,c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool))
    <=> ! [X3] : hAPP(X2,hAPP(c_Hilbert__Choice_Oinv__into(X17,X12,c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)),X2),X3)) = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_surj__iff__all) ).

fof(fact_inj__on__inv__into,axiom,
    ! [X14,X2,X17,X13,X12] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X13),c_Set_Oimage(X17,X12,X2,X14)))
     => c_Fun_Oinj__on(X12,X17,c_Hilbert__Choice_Oinv__into(X17,X12,X14,X2),X13) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__inv__into) ).

fof(fact_in__mkbot,axiom,
    ! [X6,X7,X8,X9] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X9),X8)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X7),X6)))
    <=> ( X8 != X6
        & ( X9 = X6
         => X9 != X8 )
        & ( X9 != X6
         => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X9),X8)),X7)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__mkbot) ).

fof(fact_in__mktop,axiom,
    ! [X6,X7,X8,X9] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X9),X8)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X7),X6)))
    <=> ( X9 != X6
        & ( X8 = X6
         => X9 != X8 )
        & ( X8 != X6
         => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X9),X8)),X7)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__mktop) ).

fof(help_c__COMBS__1,axiom,
    ! [X16,X36,X19,X12,X35,X17] : hAPP(c_COMBS(X17,X35,X12,X19,X36),X16) = hAPP(hAPP(X19,X16),hAPP(X36,X16)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBS__1) ).

fof(fact_Pi__mem,axiom,
    ! [X9,X13,X14,X2,X17,X12] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(X12,X17)),X2),c_FuncSet_OPi(X12,X17,X14,X13)))
     => ( hBOOL(hAPP(hAPP(c_member(X12),X9),X14))
       => hBOOL(hAPP(hAPP(c_member(X17),hAPP(X2,X9)),hAPP(X13,X9))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__mem) ).

fof(fact_inj__image__mem__iff,axiom,
    ! [X14,X24,X2,X17,X12] :
      ( c_Fun_Oinj__on(X12,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))
     => ( hBOOL(hAPP(hAPP(c_member(X17),hAPP(X2,X24)),c_Set_Oimage(X12,X17,X2,X14)))
      <=> hBOOL(hAPP(hAPP(c_member(X12),X24),X14)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__image__mem__iff) ).

fof(fact_image__surj__f__inv__f,axiom,
    ! [X14,X2,X12,X17] :
      ( c_Set_Oimage(X17,X12,X2,c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool))
     => c_Set_Oimage(X17,X12,X2,c_Set_Oimage(X12,X17,c_Hilbert__Choice_Oinv__into(X17,X12,c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)),X2),X14)) = X14 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__surj__f__inv__f) ).

fof(fact_image__inv__into__cancel,axiom,
    ! [X71,X43,X14,X2,X12,X17] :
      ( c_Set_Oimage(X17,X12,X2,X14) = X43
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X71),X43))
       => c_Set_Oimage(X17,X12,X2,c_Set_Oimage(X12,X17,c_Hilbert__Choice_Oinv__into(X17,X12,X14,X2),X71)) = X71 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__inv__into__cancel) ).

fof(fact_inj__on__def,axiom,
    ! [X14,X2,X17,X12] :
      ( c_Fun_Oinj__on(X12,X17,X2,X14)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X12),X3),X14))
         => ! [X38] :
              ( hBOOL(hAPP(hAPP(c_member(X12),X38),X14))
             => ( hAPP(X2,X3) = hAPP(X2,X38)
               => X3 = X38 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__def) ).

fof(fact_above__Lin,axiom,
    ! [X7,X8,X9] :
      ( X9 != X8
     => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X7),c_Arrow__Order__Mirabelle_OLin))
       => hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X7),X9),X8)),c_Arrow__Order__Mirabelle_OLin)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_above__Lin) ).

fof(fact_range__composition,axiom,
    ! [X1,X2,X35,X12,X17] : c_Set_Oimage(X17,X12,hAPP(c_COMBB(X35,X12,X17,X2),X1),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool))) = c_Set_Oimage(X35,X12,X2,c_Set_Oimage(X17,X35,X1,c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_range__composition) ).

fof(fact_finite__surj__inj,axiom,
    ! [X2,X14,X12] :
      ( c_Finite__Set_Ofinite(X12,X14)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X14),c_Set_Oimage(X12,X12,X2,X14)))
       => c_Fun_Oinj__on(X12,X12,X2,X14) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__surj__inj) ).

fof(fact_dictator__def,axiom,
    ! [X39,X40] :
      ( c_Arrow__Order__Mirabelle_Odictator(X40,X39)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf))
         => hAPP(X40,X3) = hAPP(X3,X39) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dictator__def) ).

fof(fact_inj__fun,axiom,
    ! [X35,X2,X17,X12] :
      ( c_Fun_Oinj__on(X12,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))
     => c_Fun_Oinj__on(X12,tc_fun(X35,X17),hAPP(c_COMBB(X17,tc_fun(X35,X17),X12,c_COMBK(X17,X35)),X2),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__fun) ).

fof(fact_funcset__id,axiom,
    ! [X14,X12] : hBOOL(hAPP(hAPP(c_member(tc_fun(X12,X12)),c_COMBI(X12)),c_FuncSet_OPi(X12,X12,X14,hAPP(c_COMBK(tc_fun(X12,tc_HOL_Obool),X12),X14)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funcset__id) ).

fof(fact_image__image,axiom,
    ! [X14,X1,X35,X2,X12,X17] : c_Set_Oimage(X17,X12,X2,c_Set_Oimage(X35,X17,X1,X14)) = c_Set_Oimage(X35,X12,hAPP(c_COMBB(X17,X12,X35,X2),X1),X14),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__image) ).

fof(fact_below__Lin,axiom,
    ! [X7,X8,X9] :
      ( X9 != X8
     => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X7),c_Arrow__Order__Mirabelle_OLin))
       => hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Obelow(X7,X9,X8)),c_Arrow__Order__Mirabelle_OLin)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_below__Lin) ).

fof(fact_in__measure,axiom,
    ! [X2,X8,X9,X12] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X12,X12)),hAPP(hAPP(c_Product__Type_OPair(X12,X12),X9),X8)),c_Wellfounded_Omeasure(X12,X2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2,X9)),hAPP(X2,X8))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__measure) ).

fof(fact_inv__into__image__cancel,axiom,
    ! [X15,X14,X2,X17,X12] :
      ( c_Fun_Oinj__on(X12,X17,X2,X14)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X15),X14))
       => c_Set_Oimage(X17,X12,c_Hilbert__Choice_Oinv__into(X12,X17,X14,X2),c_Set_Oimage(X12,X17,X2,X15)) = X15 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__image__cancel) ).

fof(fact_finite__surj,axiom,
    ! [X2,X13,X17,X14,X12] :
      ( c_Finite__Set_Ofinite(X12,X14)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17,tc_HOL_Obool),X13),c_Set_Oimage(X12,X17,X2,X14)))
       => c_Finite__Set_Ofinite(X17,X13) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__surj) ).

fof(fact_mkbot__Lin,axiom,
    ! [X9,X7] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X7),c_Arrow__Order__Mirabelle_OLin))
     => hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X7),X9)),c_Arrow__Order__Mirabelle_OLin)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mkbot__Lin) ).

fof(fact_mktop__Lin,axiom,
    ! [X9,X7] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X7),c_Arrow__Order__Mirabelle_OLin))
     => hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X7),X9)),c_Arrow__Order__Mirabelle_OLin)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mktop__Lin) ).

fof(fact_inv__image__comp,axiom,
    ! [X72,X2,X17,X12] :
      ( c_Fun_Oinj__on(X12,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))
     => c_Set_Oimage(X17,X12,c_Hilbert__Choice_Oinv__into(X12,X17,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)),X2),c_Set_Oimage(X12,X17,X2,X72)) = X72 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__image__comp) ).

fof(fact_image__inv__f__f,axiom,
    ! [X14,X2,X17,X12] :
      ( c_Fun_Oinj__on(X12,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))
     => c_Set_Oimage(X17,X12,c_Hilbert__Choice_Oinv__into(X12,X17,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)),X2),c_Set_Oimage(X12,X17,X2,X14)) = X14 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__inv__f__f) ).

fof(fact_surj__f__inv__f,axiom,
    ! [X8,X2,X12,X17] :
      ( c_Set_Oimage(X17,X12,X2,c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool))
     => hAPP(X2,hAPP(c_Hilbert__Choice_Oinv__into(X17,X12,c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)),X2),X8)) = X8 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_surj__f__inv__f) ).

fof(fact_mlex__less,axiom,
    ! [X16,X12,X8,X9,X2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2,X9)),hAPP(X2,X8)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X12,X12)),hAPP(hAPP(c_Product__Type_OPair(X12,X12),X9),X8)),c_Wellfounded_Omlex__prod(X12,X2,X16))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mlex__less) ).

fof(fact_subset__card__intvl__is__intvl,axiom,
    ! [X53,X14] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool),X14),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X53,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X53),c_Finite__Set_Ocard(tc_Nat_Onat,X14)))))
     => X14 = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X53,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X53),c_Finite__Set_Ocard(tc_Nat_Onat,X14))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__card__intvl__is__intvl) ).

fof(fact_atLeastLessThan__subset__iff,axiom,
    ! [X78,X11,X23,X24,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(X12,X24,X23)),c_SetInterval_Oord__class_OatLeastLessThan(X12,X11,X78)))
       => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X23),X24))
          | ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X11),X24))
            & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X23),X78)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThan__subset__iff) ).

fof(fact_surj__imp__inj__inv,axiom,
    ! [X2,X12,X17] :
      ( c_Set_Oimage(X17,X12,X2,c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool))
     => c_Fun_Oinj__on(X12,X17,c_Hilbert__Choice_Oinv__into(X17,X12,c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_surj__imp__inj__inv) ).

fof(fact_rangeI,axiom,
    ! [X17,X9,X2,X12] : hBOOL(hAPP(hAPP(c_member(X12),hAPP(X2,X9)),c_Set_Oimage(X17,X12,X2,c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rangeI) ).

fof(fact_inj__imp__surj__inv,axiom,
    ! [X2,X17,X12] :
      ( c_Fun_Oinj__on(X12,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))
     => c_Set_Oimage(X17,X12,c_Hilbert__Choice_Oinv__into(X12,X17,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__imp__surj__inv) ).

fof(fact_imageI,axiom,
    ! [X2,X17,X14,X9,X12] :
      ( hBOOL(hAPP(hAPP(c_member(X12),X9),X14))
     => hBOOL(hAPP(hAPP(c_member(X17),hAPP(X2,X9)),c_Set_Oimage(X12,X17,X2,X14))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_imageI) ).

fof(fact__096_Ib_M_Aa_J_A_126_058_ALab_096,axiom,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_Ib_M_Aa_J_A_126_058_ALab_096) ).

fof(fact__096_Ia_M_Ab_J_A_126_058_ALba_096,axiom,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lba____)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_Ia_M_Ab_J_A_126_058_ALba_096) ).

fof(fact_range__eqI,axiom,
    ! [X17,X12,X9,X2,X23] :
      ( X23 = hAPP(X2,X9)
     => hBOOL(hAPP(hAPP(c_member(X12),X23),c_Set_Oimage(X17,X12,X2,c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_range__eqI) ).

fof(fact_image__eqI,axiom,
    ! [X12,X14,X17,X9,X2,X23] :
      ( X23 = hAPP(X2,X9)
     => ( hBOOL(hAPP(hAPP(c_member(X17),X9),X14))
       => hBOOL(hAPP(hAPP(c_member(X12),X23),c_Set_Oimage(X17,X12,X2,X14))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__eqI) ).

fof(fact_rev__image__eqI,axiom,
    ! [X17,X2,X23,X14,X9,X12] :
      ( hBOOL(hAPP(hAPP(c_member(X12),X9),X14))
     => ( X23 = hAPP(X2,X9)
       => hBOOL(hAPP(hAPP(c_member(X17),X23),c_Set_Oimage(X12,X17,X2,X14))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__image__eqI) ).

fof(fact_inj__image__eq__iff,axiom,
    ! [X13,X14,X2,X17,X12] :
      ( c_Fun_Oinj__on(X12,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))
     => ( c_Set_Oimage(X12,X17,X2,X14) = c_Set_Oimage(X12,X17,X2,X13)
      <=> X14 = X13 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__image__eq__iff) ).

fof(fact_add__less__imp__less__right,axiom,
    ! [X32,X31,X29,X12] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),X31)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X32),X31)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X29),X32)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__right) ).

fof(fact_add__less__cancel__right,axiom,
    ! [X23,X11,X24,X12] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X24),X11)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X23),X11)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X24),X23)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__right) ).

fof(fact_add__less__imp__less__left,axiom,
    ! [X32,X29,X31,X12] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X31),X29)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X31),X32)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X29),X32)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__left) ).

fof(fact_add__less__cancel__left,axiom,
    ! [X23,X24,X11,X12] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X11),X24)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X11),X23)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X24),X23)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__left) ).

fof(fact_finite__imageD,axiom,
    ! [X14,X2,X17,X12] :
      ( c_Finite__Set_Ofinite(X12,c_Set_Oimage(X17,X12,X2,X14))
     => ( c_Fun_Oinj__on(X17,X12,X2,X14)
       => c_Finite__Set_Ofinite(X17,X14) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__imageD) ).

fof(fact_psubset__trans,axiom,
    ! [X37,X13,X14,X12] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12,tc_HOL_Obool)),X14),X13))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12,tc_HOL_Obool)),X13),X37))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12,tc_HOL_Obool)),X14),X37)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__trans) ).

fof(fact_add__le__cancel__right,axiom,
    ! [X23,X11,X24,X12] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X24),X11)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X23),X11)))
      <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X24),X23)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__right) ).

fof(fact_add__le__imp__le__right,axiom,
    ! [X32,X31,X29,X12] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),X31)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X32),X31)))
       => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X29),X32)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__imp__le__right) ).

fof(fact_add__le__cancel__left,axiom,
    ! [X23,X24,X11,X12] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X11),X24)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X11),X23)))
      <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X24),X23)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__left) ).

fof(fact_add__le__imp__le__left,axiom,
    ! [X32,X29,X31,X12] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X31),X29)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X31),X32)))
       => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X29),X32)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__imp__le__left) ).

fof(fact_insert__subset,axiom,
    ! [X13,X14,X9,X12] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),c_Set_Oinsert(X12,X9,X14)),X13))
    <=> ( hBOOL(hAPP(hAPP(c_member(X12),X9),X13))
        & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X14),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__subset) ).

fof(fact_inv__f__f,axiom,
    ! [X9,X2,X17,X12] :
      ( c_Fun_Oinj__on(X12,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))
     => hAPP(c_Hilbert__Choice_Oinv__into(X12,X17,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)),X2),hAPP(X2,X9)) = X9 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__f__f) ).

fof(fact_inv__f__eq,axiom,
    ! [X8,X9,X2,X17,X12] :
      ( c_Fun_Oinj__on(X12,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))
     => ( hAPP(X2,X9) = X8
       => hAPP(c_Hilbert__Choice_Oinv__into(X12,X17,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)),X2),X8) = X9 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__f__eq) ).

fof(fact_pred__equals__eq,axiom,
    ! [X15,X16,X12] :
      ( hAPP(hAPP(c_COMBC(X12,tc_fun(X12,tc_HOL_Obool),tc_HOL_Obool),c_member(X12)),X16) = hAPP(hAPP(c_COMBC(X12,tc_fun(X12,tc_HOL_Obool),tc_HOL_Obool),c_member(X12)),X15)
    <=> X16 = X15 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__equals__eq) ).

fof(fact_nat__add__left__cancel__less,axiom,
    ! [X10,X50,X53] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X53),X50)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X53),X10)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X50),X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).

fof(fact_inv__into__f__f,axiom,
    ! [X9,X14,X2,X17,X12] :
      ( c_Fun_Oinj__on(X12,X17,X2,X14)
     => ( hBOOL(hAPP(hAPP(c_member(X12),X9),X14))
       => hAPP(c_Hilbert__Choice_Oinv__into(X12,X17,X14,X2),hAPP(X2,X9)) = X9 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__f__f) ).

fof(fact_inv__into__f__eq,axiom,
    ! [X8,X9,X14,X2,X17,X12] :
      ( c_Fun_Oinj__on(X12,X17,X2,X14)
     => ( hBOOL(hAPP(hAPP(c_member(X12),X9),X14))
       => ( hAPP(X2,X9) = X8
         => hAPP(c_Hilbert__Choice_Oinv__into(X12,X17,X14,X2),X8) = X9 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__f__eq) ).

fof(fact_eq__card__imp__inj__on,axiom,
    ! [X2,X17,X14,X12] :
      ( c_Finite__Set_Ofinite(X12,X14)
     => ( c_Finite__Set_Ocard(X17,c_Set_Oimage(X12,X17,X2,X14)) = c_Finite__Set_Ocard(X12,X14)
       => c_Fun_Oinj__on(X12,X17,X2,X14) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__card__imp__inj__on) ).

fof(fact_inj__on__iff__eq__card,axiom,
    ! [X2,X17,X14,X12] :
      ( c_Finite__Set_Ofinite(X12,X14)
     => ( c_Fun_Oinj__on(X12,X17,X2,X14)
      <=> c_Finite__Set_Ocard(X17,c_Set_Oimage(X12,X17,X2,X14)) = c_Finite__Set_Ocard(X12,X14) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__iff__eq__card) ).

fof(fact_insert__mono,axiom,
    ! [X24,X58,X37,X12] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X37),X58))
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),c_Set_Oinsert(X12,X24,X37)),c_Set_Oinsert(X12,X24,X58))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__mono) ).

fof(help_c__COMBB__1,axiom,
    ! [X16,X36,X19,X35,X12,X17] : hAPP(hAPP(c_COMBB(X17,X12,X35,X19),X36),X16) = hAPP(X19,hAPP(X36,X16)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBB__1) ).

fof(fact_add__strict__mono,axiom,
    ! [X30,X31,X32,X29,X12] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X29),X32))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X31),X30))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),X31)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X32),X30))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__mono) ).

fof(fact_image__add__atLeastLessThan,axiom,
    ! [X77,X39,X53] : c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X53),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X39,X77)) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X39),X53),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X77),X53)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__add__atLeastLessThan) ).

fof(fact_nat__add__left__cancel__le,axiom,
    ! [X10,X50,X53] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X53),X50)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X53),X10)))
    <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X50),X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).

fof(fact_add__le__less__mono,axiom,
    ! [X30,X31,X32,X29,X12] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X29),X32))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X31),X30))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),X31)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X32),X30))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__less__mono) ).

fof(fact_add__less__le__mono,axiom,
    ! [X30,X31,X32,X29,X12] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X29),X32))
       => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X31),X30))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),X31)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X32),X30))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__le__mono) ).

fof(fact_subset__psubset__trans,axiom,
    ! [X37,X13,X14,X12] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X14),X13))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12,tc_HOL_Obool)),X13),X37))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12,tc_HOL_Obool)),X14),X37)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__psubset__trans) ).

fof(fact_psubset__subset__trans,axiom,
    ! [X37,X13,X14,X12] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12,tc_HOL_Obool)),X14),X13))
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X13),X37))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12,tc_HOL_Obool)),X14),X37)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__subset__trans) ).

fof(fact_less__eq__nat_Osimps_I2_J,axiom,
    ! [X10,X50] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X50)),X10))
    <=> hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X50),X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I2_J) ).

fof(fact_insert__image,axiom,
    ! [X2,X17,X14,X9,X12] :
      ( hBOOL(hAPP(hAPP(c_member(X12),X9),X14))
     => c_Set_Oinsert(X17,hAPP(X2,X9),c_Set_Oimage(X12,X17,X2,X14)) = c_Set_Oimage(X12,X17,X2,X14) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__image) ).

fof(fact_card__psubset,axiom,
    ! [X14,X13,X12] :
      ( c_Finite__Set_Ofinite(X12,X13)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X14),X13))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X12,X14)),c_Finite__Set_Ocard(X12,X13)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12,tc_HOL_Obool)),X14),X13)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__psubset) ).

fof(fact_add__mono,axiom,
    ! [X30,X31,X32,X29,X12] :
      ( class_Groups_Oordered__ab__semigroup__add(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X29),X32))
       => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X31),X30))
         => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),X31)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X32),X30))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mono) ).

fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
    ! [X24,X12] :
      ( class_Groups_Olinordered__ab__group__add(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X24),X24)),c_Groups_Ozero__class_Ozero(X12)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X24),c_Groups_Ozero__class_Ozero(X12))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).

fof(fact_even__less__0__iff,axiom,
    ! [X24,X12] :
      ( class_Rings_Olinordered__idom(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X24),X24)),c_Groups_Ozero__class_Ozero(X12)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X24),c_Groups_Ozero__class_Ozero(X12))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_even__less__0__iff) ).

fof(fact_add__less__mono,axiom,
    ! [X47,X45,X48,X49] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X49),X48))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),X47))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X49),X45)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X48),X47))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono) ).

fof(fact_image__insert,axiom,
    ! [X13,X24,X2,X12,X17] : c_Set_Oimage(X17,X12,X2,c_Set_Oinsert(X17,X24,X13)) = c_Set_Oinsert(X12,hAPP(X2,X24),c_Set_Oimage(X17,X12,X2,X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__insert) ).

fof(fact_finite__UNIV__surj__inj,axiom,
    ! [X2,X12] :
      ( c_Finite__Set_Ofinite(X12,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))
     => ( c_Set_Oimage(X12,X12,X2,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool))
       => c_Fun_Oinj__on(X12,X12,X2,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__UNIV__surj__inj) ).

fof(fact_subset__inj__on,axiom,
    ! [X14,X13,X2,X17,X12] :
      ( c_Fun_Oinj__on(X12,X17,X2,X13)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X14),X13))
       => c_Fun_Oinj__on(X12,X17,X2,X14) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__inj__on) ).

fof(fact_card__image,axiom,
    ! [X14,X2,X17,X12] :
      ( c_Fun_Oinj__on(X12,X17,X2,X14)
     => c_Finite__Set_Ocard(X17,c_Set_Oimage(X12,X17,X2,X14)) = c_Finite__Set_Ocard(X12,X14) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__image) ).

fof(fact_add__neg__neg,axiom,
    ! [X32,X29,X12] :
      ( class_Groups_Oordered__comm__monoid__add(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X29),c_Groups_Ozero__class_Ozero(X12)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X32),c_Groups_Ozero__class_Ozero(X12)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),X32)),c_Groups_Ozero__class_Ozero(X12))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__neg__neg) ).

fof(fact_Ints__add,axiom,
    ! [X23,X24,X12] :
      ( class_Rings_Oring__1(X12)
     => ( hBOOL(hAPP(hAPP(c_member(X12),X24),c_Int_Oring__1__class_OInts(X12)))
       => ( hBOOL(hAPP(hAPP(c_member(X12),X23),c_Int_Oring__1__class_OInts(X12)))
         => hBOOL(hAPP(hAPP(c_member(X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X24),X23)),c_Int_Oring__1__class_OInts(X12))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__add) ).

fof(fact_finite__UNIV__inj__surj,axiom,
    ! [X2,X12] :
      ( c_Finite__Set_Ofinite(X12,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))
     => ( c_Fun_Oinj__on(X12,X12,X2,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))
       => c_Set_Oimage(X12,X12,X2,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__UNIV__inj__surj) ).

fof(fact_add__strict__right__mono,axiom,
    ! [X31,X32,X29,X12] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X29),X32))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),X31)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X32),X31))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).

fof(fact_add__strict__left__mono,axiom,
    ! [X31,X32,X29,X12] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X29),X32))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X31),X29)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X31),X32))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__left__mono) ).

fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
    ! [X24,X12] :
      ( class_Groups_Olinordered__ab__group__add(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X24),X24)),c_Groups_Ozero__class_Ozero(X12)))
      <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X24),c_Groups_Ozero__class_Ozero(X12))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).

fof(fact_add__nonpos__neg,axiom,
    ! [X32,X29,X12] :
      ( class_Groups_Oordered__comm__monoid__add(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X29),c_Groups_Ozero__class_Ozero(X12)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X32),c_Groups_Ozero__class_Ozero(X12)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),X32)),c_Groups_Ozero__class_Ozero(X12))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonpos__neg) ).

fof(fact_add__neg__nonpos,axiom,
    ! [X32,X29,X12] :
      ( class_Groups_Oordered__comm__monoid__add(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X29),c_Groups_Ozero__class_Ozero(X12)))
       => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X32),c_Groups_Ozero__class_Ozero(X12)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),X32)),c_Groups_Ozero__class_Ozero(X12))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__neg__nonpos) ).

fof(fact_add__le__mono,axiom,
    ! [X47,X45,X48,X49] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X49),X48))
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X45),X47))
       => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X49),X45)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X48),X47))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono) ).

fof(fact_finite__Plus__iff,axiom,
    ! [X13,X14,X17,X12] :
      ( c_Finite__Set_Ofinite(tc_sum(X12,X17),c_Sum__Type_OPlus(X12,X17,X14,X13))
    <=> ( c_Finite__Set_Ofinite(X12,X14)
        & c_Finite__Set_Ofinite(X17,X13) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Plus__iff) ).

fof(fact_finite__PlusD_I1_J,axiom,
    ! [X13,X14,X17,X12] :
      ( c_Finite__Set_Ofinite(tc_sum(X12,X17),c_Sum__Type_OPlus(X12,X17,X14,X13))
     => c_Finite__Set_Ofinite(X12,X14) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__PlusD_I1_J) ).

fof(fact_finite__PlusD_I2_J,axiom,
    ! [X13,X14,X17,X12] :
      ( c_Finite__Set_Ofinite(tc_sum(X12,X17),c_Sum__Type_OPlus(X12,X17,X14,X13))
     => c_Finite__Set_Ofinite(X17,X13) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__PlusD_I2_J) ).

fof(fact_add__right__mono,axiom,
    ! [X31,X32,X29,X12] :
      ( class_Groups_Oordered__ab__semigroup__add(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X29),X32))
       => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),X31)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X32),X31))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__mono) ).

fof(fact_add__left__mono,axiom,
    ! [X31,X32,X29,X12] :
      ( class_Groups_Oordered__ab__semigroup__add(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X29),X32))
       => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X31),X29)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X31),X32))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__mono) ).

fof(fact_add__lessD1,axiom,
    ! [X45,X48,X49] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X49),X48)),X45))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X49),X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__lessD1) ).

fof(fact_add__nonpos__nonpos,axiom,
    ! [X32,X29,X12] :
      ( class_Groups_Oordered__comm__monoid__add(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X29),c_Groups_Ozero__class_Ozero(X12)))
       => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X32),c_Groups_Ozero__class_Ozero(X12)))
         => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),X32)),c_Groups_Ozero__class_Ozero(X12))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonpos__nonpos) ).

fof(fact_predicate2D,axiom,
    ! [X8,X9,X36,X19,X17,X12] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_fun(X17,tc_HOL_Obool)),X19),X36))
     => ( hBOOL(hAPP(hAPP(X19,X9),X8))
       => hBOOL(hAPP(hAPP(X36,X9),X8)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_predicate2D) ).

fof(fact_rev__predicate2D,axiom,
    ! [X36,X17,X12,X8,X9,X19] :
      ( hBOOL(hAPP(hAPP(X19,X9),X8))
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_fun(X17,tc_HOL_Obool)),X19),X36))
       => hBOOL(hAPP(hAPP(X36,X9),X8)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__predicate2D) ).

fof(fact_add__less__mono1,axiom,
    ! [X45,X48,X49] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X49),X48))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X49),X45)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X48),X45))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono1) ).

fof(fact_inj__on__iff,axiom,
    ! [X8,X9,X14,X2,X17,X12] :
      ( c_Fun_Oinj__on(X12,X17,X2,X14)
     => ( hBOOL(hAPP(hAPP(c_member(X12),X9),X14))
       => ( hBOOL(hAPP(hAPP(c_member(X12),X8),X14))
         => ( hAPP(X2,X9) = hAPP(X2,X8)
          <=> X9 = X8 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__iff) ).

fof(fact_inj__on__contraD,axiom,
    ! [X8,X9,X14,X2,X17,X12] :
      ( c_Fun_Oinj__on(X12,X17,X2,X14)
     => ( X9 != X8
       => ( hBOOL(hAPP(hAPP(c_member(X12),X9),X14))
         => ( hBOOL(hAPP(hAPP(c_member(X12),X8),X14))
           => hAPP(X2,X9) != hAPP(X2,X8) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__contraD) ).

fof(fact_inj__onD,axiom,
    ! [X8,X9,X14,X2,X17,X12] :
      ( c_Fun_Oinj__on(X12,X17,X2,X14)
     => ( hAPP(X2,X9) = hAPP(X2,X8)
       => ( hBOOL(hAPP(hAPP(c_member(X12),X9),X14))
         => ( hBOOL(hAPP(hAPP(c_member(X12),X8),X14))
           => X9 = X8 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__onD) ).

fof(fact_add__leD1,axiom,
    ! [X44,X45,X46] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X46),X45)),X44))
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X46),X44)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD1) ).

fof(fact_add__leD2,axiom,
    ! [X44,X45,X46] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X46),X45)),X44))
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X45),X44)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD2) ).

fof(fact_add__pos__pos,axiom,
    ! [X32,X29,X12] :
      ( class_Groups_Oordered__comm__monoid__add(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),c_Groups_Ozero__class_Ozero(X12)),X29))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),c_Groups_Ozero__class_Ozero(X12)),X32))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),c_Groups_Ozero__class_Ozero(X12)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),X32))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pos__pos) ).

fof(fact_ex__nat__less__eq,axiom,
    ! [X19,X10] :
      ( ? [X5] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5),X10))
          & hBOOL(hAPP(X19,X5)) )
    <=> ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X10)))
          & hBOOL(hAPP(X19,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ex__nat__less__eq) ).

fof(fact_add__le__mono1,axiom,
    ! [X45,X48,X49] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X49),X48))
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X49),X45)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X48),X45))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono1) ).

fof(fact_psubsetD,axiom,
    ! [X11,X13,X14,X12] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12,tc_HOL_Obool)),X14),X13))
     => ( hBOOL(hAPP(hAPP(c_member(X12),X11),X14))
       => hBOOL(hAPP(hAPP(c_member(X12),X11),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubsetD) ).

fof(fact_psubset__card__mono,axiom,
    ! [X14,X13,X12] :
      ( c_Finite__Set_Ofinite(X12,X13)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12,tc_HOL_Obool)),X14),X13))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X12,X14)),c_Finite__Set_Ocard(X12,X13))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__card__mono) ).

fof(fact_inj__on__add__nat,axiom,
    ! [X54,X53] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X53),X54),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__add__nat) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
    ! [X30,X31,X32,X29,X12] :
      ( class_Rings_Ocomm__semiring__1(X12)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),X32)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X31),X30)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),X31)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X32),X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).

fof(fact_subset__trans,axiom,
    ! [X37,X13,X14,X12] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X14),X13))
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X13),X37))
       => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X14),X37)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__trans) ).

fof(fact_add__nonneg__pos,axiom,
    ! [X32,X29,X12] :
      ( class_Groups_Oordered__comm__monoid__add(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,c_Groups_Ozero__class_Ozero(X12)),X29))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),c_Groups_Ozero__class_Ozero(X12)),X32))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),c_Groups_Ozero__class_Ozero(X12)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),X32))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__pos) ).

fof(fact_add__pos__nonneg,axiom,
    ! [X32,X29,X12] :
      ( class_Groups_Oordered__comm__monoid__add(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),c_Groups_Ozero__class_Ozero(X12)),X29))
       => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,c_Groups_Ozero__class_Ozero(X12)),X32))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),c_Groups_Ozero__class_Ozero(X12)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),X32))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pos__nonneg) ).

fof(fact_card__Plus__conv__if,axiom,
    ! [X13,X17,X14,X12] :
      ( ( ( c_Finite__Set_Ofinite(X12,X14)
          & c_Finite__Set_Ofinite(X17,X13) )
       => c_Finite__Set_Ocard(tc_sum(X12,X17),c_Sum__Type_OPlus(X12,X17,X14,X13)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Finite__Set_Ocard(X12,X14)),c_Finite__Set_Ocard(X17,X13)) )
      & ( ~ ( c_Finite__Set_Ofinite(X12,X14)
            & c_Finite__Set_Ofinite(X17,X13) )
       => c_Finite__Set_Ocard(tc_sum(X12,X17),c_Sum__Type_OPlus(X12,X17,X14,X13)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Plus__conv__if) ).

fof(fact_card__Plus,axiom,
    ! [X13,X17,X14,X12] :
      ( c_Finite__Set_Ofinite(X12,X14)
     => ( c_Finite__Set_Ofinite(X17,X13)
       => c_Finite__Set_Ocard(tc_sum(X12,X17),c_Sum__Type_OPlus(X12,X17,X14,X13)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Finite__Set_Ocard(X12,X14)),c_Finite__Set_Ocard(X17,X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Plus) ).

fof(fact_pos__add__strict,axiom,
    ! [X31,X32,X29,X12] :
      ( class_Rings_Olinordered__semidom(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),c_Groups_Ozero__class_Ozero(X12)),X29))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X32),X31))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X32),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),X31))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__add__strict) ).

fof(fact_card__insert__le,axiom,
    ! [X9,X14,X12] :
      ( c_Finite__Set_Ofinite(X12,X14)
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X12,X14)),c_Finite__Set_Ocard(X12,c_Set_Oinsert(X12,X9,X14)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__insert__le) ).

fof(fact_Ints__odd__nonzero,axiom,
    ! [X24,X12] :
      ( class_Int_Oring__char__0(X12)
     => ( hBOOL(hAPP(hAPP(c_member(X12),X24),c_Int_Oring__1__class_OInts(X12)))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),c_Groups_Oone__class_Oone(X12)),X24)),X24) != c_Groups_Ozero__class_Ozero(X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__odd__nonzero) ).

fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
    ! [X24,X12] :
      ( class_Groups_Olinordered__ab__group__add(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),c_Groups_Ozero__class_Ozero(X12)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X24),X24)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),c_Groups_Ozero__class_Ozero(X12)),X24)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).

fof(fact_add__gr__0,axiom,
    ! [X10,X50] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X50),X10)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X50))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__gr__0) ).

fof(fact_card__seteq,axiom,
    ! [X14,X13,X12] :
      ( c_Finite__Set_Ofinite(X12,X13)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X14),X13))
       => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X12,X13)),c_Finite__Set_Ocard(X12,X14)))
         => X14 = X13 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__seteq) ).

fof(fact_subset__insertI2,axiom,
    ! [X23,X13,X14,X12] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X14),X13))
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X14),c_Set_Oinsert(X12,X23,X13))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__insertI2) ).

fof(fact_add__strict__increasing2,axiom,
    ! [X31,X32,X29,X12] :
      ( class_Groups_Oordered__comm__monoid__add(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,c_Groups_Ozero__class_Ozero(X12)),X29))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X32),X31))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X32),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),X31))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__increasing2) ).

fof(fact_add__strict__increasing,axiom,
    ! [X31,X32,X29,X12] :
      ( class_Groups_Oordered__comm__monoid__add(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),c_Groups_Ozero__class_Ozero(X12)),X29))
       => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X32),X31))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X32),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),X31))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__increasing) ).

fof(fact_add__nonneg__nonneg,axiom,
    ! [X32,X29,X12] :
      ( class_Groups_Oordered__comm__monoid__add(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,c_Groups_Ozero__class_Ozero(X12)),X29))
       => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,c_Groups_Ozero__class_Ozero(X12)),X32))
         => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,c_Groups_Ozero__class_Ozero(X12)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),X32))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__nonneg) ).

fof(fact_psubset__imp__subset,axiom,
    ! [X13,X14,X12] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12,tc_HOL_Obool)),X14),X13))
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X14),X13)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__imp__subset) ).

fof(fact_subset__iff__psubset__eq,axiom,
    ! [X13,X14,X12] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X14),X13))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12,tc_HOL_Obool)),X14),X13))
        | X14 = X13 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__iff__psubset__eq) ).

fof(fact_psubset__eq,axiom,
    ! [X13,X14,X12] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12,tc_HOL_Obool)),X14),X13))
    <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X14),X13))
        & X14 != X13 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__eq) ).

fof(fact_insert__iff,axiom,
    ! [X14,X23,X24,X12] :
      ( hBOOL(hAPP(hAPP(c_member(X12),X24),c_Set_Oinsert(X12,X23,X14)))
    <=> ( X24 = X23
        | hBOOL(hAPP(hAPP(c_member(X12),X24),X14)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__iff) ).

fof(fact_insertE,axiom,
    ! [X14,X23,X24,X12] :
      ( hBOOL(hAPP(hAPP(c_member(X12),X24),c_Set_Oinsert(X12,X23,X14)))
     => ( X24 != X23
       => hBOOL(hAPP(hAPP(c_member(X12),X24),X14)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertE) ).

fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
    ! [X24,X12] :
      ( class_Groups_Olinordered__ab__group__add(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,c_Groups_Ozero__class_Ozero(X12)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X24),X24)))
      <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,c_Groups_Ozero__class_Ozero(X12)),X24)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).

fof(fact_Pi__UNIV,axiom,
    ! [X14,X17,X12] : c_FuncSet_OPi(X12,X17,X14,hAPP(c_COMBK(tc_fun(X17,tc_HOL_Obool),X12),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X12,X17),tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__UNIV) ).

fof(fact_add__increasing,axiom,
    ! [X31,X32,X29,X12] :
      ( class_Groups_Oordered__comm__monoid__add(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,c_Groups_Ozero__class_Ozero(X12)),X29))
       => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X32),X31))
         => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X32),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),X31))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__increasing) ).

fof(fact_add__increasing2,axiom,
    ! [X29,X32,X31,X12] :
      ( class_Groups_Oordered__comm__monoid__add(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,c_Groups_Ozero__class_Ozero(X12)),X31))
       => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X32),X29))
         => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X32),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),X31))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__increasing2) ).

fof(fact_finite__Plus,axiom,
    ! [X13,X17,X14,X12] :
      ( c_Finite__Set_Ofinite(X12,X14)
     => ( c_Finite__Set_Ofinite(X17,X13)
       => c_Finite__Set_Ofinite(tc_sum(X12,X17),c_Sum__Type_OPlus(X12,X17,X14,X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Plus) ).

fof(help_c__COMBC__1,axiom,
    ! [X16,X36,X19,X12,X35,X17] : hAPP(hAPP(hAPP(c_COMBC(X17,X35,X12),X19),X36),X16) = hAPP(hAPP(X19,X16),X36),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBC__1) ).

fof(fact_set__eq__subset,axiom,
    ! [X12,X13,X14] :
      ( X14 = X13
    <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X14),X13))
        & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X13),X14)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__eq__subset) ).

fof(fact_equalityI,axiom,
    ! [X13,X14,X12] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X14),X13))
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X13),X14))
       => X14 = X13 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityI) ).

fof(fact_set__rev__mp,axiom,
    ! [X13,X14,X9,X12] :
      ( hBOOL(hAPP(hAPP(c_member(X12),X9),X14))
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X14),X13))
       => hBOOL(hAPP(hAPP(c_member(X12),X9),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__rev__mp) ).

fof(fact_set__mp,axiom,
    ! [X9,X13,X14,X12] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X14),X13))
     => ( hBOOL(hAPP(hAPP(c_member(X12),X9),X14))
       => hBOOL(hAPP(hAPP(c_member(X12),X9),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__mp) ).

fof(fact_in__mono,axiom,
    ! [X9,X13,X14,X12] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X14),X13))
     => ( hBOOL(hAPP(hAPP(c_member(X12),X9),X14))
       => hBOOL(hAPP(hAPP(c_member(X12),X9),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__mono) ).

fof(fact_subsetD,axiom,
    ! [X11,X13,X14,X12] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X14),X13))
     => ( hBOOL(hAPP(hAPP(c_member(X12),X11),X14))
       => hBOOL(hAPP(hAPP(c_member(X12),X11),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subsetD) ).

fof(fact_le__funD,axiom,
    ! [X9,X1,X2,X12,X17] :
      ( class_Orderings_Oord(X17)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,X17),X2),X1))
       => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X17,hAPP(X2,X9)),hAPP(X1,X9))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funD) ).

fof(fact_le__funE,axiom,
    ! [X9,X1,X2,X12,X17] :
      ( class_Orderings_Oord(X17)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,X17),X2),X1))
       => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X17,hAPP(X2,X9)),hAPP(X1,X9))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funE) ).

fof(fact_finite__imageI,axiom,
    ! [X65,X17,X40,X12] :
      ( c_Finite__Set_Ofinite(X12,X40)
     => c_Finite__Set_Ofinite(X17,c_Set_Oimage(X12,X17,X65,X40)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__imageI) ).

fof(fact_card__mono,axiom,
    ! [X14,X13,X12] :
      ( c_Finite__Set_Ofinite(X12,X13)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X14),X13))
       => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X12,X14)),c_Finite__Set_Ocard(X12,X13))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__mono) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
    ! [X31,X32,X29,X12] :
      ( class_Rings_Ocomm__semiring__1(X12)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),X32)),X31) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),X31)),X32) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).

fof(fact_inj__eq,axiom,
    ! [X8,X9,X2,X17,X12] :
      ( c_Fun_Oinj__on(X12,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))
     => ( hAPP(X2,X9) = hAPP(X2,X8)
      <=> X9 = X8 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__eq) ).

fof(fact_injD,axiom,
    ! [X8,X9,X2,X17,X12] :
      ( c_Fun_Oinj__on(X12,X17,X2,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))
     => ( hAPP(X2,X9) = hAPP(X2,X8)
       => X9 = X8 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_injD) ).

fof(fact_atLeastLessThan__eq__iff,axiom,
    ! [X78,X11,X23,X24,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X24),X23))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X11),X78))
         => ( c_SetInterval_Oord__class_OatLeastLessThan(X12,X24,X23) = c_SetInterval_Oord__class_OatLeastLessThan(X12,X11,X78)
          <=> ( X24 = X11
              & X23 = X78 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThan__eq__iff) ).

fof(fact_atLeastLessThan__inj_I1_J,axiom,
    ! [X78,X11,X23,X24,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( c_SetInterval_Oord__class_OatLeastLessThan(X12,X24,X23) = c_SetInterval_Oord__class_OatLeastLessThan(X12,X11,X78)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X24),X23))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X11),X78))
           => X24 = X11 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThan__inj_I1_J) ).

fof(fact_atLeastLessThan__inj_I2_J,axiom,
    ! [X78,X11,X23,X24,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( c_SetInterval_Oord__class_OatLeastLessThan(X12,X24,X23) = c_SetInterval_Oord__class_OatLeastLessThan(X12,X11,X78)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X24),X23))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X11),X78))
           => X23 = X78 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThan__inj_I2_J) ).

fof(fact_less__add__Suc1,axiom,
    ! [X46,X49] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X49),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X49),X46)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc1) ).

fof(fact_less__add__Suc2,axiom,
    ! [X46,X49] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X49),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X46),X49)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc2) ).

fof(fact_insertI2,axiom,
    ! [X23,X13,X24,X12] :
      ( hBOOL(hAPP(hAPP(c_member(X12),X24),X13))
     => hBOOL(hAPP(hAPP(c_member(X12),X24),c_Set_Oinsert(X12,X23,X13))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertI2) ).

fof(fact_less__trans__Suc,axiom,
    ! [X45,X48,X49] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X49),X48))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X48),X45))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X49)),X45)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__trans__Suc) ).

fof(fact_finite__UNIV__card__ge__0,axiom,
    ! [X12] :
      ( c_Finite__Set_Ofinite(X12,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Finite__Set_Ocard(X12,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__UNIV__card__ge__0) ).

fof(fact__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_1230_O_O_060N_125_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
    ~ ! [X73] :
        ( c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,X73,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))
       => c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,X73,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) != c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_1230_O_O_060N_125_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).

fof(fact_Suc__less__eq,axiom,
    ! [X10,X50] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X50)),hAPP(c_Nat_OSuc,X10)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X50),X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__less__eq) ).

fof(fact_Suc__less__SucD,axiom,
    ! [X44,X46] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X46)),hAPP(c_Nat_OSuc,X44)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),X44)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__less__SucD) ).

fof(fact_finite__fun__UNIVD1,axiom,
    ! [X17,X12] :
      ( c_Finite__Set_Ofinite(tc_fun(X12,X17),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X12,X17),tc_HOL_Obool)))
     => ( c_Finite__Set_Ocard(X17,c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool))) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
       => c_Finite__Set_Ofinite(X12,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__fun__UNIVD1) ).

fof(fact_order__less__trans,axiom,
    ! [X20,X21,X22,X12] :
      ( class_Orderings_Opreorder(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X22),X21))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X21),X20))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X22),X20)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__trans) ).

fof(fact_xt1_I10_J,axiom,
    ! [X20,X22,X21,X12] :
      ( class_Orderings_Oorder(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X21),X22))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X20),X21))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X20),X22)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I10_J) ).

fof(fact_image__Suc__atLeastLessThan,axiom,
    ! [X77,X39] : c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X39,X77)) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X39),hAPP(c_Nat_OSuc,X77)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__Suc__atLeastLessThan) ).

fof(fact_add__nonneg__eq__0__iff,axiom,
    ! [X8,X9,X12] :
      ( class_Groups_Oordered__comm__monoid__add(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,c_Groups_Ozero__class_Ozero(X12)),X9))
       => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,c_Groups_Ozero__class_Ozero(X12)),X8))
         => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X9),X8) = c_Groups_Ozero__class_Ozero(X12)
          <=> ( X9 = c_Groups_Ozero__class_Ozero(X12)
              & X8 = c_Groups_Ozero__class_Ozero(X12) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__eq__0__iff) ).

fof(fact_UNIV__Plus__UNIV,axiom,
    ! [X17,X12] : c_Sum__Type_OPlus(X12,X17,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X12,X17),tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNIV__Plus__UNIV) ).

fof(fact_trans__less__add1,axiom,
    ! [X46,X48,X49] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X49),X48))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X49),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X48),X46))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add1) ).

fof(fact_termination__basic__simps_I1_J,axiom,
    ! [X20,X21,X22] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22),X21))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X20))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).

fof(fact_trans__less__add2,axiom,
    ! [X46,X48,X49] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X49),X48))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X49),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X46),X48))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add2) ).

fof(fact_termination__basic__simps_I2_J,axiom,
    ! [X21,X20,X22] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22),X20))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X20))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).

fof(fact_less__Suc__eq__0__disj,axiom,
    ! [X10,X50] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X50),hAPP(c_Nat_OSuc,X10)))
    <=> ( X50 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ? [X63] :
            ( X50 = hAPP(c_Nat_OSuc,X63)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X63),X10)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__0__disj) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
    ! [X31,X32,X29,X12] :
      ( class_Rings_Ocomm__semiring__1(X12)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),X32)),X31) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X32),X31)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).

fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
    ! [X31,X32,X29,X12] :
      ( class_Groups_Oab__semigroup__add(X12)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),X32)),X31) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X32),X31)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
    ! [X30,X31,X29,X12] :
      ( class_Rings_Ocomm__semiring__1(X12)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X31),X30)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),X31)),X30) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).

fof(fact_insert__code,axiom,
    ! [X9,X14,X8,X12] :
      ( hBOOL(hAPP(c_Set_Oinsert(X12,X8,X14),X9))
    <=> ( X8 = X9
        | hBOOL(hAPP(X14,X9)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__code) ).

fof(fact_zero__less__two,axiom,
    ! [X12] :
      ( class_Rings_Olinordered__semidom(X12)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),c_Groups_Ozero__class_Ozero(X12)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),c_Groups_Oone__class_Oone(X12)),c_Groups_Oone__class_Oone(X12)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__two) ).

fof(fact_Suc__le__mono,axiom,
    ! [X50,X10] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X10)),hAPP(c_Nat_OSuc,X50)))
    <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10),X50)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__mono) ).

fof(fact_order__le__less__trans,axiom,
    ! [X20,X21,X22,X12] :
      ( class_Orderings_Opreorder(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X22),X21))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X21),X20))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X22),X20)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less__trans) ).

fof(fact_order__less__le__trans,axiom,
    ! [X20,X21,X22,X12] :
      ( class_Orderings_Opreorder(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X22),X21))
       => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X21),X20))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X22),X20)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le__trans) ).

fof(fact_xt1_I8_J,axiom,
    ! [X20,X22,X21,X12] :
      ( class_Orderings_Oorder(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X21),X22))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X20),X21))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X20),X22)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I8_J) ).

fof(fact_xt1_I7_J,axiom,
    ! [X20,X22,X21,X12] :
      ( class_Orderings_Oorder(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X21),X22))
       => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X20),X21))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X20),X22)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I7_J) ).

fof(fact_finite__Plus__UNIV__iff,axiom,
    ! [X17,X12] :
      ( c_Finite__Set_Ofinite(tc_sum(X12,X17),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X12,X17),tc_HOL_Obool)))
    <=> ( c_Finite__Set_Ofinite(X12,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))
        & c_Finite__Set_Ofinite(X17,c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Plus__UNIV__iff) ).

fof(fact_finite__Prod__UNIV,axiom,
    ! [X17,X12] :
      ( c_Finite__Set_Ofinite(X12,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))
     => ( c_Finite__Set_Ofinite(X17,c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool)))
       => c_Finite__Set_Ofinite(tc_prod(X12,X17),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X12,X17),tc_HOL_Obool))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Prod__UNIV) ).

fof(fact_less__add__eq__less,axiom,
    ! [X44,X46,X47,X45] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),X47))
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X46),X47) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X45),X44)
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),X44)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__eq__less) ).

fof(fact_subset__insertI,axiom,
    ! [X24,X13,X12] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X13),c_Set_Oinsert(X12,X24,X13))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__insertI) ).

fof(fact_Suc__lessD,axiom,
    ! [X44,X46] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X46)),X44))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),X44)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessD) ).

fof(fact_Suc__mono,axiom,
    ! [X44,X46] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),X44))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X46)),hAPP(c_Nat_OSuc,X44))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mono) ).

fof(fact_trans__le__add1,axiom,
    ! [X46,X48,X49] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X49),X48))
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X49),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X48),X46))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add1) ).

fof(fact_termination__basic__simps_I3_J,axiom,
    ! [X20,X21,X22] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22),X21))
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X20))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I3_J) ).

fof(fact_trans__le__add2,axiom,
    ! [X46,X48,X49] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X49),X48))
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X49),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X46),X48))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add2) ).

fof(fact_termination__basic__simps_I4_J,axiom,
    ! [X21,X20,X22] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22),X20))
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X20))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I4_J) ).

fof(fact_finite__fun__UNIVD2,axiom,
    ! [X17,X12] :
      ( c_Finite__Set_Ofinite(tc_fun(X12,X17),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X12,X17),tc_HOL_Obool)))
     => c_Finite__Set_Ofinite(X17,c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__fun__UNIVD2) ).

fof(fact_nat__add__assoc,axiom,
    ! [X45,X44,X46] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X46),X44)),X45) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X46),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),X45)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__assoc) ).

fof(fact_Suc__le__lessD,axiom,
    ! [X44,X46] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X46)),X44))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),X44)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__lessD) ).

fof(fact_Suc__le__eq,axiom,
    ! [X10,X50] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X50)),X10))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X50),X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__eq) ).

fof(fact_less__eq__Suc__le,axiom,
    ! [X50,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10),X50))
    <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X10)),X50)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__Suc__le) ).

fof(fact_predicate1D,axiom,
    ! [X9,X36,X19,X12] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X19),X36))
     => ( hBOOL(hAPP(X19,X9))
       => hBOOL(hAPP(X36,X9)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_predicate1D) ).

fof(fact_rev__predicate1D,axiom,
    ! [X36,X12,X9,X19] :
      ( hBOOL(hAPP(X19,X9))
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X19),X36))
       => hBOOL(hAPP(X36,X9)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__predicate1D) ).

fof(fact_order__trans,axiom,
    ! [X20,X21,X22,X12] :
      ( class_Orderings_Opreorder(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X22),X21))
       => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X21),X20))
         => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X22),X20)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__trans) ).

fof(fact_xt1_I6_J,axiom,
    ! [X20,X22,X21,X12] :
      ( class_Orderings_Oorder(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X21),X22))
       => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X20),X21))
         => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X20),X22)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I6_J) ).

fof(fact_Suc__lessI,axiom,
    ! [X44,X46] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),X44))
     => ( hAPP(c_Nat_OSuc,X46) != X44
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X46)),X44)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessI) ).

fof(fact_less__add__one,axiom,
    ! [X29,X12] :
      ( class_Rings_Olinordered__semidom(X12)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X29),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),c_Groups_Oone__class_Oone(X12)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__one) ).

fof(fact_le__less__Suc__eq,axiom,
    ! [X10,X50] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X50),X10))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10),hAPP(c_Nat_OSuc,X50)))
      <=> X10 = X50 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__less__Suc__eq) ).

fof(fact_Suc__leD,axiom,
    ! [X44,X46] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X46)),X44))
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X46),X44)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__leD) ).

fof(fact_finite__nat__set__iff__bounded,axiom,
    ! [X54] :
      ( c_Finite__Set_Ofinite(tc_Nat_Onat,X54)
    <=> ? [X5] :
        ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),X54))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X5)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded) ).

fof(fact_insert__commute,axiom,
    ! [X14,X8,X9,X12] : c_Set_Oinsert(X12,X9,c_Set_Oinsert(X12,X8,X14)) = c_Set_Oinsert(X12,X8,c_Set_Oinsert(X12,X9,X14)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__commute) ).

fof(fact_insertI1,axiom,
    ! [X13,X24,X12] : hBOOL(hAPP(hAPP(c_member(X12),X24),c_Set_Oinsert(X12,X24,X13))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertI1) ).

fof(fact_less__Suc__eq,axiom,
    ! [X10,X50] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X50),hAPP(c_Nat_OSuc,X10)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X50),X10))
        | X50 = X10 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq) ).

fof(fact_Suc__leI,axiom,
    ! [X44,X46] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),X44))
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X46)),X44)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__leI) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
    ! [X30,X31,X29,X12] :
      ( class_Rings_Ocomm__semiring__1(X12)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X31),X30)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X31),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).

fof(fact_le__trans,axiom,
    ! [X45,X48,X49] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X49),X48))
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48),X45))
       => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X49),X45)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__trans) ).

fof(fact_finite__subset,axiom,
    ! [X13,X14,X12] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X14),X13))
     => ( c_Finite__Set_Ofinite(X12,X13)
       => c_Finite__Set_Ofinite(X12,X14) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__subset) ).

fof(fact_rev__finite__subset,axiom,
    ! [X14,X13,X12] :
      ( c_Finite__Set_Ofinite(X12,X13)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X14),X13))
       => c_Finite__Set_Ofinite(X12,X14) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__finite__subset) ).

fof(fact_less__iff__Suc__add,axiom,
    ! [X10,X50] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X50),X10))
    <=> ? [X55] : X10 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X50),X55)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).

fof(fact_less__Suc__eq__le,axiom,
    ! [X10,X50] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X50),hAPP(c_Nat_OSuc,X10)))
    <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X50),X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).

fof(fact_finite__nat__set__iff__bounded__le,axiom,
    ! [X54] :
      ( c_Finite__Set_Ofinite(tc_Nat_Onat,X54)
    <=> ? [X5] :
        ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),X54))
         => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X5)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded__le) ).

fof(fact_less__SucI,axiom,
    ! [X44,X46] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),X44))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),hAPP(c_Nat_OSuc,X44))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__SucI) ).

fof(fact_Ints__double__eq__0__iff,axiom,
    ! [X24,X12] :
      ( class_Int_Oring__char__0(X12)
     => ( hBOOL(hAPP(hAPP(c_member(X12),X24),c_Int_Oring__1__class_OInts(X12)))
       => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X24),X24) = c_Groups_Ozero__class_Ozero(X12)
        <=> X24 = c_Groups_Ozero__class_Ozero(X12) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__double__eq__0__iff) ).

fof(fact_nat__case__Suc,axiom,
    ! [X62,X67,X68,X12] : c_Nat_Onat_Onat__case(X12,X68,X67,hAPP(c_Nat_OSuc,X62)) = hAPP(X67,X62),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__case__Suc) ).

fof(fact_le__Suc__eq,axiom,
    ! [X10,X50] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X50),hAPP(c_Nat_OSuc,X10)))
    <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X50),X10))
        | X50 = hAPP(c_Nat_OSuc,X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__Suc__eq) ).

fof(fact_subset__UNIV,axiom,
    ! [X14,X12] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X14),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__UNIV) ).

fof(fact_nat__less__cases,axiom,
    ! [X19,X10,X50] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X50),X10))
       => hBOOL(hAPP(hAPP(X19,X10),X50)) )
     => ( ( X50 = X10
         => hBOOL(hAPP(hAPP(X19,X10),X50)) )
       => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10),X50))
           => hBOOL(hAPP(hAPP(X19,X10),X50)) )
         => hBOOL(hAPP(hAPP(X19,X10),X50)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__cases) ).

fof(fact_nat__add__left__commute,axiom,
    ! [X20,X21,X22] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X20)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22),X20)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).

fof(fact_order__eq__iff,axiom,
    ! [X8,X9,X12] :
      ( class_Orderings_Oorder(X12)
     => ( X9 = X8
      <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X9),X8))
          & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X8),X9)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__iff) ).

fof(fact_order__antisym__conv,axiom,
    ! [X9,X8,X12] :
      ( class_Orderings_Oorder(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X8),X9))
       => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X9),X8))
        <=> X9 = X8 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym__conv) ).

fof(fact_order__antisym,axiom,
    ! [X21,X22,X12] :
      ( class_Orderings_Oorder(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X22),X21))
       => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X21),X22))
         => X22 = X21 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym) ).

fof(fact_xt1_I5_J,axiom,
    ! [X22,X21,X12] :
      ( class_Orderings_Oorder(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X21),X22))
       => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X22),X21))
         => X22 = X21 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I5_J) ).

fof(fact_card__ge__0__finite,axiom,
    ! [X14,X12] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Finite__Set_Ocard(X12,X14)))
     => c_Finite__Set_Ofinite(X12,X14) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__ge__0__finite) ).

fof(fact_le__imp__less__Suc,axiom,
    ! [X44,X46] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X46),X44))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),hAPP(c_Nat_OSuc,X44))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__less__Suc) ).

fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
    ! [X14,X12] :
      ( c_Finite__Set_Ofinite(X12,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))
     => ( c_Finite__Set_Ocard(X12,X14) = c_Finite__Set_Ocard(X12,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))
       => X14 = c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__eq__UNIV__imp__eq__UNIV) ).

fof(fact_order__le__less,axiom,
    ! [X8,X9,X12] :
      ( class_Orderings_Oorder(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X9),X8))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X9),X8))
          | X9 = X8 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less) ).

fof(fact_order__less__le,axiom,
    ! [X8,X9,X12] :
      ( class_Orderings_Oorder(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X9),X8))
      <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X9),X8))
          & X9 != X8 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le) ).

fof(fact_order__less__imp__le,axiom,
    ! [X21,X22,X12] :
      ( class_Orderings_Opreorder(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X22),X21))
       => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X22),X21)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__le) ).

fof(fact_le__add1,axiom,
    ! [X46,X44] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),X46))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add1) ).

fof(fact_le__add2,axiom,
    ! [X46,X44] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X46),X44))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add2) ).

fof(fact_image__ident,axiom,
    ! [X69,X12] : c_Set_Oimage(X12,X12,c_COMBI(X12),X69) = X69,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__ident) ).

fof(fact_inj__on__id2,axiom,
    ! [X14,X12] : c_Fun_Oinj__on(X12,X12,c_COMBI(X12),X14),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__id2) ).

fof(fact_nat__case__0,axiom,
    ! [X67,X68,X12] : c_Nat_Onat_Onat__case(X12,X68,X67,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X68,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__case__0) ).

fof(fact_xt1_I11_J,axiom,
    ! [X29,X32,X12] :
      ( class_Orderings_Oorder(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X32),X29))
       => ( X29 != X32
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X32),X29)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I11_J) ).

fof(fact_order__le__neq__trans,axiom,
    ! [X32,X29,X12] :
      ( class_Orderings_Oorder(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X29),X32))
       => ( X29 != X32
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X29),X32)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__neq__trans) ).

fof(fact_order__le__imp__less__or__eq,axiom,
    ! [X21,X22,X12] :
      ( class_Orderings_Oorder(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X22),X21))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X22),X21))
          | X22 = X21 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__imp__less__or__eq) ).

fof(fact_order__neq__le__trans,axiom,
    ! [X32,X29,X12] :
      ( class_Orderings_Oorder(X12)
     => ( X29 != X32
       => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X29),X32))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X29),X32)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).

fof(fact_xt1_I12_J,axiom,
    ! [X32,X29,X12] :
      ( class_Orderings_Oorder(X12)
     => ( X29 != X32
       => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X32),X29))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X32),X29)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I12_J) ).

fof(fact_less__Suc0,axiom,
    ! [X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    <=> X10 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc0) ).

fof(fact_inj__Suc,axiom,
    ! [X54] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X54),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__Suc) ).

fof(fact_le__antisym,axiom,
    ! [X44,X46] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X46),X44))
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44),X46))
       => X46 = X44 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__antisym) ).

fof(fact_eq__mem,axiom,
    ! [X8,X9,X12] :
      ( hBOOL(hAPP(hAPP(c_member(X12),X9),hAPP(c_fequal,X8)))
    <=> X9 = X8 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__mem) ).

fof(fact_le__SucI,axiom,
    ! [X44,X46] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X46),X44))
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X46),hAPP(c_Nat_OSuc,X44))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__SucI) ).

fof(fact_nat__less__le,axiom,
    ! [X10,X50] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X50),X10))
    <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X50),X10))
        & X50 != X10 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__le) ).

fof(fact_le__eq__less__or__eq,axiom,
    ! [X10,X50] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X50),X10))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X50),X10))
        | X50 = X10 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).

fof(fact_less__imp__le__nat,axiom,
    ! [X44,X46] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),X44))
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X46),X44)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).

fof(fact_less__or__eq__imp__le,axiom,
    ! [X44,X46] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),X44))
        | X46 = X44 )
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X46),X44)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).

fof(fact_termination__basic__simps_I5_J,axiom,
    ! [X21,X22] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22),X21))
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22),X21)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).

fof(fact_insert__absorb,axiom,
    ! [X14,X24,X12] :
      ( hBOOL(hAPP(hAPP(c_member(X12),X24),X14))
     => c_Set_Oinsert(X12,X24,X14) = X14 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__absorb) ).

fof(fact_linorder__neq__iff,axiom,
    ! [X8,X9,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( X9 != X8
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X9),X8))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X8),X9)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).

fof(fact_linorder__less__linear,axiom,
    ! [X21,X22,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X22),X21))
        | X22 = X21
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X21),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__less__linear) ).

fof(fact_finite__option__UNIV,axiom,
    ! [X12] :
      ( c_Finite__Set_Ofinite(tc_Option_Ooption(X12),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X12),tc_HOL_Obool)))
    <=> c_Finite__Set_Ofinite(X12,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__option__UNIV) ).

fof(fact_le__neq__implies__less,axiom,
    ! [X44,X46] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X46),X44))
     => ( X46 != X44
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),X44)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).

fof(fact_insert__absorb2,axiom,
    ! [X14,X9,X12] : c_Set_Oinsert(X12,X9,c_Set_Oinsert(X12,X9,X14)) = c_Set_Oinsert(X12,X9,X14),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__absorb2) ).

fof(fact_iso__tuple__UNIV__I,axiom,
    ! [X9,X12] : hBOOL(hAPP(hAPP(c_member(X12),X9),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_iso__tuple__UNIV__I) ).

fof(fact_UNIV__I,axiom,
    ! [X9,X12] : hBOOL(hAPP(hAPP(c_member(X12),X9),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNIV__I) ).

fof(fact_finite__insert,axiom,
    ! [X14,X24,X12] :
      ( c_Finite__Set_Ofinite(X12,c_Set_Oinsert(X12,X24,X14))
    <=> c_Finite__Set_Ofinite(X12,X14) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__insert) ).

fof(fact_mem__def,axiom,
    ! [X14,X9,X12] :
      ( hBOOL(hAPP(hAPP(c_member(X12),X9),X14))
    <=> hBOOL(hAPP(X14,X9)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__def) ).

fof(fact_linorder__le__less__linear,axiom,
    ! [X21,X22,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X22),X21))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X21),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).

fof(fact_add__Suc,axiom,
    ! [X44,X46] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X46)),X44) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X46),X44)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc) ).

fof(fact_le__iff__add,axiom,
    ! [X10,X50] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X50),X10))
    <=> ? [X55] : X10 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X50),X55) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__add) ).

fof(fact_nat__neq__iff,axiom,
    ! [X10,X50] :
      ( X50 != X10
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X50),X10))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10),X50)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__neq__iff) ).

fof(fact_gr0__conv__Suc,axiom,
    ! [X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10))
    <=> ? [X5] : X10 = hAPP(c_Nat_OSuc,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).

fof(fact_order__less__imp__not__eq2,axiom,
    ! [X21,X22,X12] :
      ( class_Orderings_Oorder(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X22),X21))
       => X21 != X22 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).

fof(fact_order__less__imp__not__eq,axiom,
    ! [X21,X22,X12] :
      ( class_Orderings_Oorder(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X22),X21))
       => X22 != X21 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).

fof(fact_less__imp__neq,axiom,
    ! [X21,X22,X12] :
      ( class_Orderings_Oorder(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X22),X21))
       => X22 != X21 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__neq) ).

fof(fact_equalityD1,axiom,
    ! [X12,X13,X14] :
      ( X14 = X13
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X14),X13)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityD1) ).

fof(fact_equalityD2,axiom,
    ! [X12,X13,X14] :
      ( X14 = X13
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X13),X14)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityD2) ).

fof(fact_subset__refl,axiom,
    ! [X14,X12] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X14),X14)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__refl) ).

fof(fact_neq0__conv,axiom,
    ! [X10] :
      ( X10 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neq0__conv) ).

fof(fact_add__right__cancel,axiom,
    ! [X11,X24,X23,X12] :
      ( class_Groups_Ocancel__semigroup__add(X12)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X23),X24) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X11),X24)
      <=> X23 = X11 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__cancel) ).

fof(fact_add__right__imp__eq,axiom,
    ! [X31,X29,X32,X12] :
      ( class_Groups_Ocancel__semigroup__add(X12)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X32),X29) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X31),X29)
       => X32 = X31 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__imp__eq) ).

fof(fact_add__imp__eq,axiom,
    ! [X31,X32,X29,X12] :
      ( class_Groups_Ocancel__ab__semigroup__add(X12)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),X32) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),X31)
       => X32 = X31 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__imp__eq) ).

fof(fact_add__left__cancel,axiom,
    ! [X11,X23,X24,X12] :
      ( class_Groups_Ocancel__semigroup__add(X12)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X24),X23) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X24),X11)
      <=> X23 = X11 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__cancel) ).

fof(fact_add__left__imp__eq,axiom,
    ! [X31,X32,X29,X12] :
      ( class_Groups_Ocancel__semigroup__add(X12)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),X32) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),X31)
       => X32 = X31 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).

fof(fact_linorder__linear,axiom,
    ! [X21,X22,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X22),X21))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X21),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__linear) ).

fof(fact_add__Suc__right,axiom,
    ! [X44,X46] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X46),hAPP(c_Nat_OSuc,X44)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X46),X44)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__right) ).

fof(fact_add__Suc__shift,axiom,
    ! [X44,X46] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X46)),X44) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X46),hAPP(c_Nat_OSuc,X44)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__shift) ).

fof(fact_nat_Osize_I4_J,axiom,
    ! [X64] : c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,X64)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_Nat_Onat,X64)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osize_I4_J) ).

fof(fact_gr__implies__not0,axiom,
    ! [X44,X46] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),X44))
     => X44 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr__implies__not0) ).

fof(fact_nat__le__linear,axiom,
    ! [X44,X46] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X46),X44))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44),X46)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__linear) ).

fof(fact_zero__less__Suc,axiom,
    ! [X44] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X44))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__Suc) ).

fof(fact_less__not__refl2,axiom,
    ! [X46,X44] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X46))
     => X46 != X44 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl2) ).

fof(fact_less__not__refl3,axiom,
    ! [X51,X52] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X52),X51))
     => X52 != X51 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl3) ).

fof(fact_zero__less__one,axiom,
    ! [X12] :
      ( class_Rings_Olinordered__semidom(X12)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),c_Groups_Ozero__class_Ozero(X12)),c_Groups_Oone__class_Oone(X12))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__one) ).

fof(fact_Ints__0,axiom,
    ! [X12] :
      ( class_Rings_Oring__1(X12)
     => hBOOL(hAPP(hAPP(c_member(X12),c_Groups_Ozero__class_Ozero(X12)),c_Int_Oring__1__class_OInts(X12))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__0) ).

fof(fact_Ints__1,axiom,
    ! [X12] :
      ( class_Rings_Oring__1(X12)
     => hBOOL(hAPP(hAPP(c_member(X12),c_Groups_Oone__class_Oone(X12)),c_Int_Oring__1__class_OInts(X12))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__1) ).

fof(fact_nat__add__right__cancel,axiom,
    ! [X10,X53,X50] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X50),X53) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10),X53)
    <=> X50 = X10 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).

fof(fact_nat__add__left__cancel,axiom,
    ! [X10,X50,X53] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X53),X50) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X53),X10)
    <=> X50 = X10 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).

fof(fact_finite_OinsertI,axiom,
    ! [X24,X14,X12] :
      ( c_Finite__Set_Ofinite(X12,X14)
     => c_Finite__Set_Ofinite(X12,c_Set_Oinsert(X12,X24,X14)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite_OinsertI) ).

fof(fact_lessI,axiom,
    ! [X44] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),hAPP(c_Nat_OSuc,X44))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessI) ).

fof(fact_top1I,axiom,
    ! [X9,X12] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)),X9)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_top1I) ).

fof(fact_le__0__eq,axiom,
    ! [X10] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    <=> X10 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__0__eq) ).

fof(fact_add__is__1,axiom,
    ! [X10,X50] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X50),X10) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    <=> ( ( X50 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & X10 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( X50 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & X10 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__1) ).

fof(fact_one__is__add,axiom,
    ! [X10,X50] :
      ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X50),X10)
    <=> ( ( X50 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & X10 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( X50 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & X10 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__is__add) ).

fof(fact_ext,axiom,
    ! [X1,X2] :
      ( ! [X3] : hAPP(X2,X3) = hAPP(X1,X3)
     => X2 = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ext) ).

fof(fact_zero__le__one,axiom,
    ! [X12] :
      ( class_Rings_Olinordered__semidom(X12)
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,c_Groups_Ozero__class_Ozero(X12)),c_Groups_Oone__class_Oone(X12))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__one) ).

fof(fact_finite__atLeastLessThan,axiom,
    ! [X75,X76] : c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X76,X75)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__atLeastLessThan) ).

fof(fact_nat_Osize_I2_J,axiom,
    ! [X64] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X64)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(X64)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osize_I2_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
    ! [X31,X29,X12] :
      ( class_Rings_Ocomm__semiring__1(X12)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),X31) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X31),X29) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).

fof(fact_gr0I,axiom,
    ! [X44] :
      ( X44 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X44)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0I) ).

fof(fact_top__greatest,axiom,
    ! [X22,X12] :
      ( class_Orderings_Otop(X12)
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X22),c_Orderings_Otop__class_Otop(X12))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_top__greatest) ).

fof(fact_double__eq__0__iff,axiom,
    ! [X24,X12] :
      ( class_Groups_Olinordered__ab__group__add(X12)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X24),X24) = c_Groups_Ozero__class_Ozero(X12)
      <=> X24 = c_Groups_Ozero__class_Ozero(X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__eq__0__iff) ).

fof(fact_double__zero__sym,axiom,
    ! [X24,X12] :
      ( class_Groups_Olinordered__ab__group__add(X12)
     => ( c_Groups_Ozero__class_Ozero(X12) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X24),X24)
      <=> X24 = c_Groups_Ozero__class_Ozero(X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__zero__sym) ).

fof(fact_add__0__iff,axiom,
    ! [X24,X23,X12] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X12)
     => ( X23 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X23),X24)
      <=> X24 = c_Groups_Ozero__class_Ozero(X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__iff) ).

fof(fact_order__eq__refl,axiom,
    ! [X21,X22,X12] :
      ( class_Orderings_Opreorder(X12)
     => ( X22 = X21
       => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X22),X21)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__refl) ).

fof(help_c__COMBK__1,axiom,
    ! [X82,X81,X17,X12] : hAPP(hAPP(c_COMBK(X12,X17),X81),X82) = X81,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBK__1) ).

fof(fact_nat__add__commute,axiom,
    ! [X44,X46] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X46),X44) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),X46),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__commute) ).

fof(fact_order__refl,axiom,
    ! [X22,X12] :
      ( class_Orderings_Opreorder(X12)
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X22),X22)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__refl) ).

fof(fact_less__eq__nat_Osimps_I1_J,axiom,
    ! [X44] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X44)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).

fof(fact_le0,axiom,
    ! [X44] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X44)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le0) ).

fof(fact_top__apply,axiom,
    ! [X9,X17,X12] :
      ( class_Orderings_Otop(X12)
     => hAPP(c_Orderings_Otop__class_Otop(tc_fun(X17,X12)),X9) = c_Orderings_Otop__class_Otop(X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_top__apply) ).

fof(fact_add__is__0,axiom,
    ! [X10,X50] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X50),X10) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ( X50 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & X10 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__0) ).

fof(fact_eq__imp__le,axiom,
    ! [X44,X46] :
      ( X46 = X44
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X46),X44)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__imp__le) ).

fof(help_c__fequal__2,axiom,
    ! [X8,X9] :
      ( X9 != X8
      | hBOOL(hAPP(hAPP(c_fequal,X9),X8)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__2) ).

fof(fact_add__eq__self__zero,axiom,
    ! [X44,X46] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X46),X44) = X46
     => X44 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).

fof(fact_le__refl,axiom,
    ! [X44] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44),X44)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__refl) ).

fof(fact_finite__UNIV,axiom,
    ! [X12] :
      ( class_Finite__Set_Ofinite(X12)
     => c_Finite__Set_Ofinite(X12,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__UNIV) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
    ! [X29,X12] :
      ( class_Rings_Ocomm__semiring__1(X12)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),c_Groups_Ozero__class_Ozero(X12)),X29) = X29 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).

fof(fact_add__0,axiom,
    ! [X29,X12] :
      ( class_Groups_Ocomm__monoid__add(X12)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),c_Groups_Ozero__class_Ozero(X12)),X29) = X29 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0) ).

fof(fact_add__0__left,axiom,
    ! [X29,X12] :
      ( class_Groups_Omonoid__add(X12)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),c_Groups_Ozero__class_Ozero(X12)),X29) = X29 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__left) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
    ! [X29,X12] :
      ( class_Rings_Ocomm__semiring__1(X12)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),c_Groups_Ozero__class_Ozero(X12)) = X29 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).

fof(fact_add_Ocomm__neutral,axiom,
    ! [X29,X12] :
      ( class_Groups_Ocomm__monoid__add(X12)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),c_Groups_Ozero__class_Ozero(X12)) = X29 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).

fof(fact_add__0__right,axiom,
    ! [X29,X12] :
      ( class_Groups_Omonoid__add(X12)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),c_Groups_Ozero__class_Ozero(X12)) = X29 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__right) ).

fof(fact_Suc__eq__plus1__left,axiom,
    ! [X44] : hAPP(c_Nat_OSuc,X44) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X44),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).

fof(fact_Suc__eq__plus1,axiom,
    ! [X44] : hAPP(c_Nat_OSuc,X44) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).

fof(fact_plus__nat_Oadd__0,axiom,
    ! [X44] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X44) = X44,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).

fof(fact_less__eq__Suc__le__raw,axiom,
    ! [X10] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X10)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__Suc__le__raw) ).

fof(fact_Nat_Oadd__0__right,axiom,
    ! [X46] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X46),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X46,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).

fof(arity_sum__Finite__Set_Ofinite,axiom,
    ! [X80,X79] :
      ( ( class_Finite__Set_Ofinite(X79)
        & class_Finite__Set_Ofinite(X80) )
     => class_Finite__Set_Ofinite(tc_sum(X79,X80)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_sum__Finite__Set_Ofinite) ).

fof(arity_fun__Finite__Set_Ofinite,axiom,
    ! [X80,X79] :
      ( ( class_Finite__Set_Ofinite(X79)
        & class_Finite__Set_Ofinite(X80) )
     => class_Finite__Set_Ofinite(tc_fun(X79,X80)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Finite__Set_Ofinite) ).

fof(arity_prod__Finite__Set_Ofinite,axiom,
    ! [X80,X79] :
      ( ( class_Finite__Set_Ofinite(X79)
        & class_Finite__Set_Ofinite(X80) )
     => class_Finite__Set_Ofinite(tc_prod(X79,X80)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_prod__Finite__Set_Ofinite) ).

fof(fact_nat_Oinject,axiom,
    ! [X61,X62] :
      ( hAPP(c_Nat_OSuc,X62) = hAPP(c_Nat_OSuc,X61)
    <=> X62 = X61 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Oinject) ).

fof(fact_Suc__inject,axiom,
    ! [X21,X22] :
      ( hAPP(c_Nat_OSuc,X22) = hAPP(c_Nat_OSuc,X21)
     => X22 = X21 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__inject) ).

fof(arity_fun__Orderings_Otop,axiom,
    ! [X79,X80] :
      ( class_Orderings_Otop(X80)
     => class_Orderings_Otop(tc_fun(X79,X80)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Otop) ).

fof(arity_fun__Orderings_Oorder,axiom,
    ! [X79,X80] :
      ( class_Orderings_Oorder(X80)
     => class_Orderings_Oorder(tc_fun(X79,X80)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).

fof(arity_fun__Orderings_Oord,axiom,
    ! [X79,X80] :
      ( class_Orderings_Oord(X80)
     => class_Orderings_Oord(tc_fun(X79,X80)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).

fof(arity_fun__Orderings_Opreorder,axiom,
    ! [X79,X80] :
      ( class_Orderings_Opreorder(X80)
     => class_Orderings_Opreorder(tc_fun(X79,X80)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).

fof(fact_Suc__neq__Zero,axiom,
    ! [X46] : hAPP(c_Nat_OSuc,X46) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__neq__Zero) ).

fof(fact_nat_Osimps_I3_J,axiom,
    ! [X60] : hAPP(c_Nat_OSuc,X60) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osimps_I3_J) ).

fof(fact_Suc__not__Zero,axiom,
    ! [X46] : hAPP(c_Nat_OSuc,X46) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__not__Zero) ).

fof(fact_Zero__neq__Suc,axiom,
    ! [X46] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X46),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).

fof(fact_nat_Osimps_I2_J,axiom,
    ! [X59] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X59),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osimps_I2_J) ).

fof(fact_Zero__not__Suc,axiom,
    ! [X46] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X46),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).

fof(fact_finite__code,axiom,
    ! [X14,X12] :
      ( class_Finite__Set_Ofinite(X12)
     => c_Finite__Set_Ofinite(X12,X14) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__code) ).

fof(fact_finite,axiom,
    ! [X14,X12] :
      ( class_Finite__Set_Ofinite(X12)
     => c_Finite__Set_Ofinite(X12,X14) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite) ).

fof(fact_Suc__n__not__n,axiom,
    ! [X44] : hAPP(c_Nat_OSuc,X44) != X44,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).

fof(fact_n__not__Suc__n,axiom,
    ! [X44] : X44 != hAPP(c_Nat_OSuc,X44),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).

fof(help_c__COMBI__1,axiom,
    ! [X81,X12] : hAPP(c_COMBI(X12),X81) = X81,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBI__1) ).

fof(fact_zero__neq__one,axiom,
    ! [X12] :
      ( class_Rings_Ozero__neq__one(X12)
     => c_Groups_Ozero__class_Ozero(X12) != c_Groups_Oone__class_Oone(X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__neq__one) ).

fof(fact_one__neq__zero,axiom,
    ! [X12] :
      ( class_Rings_Ozero__neq__one(X12)
     => c_Groups_Oone__class_Oone(X12) != c_Groups_Ozero__class_Ozero(X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__neq__zero) ).

fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom,
    ! [X80] :
      ( class_Finite__Set_Ofinite(X80)
     => class_Finite__Set_Ofinite(tc_Option_Ooption(X80)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Option__Ooption__Finite__Set_Ofinite) ).

fof(fact_nat__size,axiom,
    ! [X44] : c_Nat_Osize__class_Osize(tc_Nat_Onat,X44) = X44,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__size) ).

fof(help_c__fFalse__1,axiom,
    ~ hBOOL(c_fFalse),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fFalse__1) ).

fof(fact__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_058_AProf_096,axiom,
    hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____)))),c_Arrow__Order__Mirabelle_OProf)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_058_AProf_096) ).

fof(fact__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ae_096,axiom,
    hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____)))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ae_096) ).

fof(fact_n_I3_J,axiom,
    hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n_I3_J) ).

fof(fact_assms_I1_J,axiom,
    hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_F),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_assms_I1_J) ).

fof(fact__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_096,axiom,
    hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,hAPP(c_Hilbert__Choice_Oinv__into(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)),v_h____),v_n____)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_096) ).

fof(fact__096P_A_058_AProf_096,axiom,
    hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_P____),c_Arrow__Order__Mirabelle_OProf)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096P_A_058_AProf_096) ).

fof(fact_Prof__def,axiom,
    c_Arrow__Order__Mirabelle_OProf = c_FuncSet_OPi(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)),hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_OLin)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Prof__def) ).

fof(fact__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096,axiom,
    hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096) ).

fof(fact__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096,axiom,
    hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lab____)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096) ).

fof(fact__096Lba_A_058_ALin_096,axiom,
    hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_Lba____),c_Arrow__Order__Mirabelle_OLin)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096Lba_A_058_ALin_096) ).

fof(fact__096Lab_A_058_ALin_096,axiom,
    hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_Lab____),c_Arrow__Order__Mirabelle_OLin)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096Lab_A_058_ALin_096) ).

fof(fact_surjh,axiom,
    c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,v_h____,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_surjh) ).

fof(fact_n_I1_J,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),v_n____),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n_I1_J) ).

fof(fact_injh,axiom,
    c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,v_h____,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_injh) ).

fof(fact_card__UNIV__unit,axiom,
    c_Finite__Set_Ocard(tc_Product__Type_Ounit,c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__UNIV__unit) ).

fof(fact_finite__indi,axiom,
    c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__indi) ).

fof(fact_nat_Osize_I3_J,axiom,
    c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osize_I3_J) ).

fof(fact_One__nat__def,axiom,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_One__nat__def) ).

fof(fact_nat_Osize_I1_J,axiom,
    c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osize_I1_J) ).

fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
    class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).

fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
    class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).

fof(arity_Nat__Onat__Groups_Ozero,axiom,
    class_Groups_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).

fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
    class_Rings_Ozero__neq__one(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).

fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
    class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).

fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
    class_Groups_Omonoid__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).

fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom,
    class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Product____Type__Ounit__Finite__Set_Ofinite) ).

fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom,
    class_Finite__Set_Ofinite(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Finite__Set_Ofinite) ).

fof(arity_HOL__Obool__Orderings_Otop,axiom,
    class_Orderings_Otop(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Otop) ).

fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
    class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).

fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).

fof(arity_Nat__Onat__Groups_Oone,axiom,
    class_Groups_Oone(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).

fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
    class_Groups_Oab__semigroup__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).

fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
    class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).

fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
    class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).

fof(arity_HOL__Obool__Orderings_Oorder,axiom,
    class_Orderings_Oorder(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).

fof(arity_Nat__Onat__Orderings_Oorder,axiom,
    class_Orderings_Oorder(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).

fof(arity_HOL__Obool__Orderings_Oord,axiom,
    class_Orderings_Oord(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).

fof(arity_Nat__Onat__Orderings_Oord,axiom,
    class_Orderings_Oord(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).

fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
    class_Orderings_Olinorder(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).

fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
    class_Orderings_Opreorder(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).

fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
    class_Orderings_Opreorder(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).

fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).

fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
    class_Rings_Olinordered__semidom(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).

fof(fact_u,axiom,
    c_Arrow__Order__Mirabelle_Ounanimity(v_F),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_u) ).

fof(fact_assms_I3_J,axiom,
    c_Arrow__Order__Mirabelle_OIIA(v_F),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_assms_I3_J) ).

fof(fact__096c_A_126_061_Ad_096,axiom,
    v_c____ != v_d____,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096c_A_126_061_Ad_096) ).

fof(fact__096a_A_126_061_Ab_096,axiom,
    v_a____ != v_b____,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096a_A_126_061_Ab_096) ).

fof(i_0_519,plain,
    ( epred1_0
  <=> ( ! [X4] :
          ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X4)),v_n____))
             => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X4)),v_e____))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X4)),v_n____))
             => ( ( hAPP(v_h____,X4) = v_n____
                 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X4)),v_c____),v_e____))) )
                & ( hAPP(v_h____,X4) != v_n____
                 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X4)),v_e____))) ) ) ) )
        <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X4)),v_n____))
             => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____)) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X4)),v_n____))
             => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____)) ) ) )
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____)))) ) ) ),
    introduced(definition) ).

fof(i_0_520,plain,
    ( epred1_0
   => ( ! [X4] :
          ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X4)),v_n____))
             => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X4)),v_e____))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X4)),v_n____))
             => ( ( hAPP(v_h____,X4) = v_n____
                 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X4)),v_c____),v_e____))) )
                & ( hAPP(v_h____,X4) != v_n____
                 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X4)),v_e____))) ) ) ) )
        <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X4)),v_n____))
             => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____)) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X4)),v_n____))
             => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____)) ) ) )
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____)))) ) ) ),
    inference(split_equiv,[status(thm)],[i_0_519]) ).

fof(i_0_521,plain,
    ! [X4] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X4)),v_n____))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X4)),v_e____))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X4)),v_n____))
         => ( ( hAPP(v_h____,X4) = v_n____
             => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X4)),v_c____),v_e____))) )
            & ( hAPP(v_h____,X4) != v_n____
             => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X4)),v_e____))) ) ) ) )
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X4)),v_n____))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X4)),v_n____))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ad_J_A_061_A_Ib_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_096]) ).

fof(i_0_522,plain,
    ( v_e____ != v_d____
   => ( v_b____ != v_a____
     => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____)))),c_Arrow__Order__Mirabelle_OProf))
       => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____)),c_Arrow__Order__Mirabelle_OProf))
         => epred1_0 ) ) ) ),
    inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[fact__096_091_124_Ae_A_126_061_Ad_059_Ab_A_126_061_Aa_059_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_A_058_AProf_059_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_ALab_Aelse_ALba_J_A_058_AProf_059_AALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ad_J_A_061_A_Ib_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_A_124_093_061_061_062_A_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ad_J_A_061_A_Ib_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_096]),c_0_519]) ).

fof(i_0_523,negated_conjecture,
    ~ ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____)))) ),
    inference(assume_negation,[status(cth)],[conj_0]) ).

fof(i_0_524,plain,
    ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hAPP(v_h____,esk47_0) != v_n____
      | hAPP(v_h____,esk47_0) = v_n____
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hAPP(v_h____,esk47_0) != v_n____
      | hAPP(v_h____,esk47_0) = v_n____
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hAPP(v_h____,esk47_0) != v_n____
      | hAPP(v_h____,esk47_0) = v_n____
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hAPP(v_h____,esk47_0) != v_n____
      | hAPP(v_h____,esk47_0) = v_n____
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
      | hAPP(v_h____,esk47_0) != v_n____
      | hAPP(v_h____,esk47_0) = v_n____
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
      | hAPP(v_h____,esk47_0) != v_n____
      | hAPP(v_h____,esk47_0) = v_n____
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
      | hAPP(v_h____,esk47_0) != v_n____
      | hAPP(v_h____,esk47_0) = v_n____
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
      | hAPP(v_h____,esk47_0) != v_n____
      | hAPP(v_h____,esk47_0) = v_n____
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
      | hAPP(v_h____,esk47_0) = v_n____
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
      | hAPP(v_h____,esk47_0) = v_n____
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
      | hAPP(v_h____,esk47_0) = v_n____
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
      | hAPP(v_h____,esk47_0) = v_n____
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
      | hAPP(v_h____,esk47_0) = v_n____
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
      | hAPP(v_h____,esk47_0) = v_n____
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
      | hAPP(v_h____,esk47_0) = v_n____
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
      | hAPP(v_h____,esk47_0) = v_n____
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hAPP(v_h____,esk47_0) != v_n____
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hAPP(v_h____,esk47_0) != v_n____
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hAPP(v_h____,esk47_0) != v_n____
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hAPP(v_h____,esk47_0) != v_n____
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
      | hAPP(v_h____,esk47_0) != v_n____
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
      | hAPP(v_h____,esk47_0) != v_n____
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
      | hAPP(v_h____,esk47_0) != v_n____
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
      | hAPP(v_h____,esk47_0) != v_n____
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hAPP(v_h____,esk47_0) != v_n____
      | hAPP(v_h____,esk47_0) = v_n____
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hAPP(v_h____,esk47_0) != v_n____
      | hAPP(v_h____,esk47_0) = v_n____
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hAPP(v_h____,esk47_0) != v_n____
      | hAPP(v_h____,esk47_0) = v_n____
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hAPP(v_h____,esk47_0) != v_n____
      | hAPP(v_h____,esk47_0) = v_n____
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
      | hAPP(v_h____,esk47_0) != v_n____
      | hAPP(v_h____,esk47_0) = v_n____
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
      | hAPP(v_h____,esk47_0) != v_n____
      | hAPP(v_h____,esk47_0) = v_n____
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
      | hAPP(v_h____,esk47_0) != v_n____
      | hAPP(v_h____,esk47_0) = v_n____
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
      | hAPP(v_h____,esk47_0) != v_n____
      | hAPP(v_h____,esk47_0) = v_n____
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
      | hAPP(v_h____,esk47_0) = v_n____
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
      | hAPP(v_h____,esk47_0) = v_n____
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
      | hAPP(v_h____,esk47_0) = v_n____
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
      | hAPP(v_h____,esk47_0) = v_n____
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
      | hAPP(v_h____,esk47_0) = v_n____
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
      | hAPP(v_h____,esk47_0) = v_n____
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
      | hAPP(v_h____,esk47_0) = v_n____
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
      | hAPP(v_h____,esk47_0) = v_n____
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hAPP(v_h____,esk47_0) != v_n____
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hAPP(v_h____,esk47_0) != v_n____
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hAPP(v_h____,esk47_0) != v_n____
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hAPP(v_h____,esk47_0) != v_n____
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
      | hAPP(v_h____,esk47_0) != v_n____
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
      | hAPP(v_h____,esk47_0) != v_n____
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
      | hAPP(v_h____,esk47_0) != v_n____
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
      | hAPP(v_h____,esk47_0) != v_n____
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
      | hAPP(v_h____,esk47_0) != v_n____
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
      | hAPP(v_h____,esk47_0) != v_n____
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
      | hAPP(v_h____,esk47_0) != v_n____
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
      | hAPP(v_h____,esk47_0) != v_n____
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
      | hAPP(v_h____,esk47_0) = v_n____
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
      | hAPP(v_h____,esk47_0) = v_n____
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
      | hAPP(v_h____,esk47_0) = v_n____
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ epred1_0 )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
      | hAPP(v_h____,esk47_0) = v_n____
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
      | ~ epred1_0 ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_520])])])]) ).

fof(i_0_525,plain,
    ~ ! [X28] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))))
       => ( ! [X5] :
              ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5),X28))
             => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),X5))),v_Lab____)),v_Lba____)))) )
         => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X28),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))) ) ),
    inference(fof_simplification,[status(thm)],[fact__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_Am_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_059_Aa_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096]) ).

fof(i_0_526,plain,
    ! [X9,X14,X40,X1,X6,X2,X17,X12] :
      ( c_Finite__Set_Ofolding__image__simple(X12,X17,X2,X6,X1,X40)
     => ( c_Finite__Set_Ofinite(X17,X14)
       => ( ~ hBOOL(hAPP(hAPP(c_member(X17),X9),X14))
         => hAPP(X40,c_Set_Oinsert(X17,X9,X14)) = hAPP(hAPP(X2,hAPP(X1,X9)),hAPP(X40,X14)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_folding__image__simple_Oinsert]) ).

fof(i_0_527,plain,
    ! [X4] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X4)),v_n____))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X4)),v_e____))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X4)),v_n____))
         => ( ( hAPP(v_h____,X4) = v_n____
             => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X4)),v_c____),v_e____))) )
            & ( hAPP(v_h____,X4) != v_n____
             => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X4)),v_e____))) ) ) ) )
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lab____)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lba____)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ae_J_A_061_A_Ia_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_J_096]) ).

fof(i_0_528,plain,
    ! [X4] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,X4)))
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X4)),v_n____))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X4)),v_e____))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X4)),v_n____))
         => ( ( hAPP(v_h____,X4) = v_n____
             => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X4)),v_c____),v_e____))) )
            & ( hAPP(v_h____,X4) != v_n____
             => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X4)),v_e____))) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J_A_061_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ad_J_096]) ).

fof(i_0_529,plain,
    ! [X14,X2,X17,X12] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X12,c_Set_Oimage(X17,X12,X2,X14))),c_Finite__Set_Ocard(X17,X14)))
     => ~ c_Fun_Oinj__on(X17,X12,X2,X14) ),
    inference(fof_simplification,[status(thm)],[fact_pigeonhole]) ).

fof(i_0_530,plain,
    ! [X14,X12] :
      ( ( c_Finite__Set_Ofinite(X12,X14)
       => c_Finite__Set_Ocard(X12,X14) = c_Finite__Set_Ofold__image(tc_Nat_Onat,X12,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X12),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X14) )
      & ( ~ c_Finite__Set_Ofinite(X12,X14)
       => c_Finite__Set_Ocard(X12,X14) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_simplification,[status(thm)],[fact_card__def]) ).

fof(i_0_531,plain,
    ! [X1600] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
        | hAPP(v_h____,X1600) != v_n____
        | hAPP(v_h____,X1600) = v_n____
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
        | hAPP(v_h____,X1600) != v_n____
        | hAPP(v_h____,X1600) = v_n____
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1600)),v_e____)))
        | hAPP(v_h____,X1600) = v_n____
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1600)),v_e____)))
        | hAPP(v_h____,X1600) = v_n____
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
        | hAPP(v_h____,X1600) != v_n____
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1600)),v_c____),v_e____)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
        | hAPP(v_h____,X1600) != v_n____
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1600)),v_c____),v_e____)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1600)),v_e____)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1600)),v_c____),v_e____)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1600)),v_e____)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1600)),v_c____),v_e____)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1600)),v_e____))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1600)),v_e____))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
        | hAPP(v_h____,X1600) != v_n____
        | hAPP(v_h____,X1600) = v_n____
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1600)),v_e____))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
        | hAPP(v_h____,X1600) != v_n____
        | hAPP(v_h____,X1600) = v_n____
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1600)),v_e____))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1600)),v_e____)))
        | hAPP(v_h____,X1600) = v_n____
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1600)),v_e____))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1600)),v_e____)))
        | hAPP(v_h____,X1600) = v_n____
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1600)),v_e____))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
        | hAPP(v_h____,X1600) != v_n____
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1600)),v_c____),v_e____)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1600)),v_e____))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
        | hAPP(v_h____,X1600) != v_n____
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1600)),v_c____),v_e____)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1600)),v_e____))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1600)),v_e____)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1600)),v_c____),v_e____)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1600)),v_e____))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1600)),v_e____)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1600)),v_c____),v_e____)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1600)),v_e____))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1600)),v_e____)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____)) )
      & ( hAPP(v_h____,X1600) != v_n____
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1600)),v_c____),v_e____)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____)) )
      & ( hAPP(v_h____,X1600) = v_n____
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1600)),v_e____)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1600)),v_e____)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____)) )
      & ( hAPP(v_h____,X1600) != v_n____
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1600)),v_c____),v_e____)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____)) )
      & ( hAPP(v_h____,X1600) = v_n____
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1600)),v_e____)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1600)),v_e____)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____)) )
      & ( hAPP(v_h____,X1600) != v_n____
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1600)),v_c____),v_e____)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____)) )
      & ( hAPP(v_h____,X1600) = v_n____
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1600)),v_e____)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1600)),v_e____)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____)) )
      & ( hAPP(v_h____,X1600) != v_n____
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1600)),v_c____),v_e____)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____)) )
      & ( hAPP(v_h____,X1600) = v_n____
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1600)),v_e____)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1600)),v_n____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_521])])]) ).

fof(i_0_532,plain,
    ! [X8,X9,X7] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X7),c_Arrow__Order__Mirabelle_OLin))
     => ( X9 != X8
       => ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X9),X8)),X7))
        <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8),X9)),X7)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_notin__Lin__iff]) ).

fof(i_0_533,plain,
    ! [X23,X24,X7] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X7),c_Arrow__Order__Mirabelle_OLin))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X24),X23)),X7))
       => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X23),X24)),X7)) ) ),
    inference(fof_simplification,[status(thm)],[fact_Lin__irrefl]) ).

fof(i_0_534,plain,
    ! [X9,X13,X14,X2,X17,X12] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(X12,X17)),X2),c_FuncSet_OPi(X12,X17,X14,X13)))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X17),hAPP(X2,X9)),hAPP(X13,X9)))
       => ~ hBOOL(hAPP(hAPP(c_member(X12),X9),X14)) ) ),
    inference(fof_simplification,[status(thm)],[fact_PiE]) ).

fof(i_0_535,plain,
    ! [X13,X14,X9,X12] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X12),X9),X14))
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X14),c_Set_Oinsert(X12,X9,X13)))
      <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X14),X13)) ) ),
    inference(fof_simplification,[status(thm)],[fact_subset__insert]) ).

fof(i_0_536,plain,
    ~ ! [X34] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),X34))
       => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X34),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(fof_simplification,[status(thm)],[fact__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_059_ALba_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096]) ).

fof(i_0_537,plain,
    ~ ! [X33] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),X33))
       => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X33),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(fof_simplification,[status(thm)],[fact__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_059_ALab_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096]) ).

fof(i_0_538,plain,
    ! [X1,X2,X12,X17] :
      ( class_Orderings_Oord(X17)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12,X17)),X2),X1))
      <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,X17),X2),X1))
          & ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,X17),X1),X2)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_less__fun__def]) ).

fof(i_0_539,plain,
    ! [X44,X45,X46] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X46),X45)),X44))
     => ~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X46),X44))
         => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X45),X44)) ) ),
    inference(fof_simplification,[status(thm)],[fact_add__leE]) ).

fof(i_0_540,plain,
    ! [X48,X49] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X49),X48)),X49)),
    inference(fof_simplification,[status(thm)],[fact_not__add__less1]) ).

fof(i_0_541,plain,
    ! [X49,X48] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X48),X49)),X49)),
    inference(fof_simplification,[status(thm)],[fact_not__add__less2]) ).

fof(i_0_542,plain,
    ! [X10,X19] :
      ( ~ hBOOL(hAPP(X19,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
     => ( hBOOL(hAPP(X19,X10))
       => ? [X55] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X55),X10))
            & ! [X4] :
                ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),X55))
               => ~ hBOOL(hAPP(X19,X4)) )
            & hBOOL(hAPP(X19,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X55),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_ex__least__nat__less]) ).

fof(i_0_543,plain,
    ! [X23,X13,X24,X12] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X12),X24),X13))
       => X24 = X23 )
     => hBOOL(hAPP(hAPP(c_member(X12),X24),c_Set_Oinsert(X12,X23,X13))) ),
    inference(fof_simplification,[status(thm)],[fact_insertCI]) ).

fof(i_0_544,plain,
    ! [X13,X14,X9,X12] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X12),X9),X14))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X12),X9),X13))
       => ( c_Set_Oinsert(X12,X9,X14) = c_Set_Oinsert(X12,X9,X13)
        <=> X14 = X13 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_insert__ident]) ).

fof(i_0_545,plain,
    ! [X10,X50] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X50),X10))
    <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X10)),X50)) ),
    inference(fof_simplification,[status(thm)],[fact_not__less__eq__eq]) ).

fof(i_0_546,plain,
    ! [X10,X50] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X50),X10))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10),hAPP(c_Nat_OSuc,X50))) ),
    inference(fof_simplification,[status(thm)],[fact_not__less__eq]) ).

fof(i_0_547,plain,
    ! [X29,X32,X12] :
      ( class_Orderings_Oorder(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X32),X29))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X29),X32)) ) ),
    inference(fof_simplification,[status(thm)],[fact_xt1_I9_J]) ).

fof(i_0_548,plain,
    ! [X8,X9,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X9),X8))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X8),X9))
          | X9 = X8 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_not__less__iff__gr__or__eq]) ).

fof(i_0_549,plain,
    ! [X21,X22,X12] :
      ( class_Orderings_Opreorder(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X22),X21))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X21),X22)) ) ),
    inference(fof_simplification,[status(thm)],[fact_order__less__asym]) ).

fof(i_0_550,plain,
    ! [X32,X29,X12] :
      ( class_Orderings_Opreorder(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X29),X32))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X32),X29)) ) ),
    inference(fof_simplification,[status(thm)],[fact_order__less__asym_H]) ).

fof(i_0_551,plain,
    ! [X21,X22,X12] :
      ( class_Orderings_Opreorder(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X22),X21))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X21),X22)) ) ),
    inference(fof_simplification,[status(thm)],[fact_order__less__imp__not__less]) ).

fof(i_0_552,plain,
    ! [X21,X22,X12] :
      ( class_Orderings_Opreorder(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X22),X21))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X21),X22)) ) ),
    inference(fof_simplification,[status(thm)],[fact_order__less__not__sym]) ).

fof(i_0_553,plain,
    ! [X9,X14,X12] :
      ( c_Finite__Set_Ofinite(X12,X14)
     => ( ~ hBOOL(hAPP(hAPP(c_member(X12),X9),X14))
       => c_Finite__Set_Ocard(X12,c_Set_Oinsert(X12,X9,X14)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Finite__Set_Ocard(X12,X14)) ) ),
    inference(fof_simplification,[status(thm)],[fact_card_Oinsert]) ).

fof(i_0_554,plain,
    ! [X8,X9,X12] :
      ( class_Orderings_Opreorder(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X9),X8))
      <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X9),X8))
          & ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X8),X9)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_less__le__not__le]) ).

fof(i_0_555,plain,
    ! [X9,X14,X12] :
      ( c_Finite__Set_Ofinite(X12,X14)
     => ( ( hBOOL(hAPP(hAPP(c_member(X12),X9),X14))
         => c_Finite__Set_Ocard(X12,c_Set_Oinsert(X12,X9,X14)) = c_Finite__Set_Ocard(X12,X14) )
        & ( ~ hBOOL(hAPP(hAPP(c_member(X12),X9),X14))
         => c_Finite__Set_Ocard(X12,c_Set_Oinsert(X12,X9,X14)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X12,X14)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_card__insert__if]) ).

fof(i_0_556,plain,
    ! [X50,X10] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10),X50))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10),hAPP(c_Nat_OSuc,X50)))
      <=> X10 = X50 ) ),
    inference(fof_simplification,[status(thm)],[fact_not__less__less__Suc__eq]) ).

fof(i_0_557,plain,
    ! [X46,X44] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X46))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),hAPP(c_Nat_OSuc,X46)))
       => X46 = X44 ) ),
    inference(fof_simplification,[status(thm)],[fact_less__antisym]) ).

fof(i_0_558,plain,
    ! [X44,X46] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),hAPP(c_Nat_OSuc,X44)))
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),X44))
       => X46 = X44 ) ),
    inference(fof_simplification,[status(thm)],[fact_less__SucE]) ).

fof(i_0_559,plain,
    ! [X8,X9,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X9),X8))
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X9),X8))
        <=> X9 = X8 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv2]) ).

fof(i_0_560,plain,
    ! [X22,X21,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X21),X22))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X22),X21)) ) ),
    inference(fof_simplification,[status(thm)],[fact_leD]) ).

fof(i_0_561,plain,
    ! [X8,X9,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X9),X8))
      <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X8),X9)) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__not__less]) ).

fof(i_0_562,plain,
    ! [X8,X9,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X9),X8))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X8),X9)) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__not__le]) ).

fof(i_0_563,plain,
    ! [X9,X14,X12] :
      ( c_Finite__Set_Ofinite(X12,X14)
     => ( ~ hBOOL(hAPP(hAPP(c_member(X12),X9),X14))
       => c_Finite__Set_Ocard(X12,c_Set_Oinsert(X12,X9,X14)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X12,X14)) ) ),
    inference(fof_simplification,[status(thm)],[fact_card__insert__disjoint]) ).

fof(i_0_564,plain,
    ! [X44,X46] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X46),hAPP(c_Nat_OSuc,X44)))
     => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X46),X44))
       => X46 = hAPP(c_Nat_OSuc,X44) ) ),
    inference(fof_simplification,[status(thm)],[fact_le__SucE]) ).

fof(i_0_565,plain,
    ! [X44] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X44)),X44)),
    inference(fof_simplification,[status(thm)],[fact_Suc__n__not__le__n]) ).

fof(i_0_566,plain,
    ! [X8,X9,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X9),X8))
       => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X9),X8))
        <=> X9 = X8 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv1]) ).

fof(i_0_567,plain,
    ! [X12] :
      ( class_Rings_Olinordered__semidom(X12)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),c_Groups_Oone__class_Oone(X12)),c_Groups_Ozero__class_Ozero(X12))) ),
    inference(fof_simplification,[status(thm)],[fact_not__one__less__zero]) ).

fof(i_0_568,plain,
    ! [X21,X22,X12] :
      ( class_Rings_Olinordered__idom(X12)
     => ( X22 != X21
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X22),X21))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X21),X22)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__neqE__linordered__idom]) ).

fof(i_0_569,plain,
    ! [X21,X22,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X22),X21))
       => ( X22 != X21
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X21),X22)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__cases]) ).

fof(i_0_570,plain,
    ! [X21,X22,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( X22 != X21
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X22),X21))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X21),X22)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__neqE]) ).

fof(i_0_571,plain,
    ! [X9,X8,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X8),X9))
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X9),X8))
        <=> X9 = X8 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv3]) ).

fof(i_0_572,plain,
    ! [X22,X21,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X21),X22))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X22),X21)) ) ),
    inference(fof_simplification,[status(thm)],[fact_not__leE]) ).

fof(i_0_573,plain,
    ! [X21,X22,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X22),X21))
       => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X21),X22)) ) ),
    inference(fof_simplification,[status(thm)],[fact_leI]) ).

fof(i_0_574,plain,
    ! [X12] :
      ( class_Rings_Olinordered__semidom(X12)
     => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,c_Groups_Oone__class_Oone(X12)),c_Groups_Ozero__class_Ozero(X12))) ),
    inference(fof_simplification,[status(thm)],[fact_not__one__le__zero]) ).

fof(i_0_575,plain,
    ! [X21,X22] :
      ( X22 != X21
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22),X21))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X22)) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__neqE__nat]) ).

fof(i_0_576,plain,
    ! [X12,X13,X14] :
      ( X14 = X13
     => ~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X14),X13))
         => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X13),X14)) ) ),
    inference(fof_simplification,[status(thm)],[fact_equalityE]) ).

fof(i_0_577,plain,
    ! [X22,X12] :
      ( class_Orderings_Opreorder(X12)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X22),X22)) ),
    inference(fof_simplification,[status(thm)],[fact_order__less__irrefl]) ).

fof(i_0_578,plain,
    ! [X21,X22,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X22),X21))
       => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X21),X22)) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__le__cases]) ).

fof(i_0_579,plain,
    ! [X44] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_simplification,[status(thm)],[fact_not__less0]) ).

fof(i_0_580,plain,
    ! [X44] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_simplification,[status(thm)],[fact_less__nat__zero__code]) ).

fof(i_0_581,plain,
    ! [X44] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_simplification,[status(thm)],[fact_less__zeroE]) ).

fof(i_0_582,plain,
    ! [X44] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X44)),
    inference(fof_simplification,[status(thm)],[fact_less__not__refl]) ).

fof(i_0_583,plain,
    ! [X44] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X44)),
    inference(fof_simplification,[status(thm)],[fact_less__irrefl__nat]) ).

fof(i_0_584,plain,
    ! [X8,X9] :
      ( ~ hBOOL(hAPP(hAPP(c_fequal,X9),X8))
      | X9 = X8 ),
    inference(fof_simplification,[status(thm)],[help_c__fequal__1]) ).

fof(i_0_585,plain,
    ! [X14,X12] :
      ( ~ c_Finite__Set_Ofinite(X12,X14)
     => c_Finite__Set_Ocard(X12,X14) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(fof_simplification,[status(thm)],[fact_card__infinite]) ).

fof(i_0_586,plain,
    ( v_e____ = v_d____
    | v_b____ = v_a____
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____)))),c_Arrow__Order__Mirabelle_OProf))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____)),c_Arrow__Order__Mirabelle_OProf))
    | epred1_0 ),
    inference(fof_nnf,[status(thm)],[i_0_522]) ).

fof(i_0_587,negated_conjecture,
    ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____)))) )
    & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____)))) ) ),
    inference(fof_nnf,[status(thm)],[i_0_523]) ).

fof(i_0_588,plain,
    ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))) )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____)))))) ) ),
    inference(fof_nnf,[status(thm)],[fact__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ae_J_A_061_Ia_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_J_096]) ).

cnf(i_0_589,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_524]) ).

cnf(i_0_590,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | hAPP(v_h____,esk47_0) != v_n____
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_524]) ).

cnf(i_0_591,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_524]) ).

cnf(i_0_592,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | hAPP(v_h____,esk47_0) = v_n____
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_524]) ).

cnf(i_0_593,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | hAPP(v_h____,esk47_0) != v_n____
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_524]) ).

cnf(i_0_594,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_524]) ).

cnf(i_0_595,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | hAPP(v_h____,esk47_0) = v_n____
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_524]) ).

cnf(i_0_596,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_524]) ).

cnf(i_0_597,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | hAPP(v_h____,esk47_0) != v_n____
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_524]) ).

cnf(i_0_598,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_524]) ).

cnf(i_0_599,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | hAPP(v_h____,esk47_0) = v_n____
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_524]) ).

cnf(i_0_600,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
    | hAPP(v_h____,esk47_0) != v_n____
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_524]) ).

cnf(i_0_601,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_524]) ).

cnf(i_0_602,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | hAPP(v_h____,esk47_0) = v_n____
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_524]) ).

fof(i_0_603,plain,
    ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_F,v_P____)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____)))))) )
    & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_F,v_P____))) ) ),
    inference(fof_nnf,[status(thm)],[fact_PW]) ).

fof(i_0_604,plain,
    ! [X1719] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk8_0),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))))
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1719),esk8_0))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),X1719))),v_Lab____)),v_Lba____)))) )
      & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk8_0),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_525])])])]) ).

fof(i_0_605,plain,
    ! [X1705] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk7_0),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))))
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1705),esk7_0))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),X1705))),v_Lab____)),v_Lba____)))) )
      & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk7_0),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_Am_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_A_G_Aa_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_096])])])]) ).

fof(i_0_606,plain,
    ! [X1611] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),X1611))),v_Lab____)),v_Lba____)),c_Arrow__Order__Mirabelle_OProf)),
    inference(variable_rename,[status(thm)],[fact_PiProf]) ).

fof(i_0_607,plain,
    ! [X1602] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1602),v_n____))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),X1602))),v_Lab____)),v_Lba____)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_n_I2_J])]) ).

fof(i_0_608,plain,
    ! [X1730,X1731,X1732,X1733] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1733,tc_fun(X1732,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X1733,tc_fun(tc_prod(X1733,X1732),tc_HOL_Obool),tc_fun(X1732,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1732,tc_fun(tc_fun(tc_prod(X1733,X1732),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1733,X1732),tc_HOL_Obool),tc_fun(X1732,tc_HOL_Obool)),X1733,c_COMBC(X1732,tc_fun(tc_prod(X1733,X1732),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1732,tc_prod(X1733,X1732)),tc_fun(X1732,tc_fun(tc_fun(tc_prod(X1733,X1732),tc_HOL_Obool),tc_HOL_Obool)),X1733,c_COMBB(tc_prod(X1733,X1732),tc_fun(tc_fun(tc_prod(X1733,X1732),tc_HOL_Obool),tc_HOL_Obool),X1732,c_member(tc_prod(X1733,X1732)))),c_Product__Type_OPair(X1733,X1732)))),X1731)),hAPP(hAPP(c_COMBC(X1733,tc_fun(tc_prod(X1733,X1732),tc_HOL_Obool),tc_fun(X1732,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1732,tc_fun(tc_fun(tc_prod(X1733,X1732),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1733,X1732),tc_HOL_Obool),tc_fun(X1732,tc_HOL_Obool)),X1733,c_COMBC(X1732,tc_fun(tc_prod(X1733,X1732),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1732,tc_prod(X1733,X1732)),tc_fun(X1732,tc_fun(tc_fun(tc_prod(X1733,X1732),tc_HOL_Obool),tc_HOL_Obool)),X1733,c_COMBB(tc_prod(X1733,X1732),tc_fun(tc_fun(tc_prod(X1733,X1732),tc_HOL_Obool),tc_HOL_Obool),X1732,c_member(tc_prod(X1733,X1732)))),c_Product__Type_OPair(X1733,X1732)))),X1730)))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1733,X1732),tc_HOL_Obool),X1731),X1730)) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1733,X1732),tc_HOL_Obool),X1731),X1730))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1733,tc_fun(X1732,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X1733,tc_fun(tc_prod(X1733,X1732),tc_HOL_Obool),tc_fun(X1732,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1732,tc_fun(tc_fun(tc_prod(X1733,X1732),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1733,X1732),tc_HOL_Obool),tc_fun(X1732,tc_HOL_Obool)),X1733,c_COMBC(X1732,tc_fun(tc_prod(X1733,X1732),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1732,tc_prod(X1733,X1732)),tc_fun(X1732,tc_fun(tc_fun(tc_prod(X1733,X1732),tc_HOL_Obool),tc_HOL_Obool)),X1733,c_COMBB(tc_prod(X1733,X1732),tc_fun(tc_fun(tc_prod(X1733,X1732),tc_HOL_Obool),tc_HOL_Obool),X1732,c_member(tc_prod(X1733,X1732)))),c_Product__Type_OPair(X1733,X1732)))),X1731)),hAPP(hAPP(c_COMBC(X1733,tc_fun(tc_prod(X1733,X1732),tc_HOL_Obool),tc_fun(X1732,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1732,tc_fun(tc_fun(tc_prod(X1733,X1732),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1733,X1732),tc_HOL_Obool),tc_fun(X1732,tc_HOL_Obool)),X1733,c_COMBC(X1732,tc_fun(tc_prod(X1733,X1732),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1732,tc_prod(X1733,X1732)),tc_fun(X1732,tc_fun(tc_fun(tc_prod(X1733,X1732),tc_HOL_Obool),tc_HOL_Obool)),X1733,c_COMBB(tc_prod(X1733,X1732),tc_fun(tc_fun(tc_prod(X1733,X1732),tc_HOL_Obool),tc_HOL_Obool),X1732,c_member(tc_prod(X1733,X1732)))),c_Product__Type_OPair(X1733,X1732)))),X1730))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__subset__eq2])]) ).

fof(i_0_609,plain,
    ! [X1697,X1698,X1699,X1700,X1701,X1702] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1702),X1701)),hAPP(v_F,X1698)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1700),X1699)),hAPP(v_F,X1697)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1702),X1701)),hAPP(X1698,esk6_6(X1697,X1698,X1699,X1700,X1701,X1702))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1700),X1699)),hAPP(X1697,esk6_6(X1697,X1698,X1699,X1700,X1701,X1702))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1697),c_Arrow__Order__Mirabelle_OProf))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1698),c_Arrow__Order__Mirabelle_OProf))
        | X1701 = X1700
        | X1702 = X1699
        | X1700 = X1699
        | X1702 = X1701 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1700),X1699)),hAPP(v_F,X1697)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1702),X1701)),hAPP(v_F,X1698)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1702),X1701)),hAPP(X1698,esk6_6(X1697,X1698,X1699,X1700,X1701,X1702))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1700),X1699)),hAPP(X1697,esk6_6(X1697,X1698,X1699,X1700,X1701,X1702))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1697),c_Arrow__Order__Mirabelle_OProf))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1698),c_Arrow__Order__Mirabelle_OProf))
        | X1701 = X1700
        | X1702 = X1699
        | X1700 = X1699
        | X1702 = X1701 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1702),X1701)),hAPP(v_F,X1698)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1700),X1699)),hAPP(v_F,X1697)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1702),X1701)),hAPP(X1698,esk6_6(X1697,X1698,X1699,X1700,X1701,X1702))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1700),X1699)),hAPP(X1697,esk6_6(X1697,X1698,X1699,X1700,X1701,X1702))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1697),c_Arrow__Order__Mirabelle_OProf))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1698),c_Arrow__Order__Mirabelle_OProf))
        | X1701 = X1700
        | X1702 = X1699
        | X1700 = X1699
        | X1702 = X1701 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1700),X1699)),hAPP(v_F,X1697)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1702),X1701)),hAPP(v_F,X1698)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1702),X1701)),hAPP(X1698,esk6_6(X1697,X1698,X1699,X1700,X1701,X1702))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1700),X1699)),hAPP(X1697,esk6_6(X1697,X1698,X1699,X1700,X1701,X1702))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1697),c_Arrow__Order__Mirabelle_OProf))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1698),c_Arrow__Order__Mirabelle_OProf))
        | X1701 = X1700
        | X1702 = X1699
        | X1700 = X1699
        | X1702 = X1701 ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__C2_C])])])]) ).

fof(i_0_610,plain,
    ! [X1690,X1691,X1692,X1693,X1694,X1695] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1695),X1694)),hAPP(X1691,esk5_6(X1690,X1691,X1692,X1693,X1694,X1695))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1693),X1692)),hAPP(X1690,esk5_6(X1690,X1691,X1692,X1693,X1694,X1695))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1695),X1694)),hAPP(v_F,X1691)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1693),X1692)),hAPP(v_F,X1690)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1690),c_Arrow__Order__Mirabelle_OProf))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1691),c_Arrow__Order__Mirabelle_OProf))
        | X1694 = X1693
        | X1695 = X1692
        | X1693 = X1692
        | X1695 = X1694 )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1695),X1694)),hAPP(X1691,esk5_6(X1690,X1691,X1692,X1693,X1694,X1695))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1693),X1692)),hAPP(X1690,esk5_6(X1690,X1691,X1692,X1693,X1694,X1695))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1695),X1694)),hAPP(v_F,X1691)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1693),X1692)),hAPP(v_F,X1690)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1690),c_Arrow__Order__Mirabelle_OProf))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1691),c_Arrow__Order__Mirabelle_OProf))
        | X1694 = X1693
        | X1695 = X1692
        | X1693 = X1692
        | X1695 = X1694 ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__C1_C])])])]) ).

fof(i_0_611,plain,
    ! [X1677,X1678,X1679,X1680,X1681,X1682] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1682),X1681)),hAPP(v_F,X1678)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1680),X1679)),hAPP(v_F,X1677)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1682),X1681)),hAPP(X1678,esk3_6(X1677,X1678,X1679,X1680,X1681,X1682))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1680),X1679)),hAPP(X1677,esk3_6(X1677,X1678,X1679,X1680,X1681,X1682))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1677),c_Arrow__Order__Mirabelle_OProf))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1678),c_Arrow__Order__Mirabelle_OProf))
        | X1680 = X1679
        | X1682 = X1681 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1680),X1679)),hAPP(v_F,X1677)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1682),X1681)),hAPP(v_F,X1678)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1682),X1681)),hAPP(X1678,esk3_6(X1677,X1678,X1679,X1680,X1681,X1682))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1680),X1679)),hAPP(X1677,esk3_6(X1677,X1678,X1679,X1680,X1681,X1682))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1677),c_Arrow__Order__Mirabelle_OProf))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1678),c_Arrow__Order__Mirabelle_OProf))
        | X1680 = X1679
        | X1682 = X1681 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1682),X1681)),hAPP(v_F,X1678)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1680),X1679)),hAPP(v_F,X1677)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1682),X1681)),hAPP(X1678,esk3_6(X1677,X1678,X1679,X1680,X1681,X1682))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1680),X1679)),hAPP(X1677,esk3_6(X1677,X1678,X1679,X1680,X1681,X1682))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1677),c_Arrow__Order__Mirabelle_OProf))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1678),c_Arrow__Order__Mirabelle_OProf))
        | X1680 = X1679
        | X1682 = X1681 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1680),X1679)),hAPP(v_F,X1677)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1682),X1681)),hAPP(v_F,X1678)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1682),X1681)),hAPP(X1678,esk3_6(X1677,X1678,X1679,X1680,X1681,X1682))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1680),X1679)),hAPP(X1677,esk3_6(X1677,X1678,X1679,X1680,X1681,X1682))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1677),c_Arrow__Order__Mirabelle_OProf))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1678),c_Arrow__Order__Mirabelle_OProf))
        | X1680 = X1679
        | X1682 = X1681 ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pairwise__neutrality])])])]) ).

fof(i_0_612,plain,
    ! [X1617,X1618,X1619,X1620] :
      ( ( hAPP(hAPP(c_COMBC(X1620,tc_fun(tc_prod(X1620,X1619),tc_HOL_Obool),tc_fun(X1619,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1619,tc_fun(tc_fun(tc_prod(X1620,X1619),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1620,X1619),tc_HOL_Obool),tc_fun(X1619,tc_HOL_Obool)),X1620,c_COMBC(X1619,tc_fun(tc_prod(X1620,X1619),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1619,tc_prod(X1620,X1619)),tc_fun(X1619,tc_fun(tc_fun(tc_prod(X1620,X1619),tc_HOL_Obool),tc_HOL_Obool)),X1620,c_COMBB(tc_prod(X1620,X1619),tc_fun(tc_fun(tc_prod(X1620,X1619),tc_HOL_Obool),tc_HOL_Obool),X1619,c_member(tc_prod(X1620,X1619)))),c_Product__Type_OPair(X1620,X1619)))),X1618) != hAPP(hAPP(c_COMBC(X1620,tc_fun(tc_prod(X1620,X1619),tc_HOL_Obool),tc_fun(X1619,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1619,tc_fun(tc_fun(tc_prod(X1620,X1619),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1620,X1619),tc_HOL_Obool),tc_fun(X1619,tc_HOL_Obool)),X1620,c_COMBC(X1619,tc_fun(tc_prod(X1620,X1619),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1619,tc_prod(X1620,X1619)),tc_fun(X1619,tc_fun(tc_fun(tc_prod(X1620,X1619),tc_HOL_Obool),tc_HOL_Obool)),X1620,c_COMBB(tc_prod(X1620,X1619),tc_fun(tc_fun(tc_prod(X1620,X1619),tc_HOL_Obool),tc_HOL_Obool),X1619,c_member(tc_prod(X1620,X1619)))),c_Product__Type_OPair(X1620,X1619)))),X1617)
        | X1618 = X1617 )
      & ( X1618 != X1617
        | hAPP(hAPP(c_COMBC(X1620,tc_fun(tc_prod(X1620,X1619),tc_HOL_Obool),tc_fun(X1619,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1619,tc_fun(tc_fun(tc_prod(X1620,X1619),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1620,X1619),tc_HOL_Obool),tc_fun(X1619,tc_HOL_Obool)),X1620,c_COMBC(X1619,tc_fun(tc_prod(X1620,X1619),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1619,tc_prod(X1620,X1619)),tc_fun(X1619,tc_fun(tc_fun(tc_prod(X1620,X1619),tc_HOL_Obool),tc_HOL_Obool)),X1620,c_COMBB(tc_prod(X1620,X1619),tc_fun(tc_fun(tc_prod(X1620,X1619),tc_HOL_Obool),tc_HOL_Obool),X1619,c_member(tc_prod(X1620,X1619)))),c_Product__Type_OPair(X1620,X1619)))),X1618) = hAPP(hAPP(c_COMBC(X1620,tc_fun(tc_prod(X1620,X1619),tc_HOL_Obool),tc_fun(X1619,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1619,tc_fun(tc_fun(tc_prod(X1620,X1619),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1620,X1619),tc_HOL_Obool),tc_fun(X1619,tc_HOL_Obool)),X1620,c_COMBC(X1619,tc_fun(tc_prod(X1620,X1619),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1619,tc_prod(X1620,X1619)),tc_fun(X1619,tc_fun(tc_fun(tc_prod(X1620,X1619),tc_HOL_Obool),tc_HOL_Obool)),X1620,c_COMBB(tc_prod(X1620,X1619),tc_fun(tc_fun(tc_prod(X1620,X1619),tc_HOL_Obool),tc_HOL_Obool),X1619,c_member(tc_prod(X1620,X1619)))),c_Product__Type_OPair(X1620,X1619)))),X1617) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__equals__eq2])]) ).

fof(i_0_613,plain,
    ! [X2448,X2449,X2450,X2451,X2452] :
      ( ( hBOOL(hAPP(hAPP(c_member(X2452),esk28_5(X2448,X2449,X2450,X2451,X2452)),X2451))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X2452,X2450),tc_HOL_Obool),c_FuncSet_OPi(X2452,X2450,X2451,X2449)),c_FuncSet_OPi(X2452,X2450,X2451,X2448))) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2450,tc_HOL_Obool),hAPP(X2449,esk28_5(X2448,X2449,X2450,X2451,X2452))),hAPP(X2448,esk28_5(X2448,X2449,X2450,X2451,X2452))))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X2452,X2450),tc_HOL_Obool),c_FuncSet_OPi(X2452,X2450,X2451,X2449)),c_FuncSet_OPi(X2452,X2450,X2451,X2448))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__mono])])])]) ).

fof(i_0_614,plain,
    ! [X2461,X2462,X2463,X2464,X2465] :
      ( ( hBOOL(hAPP(hAPP(c_member(X2465),esk29_5(X2461,X2462,X2463,X2464,X2465)),X2464))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X2465,X2463)),X2462),c_FuncSet_OPi(X2465,X2463,X2464,X2461))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X2463),hAPP(X2462,esk29_5(X2461,X2462,X2463,X2464,X2465))),hAPP(X2461,esk29_5(X2461,X2462,X2463,X2464,X2465))))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X2465,X2463)),X2462),c_FuncSet_OPi(X2465,X2463,X2464,X2461))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__I])])])]) ).

fof(i_0_615,plain,
    ! [X2363,X2364,X2365,X2366,X2367,X2369,X2374,X2375] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2366),X2367)),hAPP(X2363,X2364)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2366),X2367)),hAPP(X2363,X2365)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2366),X2367)),hAPP(X2364,esk19_5(X2363,X2364,X2365,X2366,X2367))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2366),X2367)),hAPP(X2365,esk19_5(X2363,X2364,X2365,X2366,X2367))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2365),c_Arrow__Order__Mirabelle_OProf))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2364),c_Arrow__Order__Mirabelle_OProf))
        | ~ c_Arrow__Order__Mirabelle_OIIA(X2363) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2366),X2367)),hAPP(X2363,X2365)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2366),X2367)),hAPP(X2363,X2364)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2366),X2367)),hAPP(X2364,esk19_5(X2363,X2364,X2365,X2366,X2367))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2366),X2367)),hAPP(X2365,esk19_5(X2363,X2364,X2365,X2366,X2367))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2365),c_Arrow__Order__Mirabelle_OProf))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2364),c_Arrow__Order__Mirabelle_OProf))
        | ~ c_Arrow__Order__Mirabelle_OIIA(X2363) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2366),X2367)),hAPP(X2363,X2364)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2366),X2367)),hAPP(X2363,X2365)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2366),X2367)),hAPP(X2364,esk19_5(X2363,X2364,X2365,X2366,X2367))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2366),X2367)),hAPP(X2365,esk19_5(X2363,X2364,X2365,X2366,X2367))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2365),c_Arrow__Order__Mirabelle_OProf))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2364),c_Arrow__Order__Mirabelle_OProf))
        | ~ c_Arrow__Order__Mirabelle_OIIA(X2363) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2366),X2367)),hAPP(X2363,X2365)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2366),X2367)),hAPP(X2363,X2364)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2366),X2367)),hAPP(X2364,esk19_5(X2363,X2364,X2365,X2366,X2367))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2366),X2367)),hAPP(X2365,esk19_5(X2363,X2364,X2365,X2366,X2367))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2365),c_Arrow__Order__Mirabelle_OProf))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2364),c_Arrow__Order__Mirabelle_OProf))
        | ~ c_Arrow__Order__Mirabelle_OIIA(X2363) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk20_1(X2369)),c_Arrow__Order__Mirabelle_OProf))
        | c_Arrow__Order__Mirabelle_OIIA(X2369) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk21_1(X2369)),c_Arrow__Order__Mirabelle_OProf))
        | c_Arrow__Order__Mirabelle_OIIA(X2369) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk22_1(X2369)),esk23_1(X2369))),hAPP(esk20_1(X2369),X2374)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk22_1(X2369)),esk23_1(X2369))),hAPP(esk21_1(X2369),X2374)))
        | c_Arrow__Order__Mirabelle_OIIA(X2369) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk22_1(X2369)),esk23_1(X2369))),hAPP(esk21_1(X2369),X2375)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk22_1(X2369)),esk23_1(X2369))),hAPP(esk20_1(X2369),X2375)))
        | c_Arrow__Order__Mirabelle_OIIA(X2369) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk22_1(X2369)),esk23_1(X2369))),hAPP(X2369,esk20_1(X2369))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk22_1(X2369)),esk23_1(X2369))),hAPP(X2369,esk21_1(X2369))))
        | c_Arrow__Order__Mirabelle_OIIA(X2369) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk22_1(X2369)),esk23_1(X2369))),hAPP(X2369,esk20_1(X2369))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk22_1(X2369)),esk23_1(X2369))),hAPP(X2369,esk21_1(X2369))))
        | c_Arrow__Order__Mirabelle_OIIA(X2369) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_IIA__def])])])])])]) ).

fof(i_0_616,plain,
    ! [X1684,X1685,X1686,X1687,X1688] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1688),X1687)),hAPP(v_F,X1685)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1687),X1686)),hAPP(v_F,X1684)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1688),X1687)),hAPP(X1685,esk4_5(X1684,X1685,X1686,X1687,X1688))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1687),X1686)),hAPP(X1684,esk4_5(X1684,X1685,X1686,X1687,X1688))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1684),c_Arrow__Order__Mirabelle_OProf))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1685),c_Arrow__Order__Mirabelle_OProf))
        | X1688 = X1686
        | X1687 = X1686
        | X1688 = X1687 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1687),X1686)),hAPP(v_F,X1684)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1688),X1687)),hAPP(v_F,X1685)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1688),X1687)),hAPP(X1685,esk4_5(X1684,X1685,X1686,X1687,X1688))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1687),X1686)),hAPP(X1684,esk4_5(X1684,X1685,X1686,X1687,X1688))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1684),c_Arrow__Order__Mirabelle_OProf))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1685),c_Arrow__Order__Mirabelle_OProf))
        | X1688 = X1686
        | X1687 = X1686
        | X1688 = X1687 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1688),X1687)),hAPP(v_F,X1685)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1687),X1686)),hAPP(v_F,X1684)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1688),X1687)),hAPP(X1685,esk4_5(X1684,X1685,X1686,X1687,X1688))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1687),X1686)),hAPP(X1684,esk4_5(X1684,X1685,X1686,X1687,X1688))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1684),c_Arrow__Order__Mirabelle_OProf))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1685),c_Arrow__Order__Mirabelle_OProf))
        | X1688 = X1686
        | X1687 = X1686
        | X1688 = X1687 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1687),X1686)),hAPP(v_F,X1684)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1688),X1687)),hAPP(v_F,X1685)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1688),X1687)),hAPP(X1685,esk4_5(X1684,X1685,X1686,X1687,X1688))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1687),X1686)),hAPP(X1684,esk4_5(X1684,X1685,X1686,X1687,X1688))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1684),c_Arrow__Order__Mirabelle_OProf))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1685),c_Arrow__Order__Mirabelle_OProf))
        | X1688 = X1686
        | X1687 = X1686
        | X1688 = X1687 ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__C4_C])])])]) ).

fof(i_0_617,plain,
    ! [X2228,X2229] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk14_2(X2228,X2229)),c_Arrow__Order__Mirabelle_OProf))
        | c_Arrow__Order__Mirabelle_Odictator(X2229,X2228)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2229),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin)))) )
      & ( esk15_2(X2228,X2229) != esk16_2(X2228,X2229)
        | c_Arrow__Order__Mirabelle_Odictator(X2229,X2228)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2229),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin)))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk15_2(X2228,X2229)),esk16_2(X2228,X2229))),hAPP(esk14_2(X2228,X2229),X2228)))
        | c_Arrow__Order__Mirabelle_Odictator(X2229,X2228)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2229),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk15_2(X2228,X2229)),esk16_2(X2228,X2229))),hAPP(X2229,esk14_2(X2228,X2229))))
        | c_Arrow__Order__Mirabelle_Odictator(X2229,X2228)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2229),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin)))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dictatorI])])])]) ).

fof(i_0_618,plain,
    ! [X2355,X2356,X2357,X2358,X2359,X2360,X2361,X2362] :
      ( ( X2360 = X2358
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X2362,X2362)),hAPP(hAPP(c_Product__Type_OPair(X2362,X2362),X2360),X2358)),X2356))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2362,X2361),tc_prod(X2362,X2361))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2362,X2361),tc_prod(X2362,X2361)),hAPP(hAPP(c_Product__Type_OPair(X2362,X2361),X2360),X2359)),hAPP(hAPP(c_Product__Type_OPair(X2362,X2361),X2358),X2357))),c_Wellfounded_Olex__prod(X2362,X2361,X2356,X2355))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2361,X2361)),hAPP(hAPP(c_Product__Type_OPair(X2361,X2361),X2359),X2357)),X2355))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X2362,X2362)),hAPP(hAPP(c_Product__Type_OPair(X2362,X2362),X2360),X2358)),X2356))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2362,X2361),tc_prod(X2362,X2361))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2362,X2361),tc_prod(X2362,X2361)),hAPP(hAPP(c_Product__Type_OPair(X2362,X2361),X2360),X2359)),hAPP(hAPP(c_Product__Type_OPair(X2362,X2361),X2358),X2357))),c_Wellfounded_Olex__prod(X2362,X2361,X2356,X2355))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2362,X2362)),hAPP(hAPP(c_Product__Type_OPair(X2362,X2362),X2360),X2358)),X2356))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2362,X2361),tc_prod(X2362,X2361))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2362,X2361),tc_prod(X2362,X2361)),hAPP(hAPP(c_Product__Type_OPair(X2362,X2361),X2360),X2359)),hAPP(hAPP(c_Product__Type_OPair(X2362,X2361),X2358),X2357))),c_Wellfounded_Olex__prod(X2362,X2361,X2356,X2355))) )
      & ( X2360 != X2358
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2361,X2361)),hAPP(hAPP(c_Product__Type_OPair(X2361,X2361),X2359),X2357)),X2355))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2362,X2361),tc_prod(X2362,X2361))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2362,X2361),tc_prod(X2362,X2361)),hAPP(hAPP(c_Product__Type_OPair(X2362,X2361),X2360),X2359)),hAPP(hAPP(c_Product__Type_OPair(X2362,X2361),X2358),X2357))),c_Wellfounded_Olex__prod(X2362,X2361,X2356,X2355))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__lex__prod])])]) ).

fof(i_0_619,plain,
    ! [X1672,X1673,X1674,X1675] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1675),X1674)),hAPP(v_F,X1673)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1674),X1675)),hAPP(v_F,X1672)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1675),X1674)),hAPP(X1673,esk2_4(X1672,X1673,X1674,X1675))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1674),X1675)),hAPP(X1672,esk2_4(X1672,X1673,X1674,X1675))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1672),c_Arrow__Order__Mirabelle_OProf))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1673),c_Arrow__Order__Mirabelle_OProf))
        | X1675 = X1674 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1674),X1675)),hAPP(v_F,X1672)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1675),X1674)),hAPP(v_F,X1673)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1675),X1674)),hAPP(X1673,esk2_4(X1672,X1673,X1674,X1675))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1674),X1675)),hAPP(X1672,esk2_4(X1672,X1673,X1674,X1675))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1672),c_Arrow__Order__Mirabelle_OProf))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1673),c_Arrow__Order__Mirabelle_OProf))
        | X1675 = X1674 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1675),X1674)),hAPP(v_F,X1673)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1674),X1675)),hAPP(v_F,X1672)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1675),X1674)),hAPP(X1673,esk2_4(X1672,X1673,X1674,X1675))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1674),X1675)),hAPP(X1672,esk2_4(X1672,X1673,X1674,X1675))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1672),c_Arrow__Order__Mirabelle_OProf))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1673),c_Arrow__Order__Mirabelle_OProf))
        | X1675 = X1674 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1674),X1675)),hAPP(v_F,X1672)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1675),X1674)),hAPP(v_F,X1673)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1675),X1674)),hAPP(X1673,esk2_4(X1672,X1673,X1674,X1675))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1674),X1675)),hAPP(X1672,esk2_4(X1672,X1673,X1674,X1675))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1672),c_Arrow__Order__Mirabelle_OProf))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1673),c_Arrow__Order__Mirabelle_OProf))
        | X1675 = X1674 ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__C3_C])])])]) ).

fof(i_0_620,plain,
    ! [X2823,X2824,X2825,X2826,X2827,X2828,X2829] :
      ( ~ c_Finite__Set_Ofolding__image__simple(X2829,X2828,X2827,X2826,X2825,X2824)
      | ~ c_Finite__Set_Ofinite(X2828,X2823)
      | hAPP(X2824,X2823) = c_Finite__Set_Ofold__image(X2829,X2828,X2827,X2825,X2826,X2823) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oeq__fold__g])]) ).

fof(i_0_621,plain,
    ! [X2932,X2933,X2934,X2935,X2936,X2938,X2939,X2940,X2941,X2942,X2943] :
      ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2934,tc_HOL_Obool),esk37_5(X2932,X2933,X2934,X2935,X2936)),X2932))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2936,tc_HOL_Obool),X2935),c_Set_Oimage(X2934,X2936,X2933,X2932))) )
      & ( X2935 = c_Set_Oimage(X2934,X2936,X2933,esk37_5(X2932,X2933,X2934,X2935,X2936))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2936,tc_HOL_Obool),X2935),c_Set_Oimage(X2934,X2936,X2933,X2932))) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2940,tc_HOL_Obool),X2943),X2938))
        | X2941 != c_Set_Oimage(X2940,X2942,X2939,X2943)
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2942,tc_HOL_Obool),X2941),c_Set_Oimage(X2940,X2942,X2939,X2938))) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__image__iff])])])])])]) ).

fof(i_0_622,plain,
    ! [X1626,X1627,X1628,X1629,X1630,X1631,X1632] :
      ( ~ hBOOL(hAPP(X1632,X1631))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1630,X1630)),hAPP(hAPP(c_Product__Type_OPair(X1630,X1630),X1629),X1628)),hAPP(X1627,X1631)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1626,X1630),tc_prod(X1626,X1630))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1626,X1630),tc_prod(X1626,X1630)),hAPP(hAPP(c_Product__Type_OPair(X1626,X1630),X1631),X1629)),hAPP(hAPP(c_Product__Type_OPair(X1626,X1630),X1631),X1628))),c_Recdef_Osame__fst(X1626,X1630,X1632,X1627))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_same__fstI])]) ).

fof(i_0_623,plain,
    ! [X1819,X1820,X1821,X1822,X1823] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1821,X1822),X1820),X1819))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1822,hAPP(X1820,X1823)),hAPP(X1819,X1823)))
        | ~ class_Orderings_Oord(X1822) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1822,hAPP(X1820,esk9_4(X1819,X1820,X1821,X1822))),hAPP(X1819,esk9_4(X1819,X1820,X1821,X1822))))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1821,X1822),X1820),X1819))
        | ~ class_Orderings_Oord(X1822) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__fun__def])])])])]) ).

fof(i_0_624,plain,
    ! [X2554,X2555,X2556,X2557,X2558,X2559,X2560,X2561] :
      ( ~ c_Finite__Set_Ofolding__image__simple(X2561,X2560,X2559,X2558,X2557,X2556)
      | ~ c_Finite__Set_Ofinite(X2560,X2555)
      | hBOOL(hAPP(hAPP(c_member(X2560),X2554),X2555))
      | hAPP(X2556,c_Set_Oinsert(X2560,X2554,X2555)) = hAPP(hAPP(X2559,hAPP(X2557,X2554)),hAPP(X2556,X2555)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_526])]) ).

fof(i_0_625,plain,
    ! [X3062,X3063,X3064,X3065,X3066,X3067] :
      ( ~ c_Fun_Oinj__on(X3067,X3066,X3065,X3064)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3066,tc_HOL_Obool),c_Set_Oimage(X3067,X3066,X3065,X3064)),X3063))
      | ~ c_Fun_Oinj__on(X3066,X3067,X3062,X3063)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3067,tc_HOL_Obool),c_Set_Oimage(X3066,X3067,X3062,X3063)),X3064))
      | ~ c_Finite__Set_Ofinite(X3067,X3064)
      | ~ c_Finite__Set_Ofinite(X3066,X3063)
      | c_Finite__Set_Ocard(X3067,X3064) = c_Finite__Set_Ocard(X3066,X3063) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__bij__eq])]) ).

fof(i_0_626,plain,
    ! [X2376,X2377,X2378,X2379,X2381,X2385] :
      ( ( ~ c_Arrow__Order__Mirabelle_Ounanimity(X2376)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2377),c_Arrow__Order__Mirabelle_OProf))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2378),X2379)),hAPP(X2377,esk24_4(X2376,X2377,X2378,X2379))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2378),X2379)),hAPP(X2376,X2377))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk25_1(X2381)),c_Arrow__Order__Mirabelle_OProf))
        | c_Arrow__Order__Mirabelle_Ounanimity(X2381) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk26_1(X2381)),esk27_1(X2381))),hAPP(esk25_1(X2381),X2385)))
        | c_Arrow__Order__Mirabelle_Ounanimity(X2381) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk26_1(X2381)),esk27_1(X2381))),hAPP(X2381,esk25_1(X2381))))
        | c_Arrow__Order__Mirabelle_Ounanimity(X2381) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unanimity__def])])])])])]) ).

fof(i_0_627,plain,
    ! [X1612] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lab____))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),v_n____))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),v_n____)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lba____))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),v_n____))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),v_n____)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lab____))
        | hAPP(v_h____,X1612) != v_n____
        | hAPP(v_h____,X1612) = v_n____
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),v_n____)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lba____))
        | hAPP(v_h____,X1612) != v_n____
        | hAPP(v_h____,X1612) = v_n____
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),v_n____)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lab____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1612)),v_e____)))
        | hAPP(v_h____,X1612) = v_n____
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),v_n____)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lba____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1612)),v_e____)))
        | hAPP(v_h____,X1612) = v_n____
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),v_n____)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lab____))
        | hAPP(v_h____,X1612) != v_n____
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1612)),v_c____),v_e____)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),v_n____)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lba____))
        | hAPP(v_h____,X1612) != v_n____
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1612)),v_c____),v_e____)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),v_n____)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lab____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1612)),v_e____)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1612)),v_c____),v_e____)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),v_n____)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lba____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1612)),v_e____)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1612)),v_c____),v_e____)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),v_n____)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lab____))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),v_n____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1612)),v_e____))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lba____))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),v_n____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1612)),v_e____))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lab____))
        | hAPP(v_h____,X1612) != v_n____
        | hAPP(v_h____,X1612) = v_n____
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1612)),v_e____))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lba____))
        | hAPP(v_h____,X1612) != v_n____
        | hAPP(v_h____,X1612) = v_n____
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1612)),v_e____))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lab____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1612)),v_e____)))
        | hAPP(v_h____,X1612) = v_n____
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1612)),v_e____))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lba____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1612)),v_e____)))
        | hAPP(v_h____,X1612) = v_n____
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1612)),v_e____))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lab____))
        | hAPP(v_h____,X1612) != v_n____
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1612)),v_c____),v_e____)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1612)),v_e____))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lba____))
        | hAPP(v_h____,X1612) != v_n____
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1612)),v_c____),v_e____)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1612)),v_e____))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lab____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1612)),v_e____)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1612)),v_c____),v_e____)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1612)),v_e____))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lba____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1612)),v_e____)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1612)),v_c____),v_e____)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1612)),v_e____))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),v_n____))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1612)),v_e____)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
      & ( hAPP(v_h____,X1612) != v_n____
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1612)),v_c____),v_e____)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),v_n____))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
      & ( hAPP(v_h____,X1612) = v_n____
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1612)),v_e____)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),v_n____))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),v_n____))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1612)),v_e____)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lba____))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
      & ( hAPP(v_h____,X1612) != v_n____
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1612)),v_c____),v_e____)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),v_n____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lba____))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
      & ( hAPP(v_h____,X1612) = v_n____
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1612)),v_e____)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),v_n____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lba____))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),v_n____))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1612)),v_e____)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lab____)) )
      & ( hAPP(v_h____,X1612) != v_n____
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1612)),v_c____),v_e____)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),v_n____))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lab____)) )
      & ( hAPP(v_h____,X1612) = v_n____
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1612)),v_e____)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),v_n____))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lab____)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),v_n____))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1612)),v_e____)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lba____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lab____)) )
      & ( hAPP(v_h____,X1612) != v_n____
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1612)),v_c____),v_e____)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),v_n____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lba____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lab____)) )
      & ( hAPP(v_h____,X1612) = v_n____
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1612)),v_e____)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1612)),v_n____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lba____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lab____)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_527])])]) ).

fof(i_0_628,plain,
    ! [X2393,X2394,X2395,X2396,X2397,X2398] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2398,X2397)),X2396),c_FuncSet_OPi(X2398,X2397,X2395,hAPP(c_COMBK(tc_fun(X2397,tc_HOL_Obool),X2398),X2394))))
      | ~ c_Fun_Oinj__on(X2398,X2397,X2396,X2395)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2397,X2398)),X2393),c_FuncSet_OPi(X2397,X2398,X2394,hAPP(c_COMBK(tc_fun(X2398,tc_HOL_Obool),X2397),X2395))))
      | ~ c_Fun_Oinj__on(X2397,X2398,X2393,X2394)
      | ~ c_Finite__Set_Ofinite(X2398,X2395)
      | ~ c_Finite__Set_Ofinite(X2397,X2394)
      | c_Finite__Set_Ocard(X2398,X2395) = c_Finite__Set_Ocard(X2397,X2394) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__bij])]) ).

fof(i_0_629,plain,
    ! [X1748,X1749,X1750] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1750,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1750,tc_fun(X1750,tc_HOL_Obool),tc_HOL_Obool),c_member(X1750)),X1749)),hAPP(hAPP(c_COMBC(X1750,tc_fun(X1750,tc_HOL_Obool),tc_HOL_Obool),c_member(X1750)),X1748)))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1750,tc_HOL_Obool),X1749),X1748)) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1750,tc_HOL_Obool),X1749),X1748))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1750,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1750,tc_fun(X1750,tc_HOL_Obool),tc_HOL_Obool),c_member(X1750)),X1749)),hAPP(hAPP(c_COMBC(X1750,tc_fun(X1750,tc_HOL_Obool),tc_HOL_Obool),c_member(X1750)),X1748))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__subset__eq])]) ).

fof(i_0_630,plain,
    ! [X1601] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1601)),v_n____))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1601)),v_e____)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,X1601))) )
      & ( hAPP(v_h____,X1601) != v_n____
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1601)),v_c____),v_e____)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1601)),v_n____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,X1601))) )
      & ( hAPP(v_h____,X1601) = v_n____
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1601)),v_e____)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1601)),v_n____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,X1601))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1601)),v_n____))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1601)),v_n____))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,X1601))) )
      & ( hAPP(v_h____,X1601) != v_n____
        | hAPP(v_h____,X1601) = v_n____
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1601)),v_n____))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,X1601))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1601)),v_e____)))
        | hAPP(v_h____,X1601) = v_n____
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1601)),v_n____))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,X1601))) )
      & ( hAPP(v_h____,X1601) != v_n____
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1601)),v_c____),v_e____)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1601)),v_n____))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,X1601))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1601)),v_e____)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1601)),v_c____),v_e____)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1601)),v_n____))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,X1601))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1601)),v_n____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1601)),v_e____)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,X1601))) )
      & ( hAPP(v_h____,X1601) != v_n____
        | hAPP(v_h____,X1601) = v_n____
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1601)),v_e____)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,X1601))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1601)),v_e____)))
        | hAPP(v_h____,X1601) = v_n____
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1601)),v_e____)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,X1601))) )
      & ( hAPP(v_h____,X1601) != v_n____
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1601)),v_c____),v_e____)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1601)),v_e____)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,X1601))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1601)),v_e____)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1601)),v_c____),v_e____)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1601)),v_e____)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,X1601))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_528])])]) ).

fof(i_0_631,plain,
    ! [X3029,X3030,X3031,X3032] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X3032,c_Set_Oimage(X3031,X3032,X3030,X3029))),c_Finite__Set_Ocard(X3031,X3029)))
      | ~ c_Fun_Oinj__on(X3031,X3032,X3030,X3029) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_529])]) ).

fof(i_0_632,plain,
    ! [X3074,X3075,X3076,X3077,X3078] :
      ( ( ~ c_Fun_Oinj__on(X3077,X3075,X3078,X3076)
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3075,tc_HOL_Obool),c_Set_Oimage(X3077,X3075,X3078,X3076)),X3074))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X3077,X3076)),c_Finite__Set_Ocard(X3075,X3074)))
        | ~ c_Finite__Set_Ofinite(X3075,X3074)
        | ~ c_Finite__Set_Ofinite(X3077,X3076) )
      & ( c_Fun_Oinj__on(X3077,X3075,esk40_4(X3074,X3075,X3076,X3077),X3076)
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X3077,X3076)),c_Finite__Set_Ocard(X3075,X3074)))
        | ~ c_Finite__Set_Ofinite(X3075,X3074)
        | ~ c_Finite__Set_Ofinite(X3077,X3076) )
      & ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3075,tc_HOL_Obool),c_Set_Oimage(X3077,X3075,esk40_4(X3074,X3075,X3076,X3077),X3076)),X3074))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X3077,X3076)),c_Finite__Set_Ocard(X3075,X3074)))
        | ~ c_Finite__Set_Ofinite(X3075,X3074)
        | ~ c_Finite__Set_Ofinite(X3077,X3076) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__iff__card__le])])])])]) ).

fof(i_0_633,plain,
    ! [X1923,X1924,X1925,X1926,X1927] :
      ( ( X1924 != X1923
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1924),X1923)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1925),X1927),X1926)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1925),c_Arrow__Order__Mirabelle_OLin))
        | X1927 = X1926 )
      & ( X1924 != X1926
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1927),X1923)),X1925))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1924),X1923)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1925),X1927),X1926)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1925),c_Arrow__Order__Mirabelle_OLin))
        | X1927 = X1926 )
      & ( X1923 != X1926
        | X1924 = X1927
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1924),X1927)),X1925))
        | X1924 = X1926
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1924),X1923)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1925),X1927),X1926)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1925),c_Arrow__Order__Mirabelle_OLin))
        | X1927 = X1926 )
      & ( X1923 = X1926
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1924),X1923)),X1925))
        | X1924 = X1926
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1924),X1923)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1925),X1927),X1926)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1925),c_Arrow__Order__Mirabelle_OLin))
        | X1927 = X1926 )
      & ( X1924 != X1926
        | X1924 = X1926
        | X1924 = X1923
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1924),X1923)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1925),X1927),X1926)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1925),c_Arrow__Order__Mirabelle_OLin))
        | X1927 = X1926 )
      & ( X1923 != X1926
        | X1923 = X1926
        | X1924 = X1926
        | X1924 = X1923
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1924),X1923)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1925),X1927),X1926)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1925),c_Arrow__Order__Mirabelle_OLin))
        | X1927 = X1926 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1924),X1923)),X1925))
        | X1923 = X1926
        | X1924 = X1926
        | X1924 = X1923
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1924),X1923)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1925),X1927),X1926)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1925),c_Arrow__Order__Mirabelle_OLin))
        | X1927 = X1926 )
      & ( X1923 != X1926
        | X1924 != X1927
        | X1924 = X1926
        | X1924 = X1923
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1924),X1923)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1925),X1927),X1926)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1925),c_Arrow__Order__Mirabelle_OLin))
        | X1927 = X1926 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1924),X1923)),X1925))
        | X1924 != X1927
        | X1924 = X1926
        | X1924 = X1923
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1924),X1923)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1925),X1927),X1926)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1925),c_Arrow__Order__Mirabelle_OLin))
        | X1927 = X1926 )
      & ( X1923 != X1926
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1924),X1927)),X1925))
        | X1924 = X1926
        | X1924 = X1923
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1924),X1923)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1925),X1927),X1926)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1925),c_Arrow__Order__Mirabelle_OLin))
        | X1927 = X1926 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1924),X1923)),X1925))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1924),X1927)),X1925))
        | X1924 = X1926
        | X1924 = X1923
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1924),X1923)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1925),X1927),X1926)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1925),c_Arrow__Order__Mirabelle_OLin))
        | X1927 = X1926 )
      & ( X1924 != X1926
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1927),X1923)),X1925))
        | X1924 = X1923
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1924),X1923)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1925),X1927),X1926)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1925),c_Arrow__Order__Mirabelle_OLin))
        | X1927 = X1926 )
      & ( X1923 != X1926
        | X1923 = X1926
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1927),X1923)),X1925))
        | X1924 = X1923
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1924),X1923)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1925),X1927),X1926)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1925),c_Arrow__Order__Mirabelle_OLin))
        | X1927 = X1926 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1924),X1923)),X1925))
        | X1923 = X1926
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1927),X1923)),X1925))
        | X1924 = X1923
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1924),X1923)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1925),X1927),X1926)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1925),c_Arrow__Order__Mirabelle_OLin))
        | X1927 = X1926 )
      & ( X1923 != X1926
        | X1924 != X1927
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1927),X1923)),X1925))
        | X1924 = X1923
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1924),X1923)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1925),X1927),X1926)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1925),c_Arrow__Order__Mirabelle_OLin))
        | X1927 = X1926 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1924),X1923)),X1925))
        | X1924 != X1927
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1927),X1923)),X1925))
        | X1924 = X1923
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1924),X1923)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1925),X1927),X1926)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1925),c_Arrow__Order__Mirabelle_OLin))
        | X1927 = X1926 )
      & ( X1923 != X1926
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1924),X1927)),X1925))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1927),X1923)),X1925))
        | X1924 = X1923
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1924),X1923)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1925),X1927),X1926)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1925),c_Arrow__Order__Mirabelle_OLin))
        | X1927 = X1926 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1924),X1923)),X1925))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1924),X1927)),X1925))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1927),X1923)),X1925))
        | X1924 = X1923
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1924),X1923)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1925),X1927),X1926)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1925),c_Arrow__Order__Mirabelle_OLin))
        | X1927 = X1926 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__above])])]) ).

fof(i_0_634,plain,
    ! [X2060,X2061,X2062,X2063,X2064] :
      ( ( X2061 != X2060
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2061),X2060)),c_Arrow__Order__Mirabelle_Obelow(X2062,X2064,X2063)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2062),c_Arrow__Order__Mirabelle_OLin))
        | X2064 = X2063 )
      & ( X2060 != X2064
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2061),X2063)),X2062))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2061),X2060)),c_Arrow__Order__Mirabelle_Obelow(X2062,X2064,X2063)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2062),c_Arrow__Order__Mirabelle_OLin))
        | X2064 = X2063 )
      & ( X2061 != X2064
        | X2060 = X2063
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2063),X2060)),X2062))
        | X2060 = X2064
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2061),X2060)),c_Arrow__Order__Mirabelle_Obelow(X2062,X2064,X2063)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2062),c_Arrow__Order__Mirabelle_OLin))
        | X2064 = X2063 )
      & ( X2061 = X2064
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2061),X2060)),X2062))
        | X2060 = X2064
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2061),X2060)),c_Arrow__Order__Mirabelle_Obelow(X2062,X2064,X2063)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2062),c_Arrow__Order__Mirabelle_OLin))
        | X2064 = X2063 )
      & ( X2060 != X2064
        | X2060 = X2064
        | X2061 = X2060
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2061),X2060)),c_Arrow__Order__Mirabelle_Obelow(X2062,X2064,X2063)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2062),c_Arrow__Order__Mirabelle_OLin))
        | X2064 = X2063 )
      & ( X2061 != X2064
        | X2061 = X2064
        | X2060 = X2064
        | X2061 = X2060
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2061),X2060)),c_Arrow__Order__Mirabelle_Obelow(X2062,X2064,X2063)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2062),c_Arrow__Order__Mirabelle_OLin))
        | X2064 = X2063 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2061),X2060)),X2062))
        | X2061 = X2064
        | X2060 = X2064
        | X2061 = X2060
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2061),X2060)),c_Arrow__Order__Mirabelle_Obelow(X2062,X2064,X2063)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2062),c_Arrow__Order__Mirabelle_OLin))
        | X2064 = X2063 )
      & ( X2061 != X2064
        | X2060 != X2063
        | X2060 = X2064
        | X2061 = X2060
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2061),X2060)),c_Arrow__Order__Mirabelle_Obelow(X2062,X2064,X2063)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2062),c_Arrow__Order__Mirabelle_OLin))
        | X2064 = X2063 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2061),X2060)),X2062))
        | X2060 != X2063
        | X2060 = X2064
        | X2061 = X2060
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2061),X2060)),c_Arrow__Order__Mirabelle_Obelow(X2062,X2064,X2063)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2062),c_Arrow__Order__Mirabelle_OLin))
        | X2064 = X2063 )
      & ( X2061 != X2064
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2063),X2060)),X2062))
        | X2060 = X2064
        | X2061 = X2060
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2061),X2060)),c_Arrow__Order__Mirabelle_Obelow(X2062,X2064,X2063)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2062),c_Arrow__Order__Mirabelle_OLin))
        | X2064 = X2063 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2061),X2060)),X2062))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2063),X2060)),X2062))
        | X2060 = X2064
        | X2061 = X2060
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2061),X2060)),c_Arrow__Order__Mirabelle_Obelow(X2062,X2064,X2063)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2062),c_Arrow__Order__Mirabelle_OLin))
        | X2064 = X2063 )
      & ( X2060 != X2064
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2061),X2063)),X2062))
        | X2061 = X2060
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2061),X2060)),c_Arrow__Order__Mirabelle_Obelow(X2062,X2064,X2063)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2062),c_Arrow__Order__Mirabelle_OLin))
        | X2064 = X2063 )
      & ( X2061 != X2064
        | X2061 = X2064
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2061),X2063)),X2062))
        | X2061 = X2060
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2061),X2060)),c_Arrow__Order__Mirabelle_Obelow(X2062,X2064,X2063)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2062),c_Arrow__Order__Mirabelle_OLin))
        | X2064 = X2063 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2061),X2060)),X2062))
        | X2061 = X2064
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2061),X2063)),X2062))
        | X2061 = X2060
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2061),X2060)),c_Arrow__Order__Mirabelle_Obelow(X2062,X2064,X2063)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2062),c_Arrow__Order__Mirabelle_OLin))
        | X2064 = X2063 )
      & ( X2061 != X2064
        | X2060 != X2063
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2061),X2063)),X2062))
        | X2061 = X2060
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2061),X2060)),c_Arrow__Order__Mirabelle_Obelow(X2062,X2064,X2063)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2062),c_Arrow__Order__Mirabelle_OLin))
        | X2064 = X2063 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2061),X2060)),X2062))
        | X2060 != X2063
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2061),X2063)),X2062))
        | X2061 = X2060
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2061),X2060)),c_Arrow__Order__Mirabelle_Obelow(X2062,X2064,X2063)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2062),c_Arrow__Order__Mirabelle_OLin))
        | X2064 = X2063 )
      & ( X2061 != X2064
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2063),X2060)),X2062))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2061),X2063)),X2062))
        | X2061 = X2060
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2061),X2060)),c_Arrow__Order__Mirabelle_Obelow(X2062,X2064,X2063)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2062),c_Arrow__Order__Mirabelle_OLin))
        | X2064 = X2063 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2061),X2060)),X2062))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2063),X2060)),X2062))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2061),X2063)),X2062))
        | X2061 = X2060
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2061),X2060)),c_Arrow__Order__Mirabelle_Obelow(X2062,X2064,X2063)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2062),c_Arrow__Order__Mirabelle_OLin))
        | X2064 = X2063 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__below])])]) ).

fof(i_0_635,plain,
    ! [X2830,X2831] :
      ( ~ c_Finite__Set_Ofinite(X2831,X2830)
      | c_Finite__Set_Ocard(X2831,X2830) = c_Finite__Set_Ofold__image(tc_Nat_Onat,X2831,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X2831),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2830) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card_Oeq__fold__g])]) ).

fof(i_0_636,plain,
    ! [X2821,X2822] :
      ( ( ~ c_Finite__Set_Ofinite(X2822,X2821)
        | c_Finite__Set_Ocard(X2822,X2821) = c_Finite__Set_Ofold__image(tc_Nat_Onat,X2822,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X2822),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2821) )
      & ( c_Finite__Set_Ofinite(X2822,X2821)
        | c_Finite__Set_Ocard(X2822,X2821) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_530])]) ).

fof(i_0_637,plain,
    ! [X2987,X2988,X2989,X2990,X2991] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X2991),X2990),c_Set_Oimage(X2989,X2991,X2988,X2987)))
      | hBOOL(hAPP(hAPP(c_member(X2989),hAPP(c_Hilbert__Choice_Oinv__into(X2989,X2991,X2987,X2988),X2990)),X2987)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__into])]) ).

fof(i_0_638,plain,
    ! [X2867,X2868,X2869,X2870,X2871] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2870,tc_HOL_Obool),c_Set_Oimage(X2871,X2870,X2869,X2868)),c_Set_Oimage(X2871,X2870,X2869,X2867)))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2871,tc_HOL_Obool),X2868),X2867))
        | ~ c_Fun_Oinj__on(X2871,X2870,X2869,c_Orderings_Otop__class_Otop(tc_fun(X2871,tc_HOL_Obool))) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2871,tc_HOL_Obool),X2868),X2867))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2870,tc_HOL_Obool),c_Set_Oimage(X2871,X2870,X2869,X2868)),c_Set_Oimage(X2871,X2870,X2869,X2867)))
        | ~ c_Fun_Oinj__on(X2871,X2870,X2869,c_Orderings_Otop__class_Otop(tc_fun(X2871,tc_HOL_Obool))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__image__subset__iff])])]) ).

fof(i_0_639,plain,
    ! [X2445,X2446,X2447] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2447,tc_HOL_Obool)),X2446),X2445))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X2447,tc_HOL_Obool),tc_fun(X2447,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X2447,tc_HOL_Obool),tc_fun(X2447,tc_HOL_Obool)),X2446),X2445)),c_Wellfounded_Ofinite__psubset(X2447))) )
      & ( c_Finite__Set_Ofinite(X2447,X2445)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X2447,tc_HOL_Obool),tc_fun(X2447,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X2447,tc_HOL_Obool),tc_fun(X2447,tc_HOL_Obool)),X2446),X2445)),c_Wellfounded_Ofinite__psubset(X2447))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2447,tc_HOL_Obool)),X2446),X2445))
        | ~ c_Finite__Set_Ofinite(X2447,X2445)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X2447,tc_HOL_Obool),tc_fun(X2447,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X2447,tc_HOL_Obool),tc_fun(X2447,tc_HOL_Obool)),X2446),X2445)),c_Wellfounded_Ofinite__psubset(X2447))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__finite__psubset])])]) ).

cnf(i_0_640,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1)),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1)),v_c____),v_e____))) ),
    inference(split_conjunct,[status(thm)],[i_0_531]) ).

fof(i_0_641,plain,
    ! [X3057,X3058,X3059,X3060,X3061] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3061,X3060)),X3059),c_FuncSet_OPi(X3061,X3060,X3058,hAPP(c_COMBK(tc_fun(X3060,tc_HOL_Obool),X3061),X3057))))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3060,tc_HOL_Obool),c_Set_Oimage(X3061,X3060,X3059,X3058)),X3057)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_funcset__image])]) ).

fof(i_0_642,plain,
    ! [X2981,X2982,X2983,X2984,X2985,X2986] :
      ( hAPP(c_Hilbert__Choice_Oinv__into(X2986,X2985,X2984,X2983),X2982) != hAPP(c_Hilbert__Choice_Oinv__into(X2986,X2985,X2984,X2983),X2981)
      | ~ hBOOL(hAPP(hAPP(c_member(X2985),X2982),c_Set_Oimage(X2986,X2985,X2983,X2984)))
      | ~ hBOOL(hAPP(hAPP(c_member(X2985),X2981),c_Set_Oimage(X2986,X2985,X2983,X2984)))
      | X2982 = X2981 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__injective])]) ).

fof(i_0_643,plain,
    ! [X2805,X2806] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2806),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2806),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2806),c_Groups_Oone__class_Oone(X2806)),X2805)),X2805)),c_Groups_Ozero__class_Ozero(X2806)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2806),X2805),c_Groups_Ozero__class_Ozero(X2806)))
        | ~ hBOOL(hAPP(hAPP(c_member(X2806),X2805),c_Int_Oring__1__class_OInts(X2806)))
        | ~ class_Rings_Olinordered__idom(X2806) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2806),X2805),c_Groups_Ozero__class_Ozero(X2806)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2806),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2806),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2806),c_Groups_Oone__class_Oone(X2806)),X2805)),X2805)),c_Groups_Ozero__class_Ozero(X2806)))
        | ~ hBOOL(hAPP(hAPP(c_member(X2806),X2805),c_Int_Oring__1__class_OInts(X2806)))
        | ~ class_Rings_Olinordered__idom(X2806) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__odd__less__0])])]) ).

fof(i_0_644,plain,
    ! [X2849,X2850,X2851,X2852,X2854,X2855] :
      ( ( X2849 = hAPP(X2850,esk34_4(X2849,X2850,X2851,X2852))
        | ~ hBOOL(hAPP(hAPP(c_member(X2851),X2849),c_Set_Oimage(X2852,X2851,X2850,c_Orderings_Otop__class_Otop(tc_fun(X2852,tc_HOL_Obool)))))
        | ~ c_Fun_Oinj__on(X2852,X2851,X2850,c_Orderings_Otop__class_Otop(tc_fun(X2852,tc_HOL_Obool))) )
      & ( X2849 != hAPP(X2850,X2854)
        | X2854 = esk34_4(X2849,X2850,X2851,X2852)
        | ~ hBOOL(hAPP(hAPP(c_member(X2851),X2849),c_Set_Oimage(X2852,X2851,X2850,c_Orderings_Otop__class_Otop(tc_fun(X2852,tc_HOL_Obool)))))
        | ~ c_Fun_Oinj__on(X2852,X2851,X2850,c_Orderings_Otop__class_Otop(tc_fun(X2852,tc_HOL_Obool))) )
      & ( X2849 = hAPP(X2850,esk35_5(X2849,X2850,X2851,X2852,X2855))
        | X2849 != hAPP(X2850,X2855)
        | hBOOL(hAPP(hAPP(c_member(X2851),X2849),c_Set_Oimage(X2852,X2851,X2850,c_Orderings_Otop__class_Otop(tc_fun(X2852,tc_HOL_Obool)))))
        | ~ c_Fun_Oinj__on(X2852,X2851,X2850,c_Orderings_Otop__class_Otop(tc_fun(X2852,tc_HOL_Obool))) )
      & ( esk35_5(X2849,X2850,X2851,X2852,X2855) != X2855
        | X2849 != hAPP(X2850,X2855)
        | hBOOL(hAPP(hAPP(c_member(X2851),X2849),c_Set_Oimage(X2852,X2851,X2850,c_Orderings_Otop__class_Otop(tc_fun(X2852,tc_HOL_Obool)))))
        | ~ c_Fun_Oinj__on(X2852,X2851,X2850,c_Orderings_Otop__class_Otop(tc_fun(X2852,tc_HOL_Obool))) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_range__ex1__eq])])])])]) ).

fof(i_0_645,plain,
    ! [X2872,X2873,X2874,X2875] :
      ( ~ c_Finite__Set_Ofinite(X2875,X2874)
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2873,c_Set_Oimage(X2875,X2873,X2872,X2874))),c_Finite__Set_Ocard(X2875,X2874))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__image__le])]) ).

fof(i_0_646,plain,
    ! [X2954,X2955,X2956,X2957,X2958] :
      ( ~ c_Fun_Oinj__on(X2958,X2957,X2956,X2955)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2958,tc_HOL_Obool)),X2954),X2955))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2957,tc_HOL_Obool)),c_Set_Oimage(X2958,X2957,X2956,X2954)),c_Set_Oimage(X2958,X2957,X2956,X2955))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__strict__subset])]) ).

fof(i_0_647,plain,
    ! [X2857,X2858,X2859] :
      ( ~ c_Finite__Set_Ofinite(X2859,X2858)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2859,tc_HOL_Obool),c_Set_Oimage(X2859,X2859,X2857,X2858)),X2858))
      | ~ c_Fun_Oinj__on(X2859,X2859,X2857,X2858)
      | c_Set_Oimage(X2859,X2859,X2857,X2858) = X2858 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_endo__inj__surj])]) ).

fof(i_0_648,plain,
    ! [X3068,X3069,X3070,X3071,X3072] :
      ( ~ c_Fun_Oinj__on(X3072,X3071,X3070,X3069)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3071,tc_HOL_Obool),c_Set_Oimage(X3072,X3071,X3070,X3069)),X3068))
      | ~ c_Finite__Set_Ofinite(X3071,X3068)
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X3072,X3069)),c_Finite__Set_Ocard(X3071,X3068))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__inj__on__le])]) ).

fof(i_0_649,plain,
    ! [X2896,X2897,X2898,X2899,X2900,X2902,X2903,X2904,X2905,X2906,X2907] :
      ( ( hBOOL(hAPP(hAPP(c_member(X2898),esk36_4(X2896,X2897,X2898,X2899)),X2896))
        | ~ hBOOL(hAPP(hAPP(c_member(X2900),X2899),c_Set_Oimage(X2898,X2900,X2897,X2896))) )
      & ( X2899 = hAPP(X2897,esk36_4(X2896,X2897,X2898,X2899))
        | ~ hBOOL(hAPP(hAPP(c_member(X2900),X2899),c_Set_Oimage(X2898,X2900,X2897,X2896))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X2904),X2906),X2902))
        | X2905 != hAPP(X2903,X2906)
        | hBOOL(hAPP(hAPP(c_member(X2907),X2905),c_Set_Oimage(X2904,X2907,X2903,X2902))) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__iff])])])])])]) ).

fof(i_0_650,plain,
    ! [X1758,X1759,X1760] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1759),X1758)),X1760))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1758),X1759)),X1760))
        | X1759 = X1758
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1760),c_Arrow__Order__Mirabelle_OLin)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1758),X1759)),X1760))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1759),X1758)),X1760))
        | X1759 = X1758
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1760),c_Arrow__Order__Mirabelle_OLin)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_532])])]) ).

fof(i_0_651,plain,
    ! [X1761,X1762,X1763] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1763),c_Arrow__Order__Mirabelle_OLin))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1762),X1761)),X1763))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1761),X1762)),X1763)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_533])]) ).

fof(i_0_652,plain,
    ! [X2388,X2389,X2390,X2391,X2392] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2392,X2391)),X2390),c_FuncSet_OPi(X2392,X2391,X2389,hAPP(c_COMBK(tc_fun(X2391,tc_HOL_Obool),X2392),X2388))))
      | ~ c_Fun_Oinj__on(X2392,X2391,X2390,X2389)
      | ~ c_Finite__Set_Ofinite(X2391,X2388)
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2392,X2389)),c_Finite__Set_Ocard(X2391,X2388))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__inj])]) ).

fof(i_0_653,plain,
    ! [X2239,X2240,X2241,X2242,X2243] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2243,tc_HOL_Obool),X2242),X2241))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X2243,X2240),tc_HOL_Obool),c_FuncSet_OPi(X2243,X2240,X2241,X2239)),c_FuncSet_OPi(X2243,X2240,X2242,X2239))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__anti__mono])]) ).

fof(i_0_654,plain,
    ! [X2884,X2885,X2886,X2887,X2888] :
      ( ~ c_Finite__Set_Ofinite(X2888,c_Set_Oimage(X2887,X2888,X2886,c_Orderings_Otop__class_Otop(tc_fun(X2887,tc_HOL_Obool))))
      | c_Finite__Set_Ofinite(X2885,c_Set_Oimage(X2887,X2885,hAPP(c_COMBB(X2888,X2885,X2887,X2884),X2886),c_Orderings_Otop__class_Otop(tc_fun(X2887,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__range__imageI])]) ).

fof(i_0_655,plain,
    ! [X1922] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1922),c_Arrow__Order__Mirabelle_OLin))
      | hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi),X1922)),c_Arrow__Order__Mirabelle_OProf)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_const__Lin__Prof])]) ).

fof(i_0_656,plain,
    ! [X2211,X2212,X2213,X2214,X2215,X2216] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2216,X2215)),X2214),c_FuncSet_OPi(X2216,X2215,X2213,hAPP(c_COMBK(tc_fun(X2215,tc_HOL_Obool),X2216),X2212))))
      | ~ hBOOL(hAPP(hAPP(c_member(X2216),X2211),X2213))
      | hBOOL(hAPP(hAPP(c_member(X2215),hAPP(X2214,X2211)),X2212)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_funcset__mem])]) ).

cnf(i_0_657,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | hAPP(v_h____,X1) != v_n____
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1)),v_c____),v_e____))) ),
    inference(split_conjunct,[status(thm)],[i_0_531]) ).

fof(i_0_658,plain,
    ! [X2944,X2945,X2946,X2947,X2948] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2948,tc_HOL_Obool),X2947),X2946))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2945,tc_HOL_Obool),c_Set_Oimage(X2948,X2945,X2944,X2947)),c_Set_Oimage(X2948,X2945,X2944,X2946))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__mono])]) ).

fof(i_0_659,plain,
    ! [X2435,X2436,X2437,X2438,X2439] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X2439,X2438)),hAPP(X2439,X2437)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2436,X2436)),hAPP(hAPP(c_Product__Type_OPair(X2436,X2436),X2438),X2437)),X2435))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X2436,X2436)),hAPP(hAPP(c_Product__Type_OPair(X2436,X2436),X2438),X2437)),c_Wellfounded_Omlex__prod(X2436,X2439,X2435))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mlex__leq])]) ).

cnf(i_0_660,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1)),v_c____),v_e____)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | hAPP(v_h____,X1) != v_n____
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____)) ),
    inference(split_conjunct,[status(thm)],[i_0_531]) ).

cnf(i_0_661,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1)),v_e____))) ),
    inference(split_conjunct,[status(thm)],[i_0_531]) ).

fof(i_0_662,plain,
    ! [X1621,X1622,X1623,X1624,X1625] :
      ( ( ~ c_FunDef_Oin__rel(X1625,X1624,X1623,X1622,X1621)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X1625,X1624)),hAPP(hAPP(c_Product__Type_OPair(X1625,X1624),X1622),X1621)),X1623)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1625,X1624)),hAPP(hAPP(c_Product__Type_OPair(X1625,X1624),X1622),X1621)),X1623))
        | c_FunDef_Oin__rel(X1625,X1624,X1623,X1622,X1621) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__rel__def])]) ).

cnf(i_0_663,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | hAPP(v_h____,X1) = v_n____
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1)),v_e____))) ),
    inference(split_conjunct,[status(thm)],[i_0_531]) ).

cnf(i_0_664,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1)),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____)) ),
    inference(split_conjunct,[status(thm)],[i_0_531]) ).

fof(i_0_665,plain,
    ! [X2992,X2993,X2994,X2995,X2996] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X2996),X2995),c_Set_Oimage(X2994,X2996,X2993,X2992)))
      | hAPP(X2993,hAPP(c_Hilbert__Choice_Oinv__into(X2994,X2996,X2992,X2993),X2995)) = X2995 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_f__inv__into__f])]) ).

cnf(i_0_666,plain,
    ( hAPP(v_h____,X1) = v_n____
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1)),v_e____)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____)) ),
    inference(split_conjunct,[status(thm)],[i_0_531]) ).

fof(i_0_667,plain,
    ! [X2967,X2968,X2969,X2970,X2971,X2972,X2973] :
      ( ( c_Set_Oimage(X2969,X2968,X2967,c_Orderings_Otop__class_Otop(tc_fun(X2969,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X2968,tc_HOL_Obool))
        | hAPP(X2967,hAPP(c_Hilbert__Choice_Oinv__into(X2969,X2968,c_Orderings_Otop__class_Otop(tc_fun(X2969,tc_HOL_Obool)),X2967),X2970)) = X2970 )
      & ( hAPP(X2971,hAPP(c_Hilbert__Choice_Oinv__into(X2973,X2972,c_Orderings_Otop__class_Otop(tc_fun(X2973,tc_HOL_Obool)),X2971),esk38_3(X2971,X2972,X2973))) != esk38_3(X2971,X2972,X2973)
        | c_Set_Oimage(X2973,X2972,X2971,c_Orderings_Otop__class_Otop(tc_fun(X2973,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X2972,tc_HOL_Obool)) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__iff__all])])])])]) ).

fof(i_0_668,plain,
    ! [X3033,X3034,X3035,X3036,X3037] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3037,tc_HOL_Obool),X3036),c_Set_Oimage(X3035,X3037,X3034,X3033)))
      | c_Fun_Oinj__on(X3037,X3035,c_Hilbert__Choice_Oinv__into(X3035,X3037,X3033,X3034),X3036) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__inv__into])]) ).

fof(i_0_669,plain,
    ! [X1603,X1604,X1605,X1606] :
      ( ( X1605 != X1603
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1606),X1605)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1604),X1603))) )
      & ( X1606 != X1603
        | X1606 != X1605
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1606),X1605)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1604),X1603))) )
      & ( X1606 = X1603
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1606),X1605)),X1604))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1606),X1605)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1604),X1603))) )
      & ( X1606 != X1603
        | X1606 = X1603
        | X1605 = X1603
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1606),X1605)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1604),X1603))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1606),X1605)),X1604))
        | X1606 = X1603
        | X1605 = X1603
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1606),X1605)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1604),X1603))) )
      & ( X1606 != X1603
        | X1606 = X1605
        | X1605 = X1603
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1606),X1605)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1604),X1603))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1606),X1605)),X1604))
        | X1606 = X1605
        | X1605 = X1603
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1606),X1605)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1604),X1603))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__mkbot])])]) ).

fof(i_0_670,plain,
    ! [X1607,X1608,X1609,X1610] :
      ( ( X1610 != X1607
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1610),X1609)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1608),X1607))) )
      & ( X1609 != X1607
        | X1610 != X1609
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1610),X1609)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1608),X1607))) )
      & ( X1609 = X1607
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1610),X1609)),X1608))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1610),X1609)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1608),X1607))) )
      & ( X1609 != X1607
        | X1609 = X1607
        | X1610 = X1607
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1610),X1609)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1608),X1607))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1610),X1609)),X1608))
        | X1609 = X1607
        | X1610 = X1607
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1610),X1609)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1608),X1607))) )
      & ( X1609 != X1607
        | X1610 = X1609
        | X1610 = X1607
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1610),X1609)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1608),X1607))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1610),X1609)),X1608))
        | X1610 = X1609
        | X1610 = X1607
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1610),X1609)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1608),X1607))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__mktop])])]) ).

fof(i_0_671,plain,
    ! [X3162,X3163,X3164,X3165,X3166,X3167] : hAPP(c_COMBS(X3167,X3166,X3165,X3164,X3163),X3162) = hAPP(hAPP(X3164,X3162),hAPP(X3163,X3162)),
    inference(variable_rename,[status(thm)],[help_c__COMBS__1]) ).

fof(i_0_672,plain,
    ! [X2217,X2218,X2219,X2220,X2221,X2222] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2222,X2221)),X2220),c_FuncSet_OPi(X2222,X2221,X2219,X2218)))
      | ~ hBOOL(hAPP(hAPP(c_member(X2222),X2217),X2219))
      | hBOOL(hAPP(hAPP(c_member(X2221),hAPP(X2220,X2217)),hAPP(X2218,X2217))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__mem])]) ).

fof(i_0_673,plain,
    ! [X2205,X2206,X2207,X2208,X2209,X2210] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2210,X2209)),X2208),c_FuncSet_OPi(X2210,X2209,X2207,X2206)))
      | hBOOL(hAPP(hAPP(c_member(X2209),hAPP(X2208,X2205)),hAPP(X2206,X2205)))
      | ~ hBOOL(hAPP(hAPP(c_member(X2210),X2205),X2207)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_534])]) ).

fof(i_0_674,plain,
    ! [X2844,X2845,X2846,X2847,X2848] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X2847),hAPP(X2846,X2845)),c_Set_Oimage(X2848,X2847,X2846,X2844)))
        | hBOOL(hAPP(hAPP(c_member(X2848),X2845),X2844))
        | ~ c_Fun_Oinj__on(X2848,X2847,X2846,c_Orderings_Otop__class_Otop(tc_fun(X2848,tc_HOL_Obool))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X2848),X2845),X2844))
        | hBOOL(hAPP(hAPP(c_member(X2847),hAPP(X2846,X2845)),c_Set_Oimage(X2848,X2847,X2846,X2844)))
        | ~ c_Fun_Oinj__on(X2848,X2847,X2846,c_Orderings_Otop__class_Otop(tc_fun(X2848,tc_HOL_Obool))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__image__mem__iff])])]) ).

fof(i_0_675,plain,
    ! [X2959,X2960,X2961,X2962] :
      ( c_Set_Oimage(X2962,X2961,X2960,c_Orderings_Otop__class_Otop(tc_fun(X2962,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X2961,tc_HOL_Obool))
      | c_Set_Oimage(X2962,X2961,X2960,c_Set_Oimage(X2961,X2962,c_Hilbert__Choice_Oinv__into(X2962,X2961,c_Orderings_Otop__class_Otop(tc_fun(X2962,tc_HOL_Obool)),X2960),X2959)) = X2959 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__surj__f__inv__f])]) ).

fof(i_0_676,plain,
    ! [X2975,X2976,X2977,X2978,X2979,X2980] :
      ( c_Set_Oimage(X2980,X2979,X2978,X2977) != X2976
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2979,tc_HOL_Obool),X2975),X2976))
      | c_Set_Oimage(X2980,X2979,X2978,c_Set_Oimage(X2979,X2980,c_Hilbert__Choice_Oinv__into(X2980,X2979,X2977,X2978),X2975)) = X2975 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__inv__into__cancel])]) ).

fof(i_0_677,plain,
    ! [X2158,X2159,X2160,X2161,X2162,X2163,X2164,X2165,X2166,X2167] :
      ( ( ~ c_Fun_Oinj__on(X2161,X2160,X2159,X2158)
        | ~ hBOOL(hAPP(hAPP(c_member(X2161),X2162),X2158))
        | ~ hBOOL(hAPP(hAPP(c_member(X2161),X2163),X2158))
        | hAPP(X2159,X2162) != hAPP(X2159,X2163)
        | X2162 = X2163 )
      & ( hBOOL(hAPP(hAPP(c_member(X2167),esk12_4(X2164,X2165,X2166,X2167)),X2164))
        | c_Fun_Oinj__on(X2167,X2166,X2165,X2164) )
      & ( hBOOL(hAPP(hAPP(c_member(X2167),esk13_4(X2164,X2165,X2166,X2167)),X2164))
        | c_Fun_Oinj__on(X2167,X2166,X2165,X2164) )
      & ( hAPP(X2165,esk12_4(X2164,X2165,X2166,X2167)) = hAPP(X2165,esk13_4(X2164,X2165,X2166,X2167))
        | c_Fun_Oinj__on(X2167,X2166,X2165,X2164) )
      & ( esk12_4(X2164,X2165,X2166,X2167) != esk13_4(X2164,X2165,X2166,X2167)
        | c_Fun_Oinj__on(X2167,X2166,X2165,X2164) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__def])])])])])]) ).

fof(i_0_678,plain,
    ! [X1751,X1752,X1753] :
      ( X1753 = X1752
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1751),c_Arrow__Order__Mirabelle_OLin))
      | hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1751),X1753),X1752)),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_above__Lin])]) ).

fof(i_0_679,plain,
    ! [X2919,X2920,X2921,X2922,X2923] : c_Set_Oimage(X2923,X2922,hAPP(c_COMBB(X2921,X2922,X2923,X2920),X2919),c_Orderings_Otop__class_Otop(tc_fun(X2923,tc_HOL_Obool))) = c_Set_Oimage(X2921,X2922,X2920,c_Set_Oimage(X2923,X2921,X2919,c_Orderings_Otop__class_Otop(tc_fun(X2923,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_range__composition]) ).

fof(i_0_680,plain,
    ! [X2860,X2861,X2862] :
      ( ~ c_Finite__Set_Ofinite(X2862,X2861)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2862,tc_HOL_Obool),X2861),c_Set_Oimage(X2862,X2862,X2860,X2861)))
      | c_Fun_Oinj__on(X2862,X2862,X2860,X2861) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__surj__inj])]) ).

fof(i_0_681,plain,
    ! [X2233,X2234,X2235,X2236,X2237] :
      ( ( ~ c_Arrow__Order__Mirabelle_Odictator(X2234,X2233)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2235),c_Arrow__Order__Mirabelle_OProf))
        | hAPP(X2234,X2235) = hAPP(X2235,X2233) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk17_2(X2236,X2237)),c_Arrow__Order__Mirabelle_OProf))
        | c_Arrow__Order__Mirabelle_Odictator(X2237,X2236) )
      & ( hAPP(X2237,esk17_2(X2236,X2237)) != hAPP(esk17_2(X2236,X2237),X2236)
        | c_Arrow__Order__Mirabelle_Odictator(X2237,X2236) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dictator__def])])])])])]) ).

fof(i_0_682,plain,
    ! [X2085,X2086,X2087,X2088] :
      ( ~ c_Fun_Oinj__on(X2088,X2087,X2086,c_Orderings_Otop__class_Otop(tc_fun(X2088,tc_HOL_Obool)))
      | c_Fun_Oinj__on(X2088,tc_fun(X2085,X2087),hAPP(c_COMBB(X2087,tc_fun(X2085,X2087),X2088,c_COMBK(X2087,X2085)),X2086),c_Orderings_Otop__class_Otop(tc_fun(X2088,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__fun])]) ).

fof(i_0_683,plain,
    ! [X2226,X2227] : hBOOL(hAPP(hAPP(c_member(tc_fun(X2227,X2227)),c_COMBI(X2227)),c_FuncSet_OPi(X2227,X2227,X2226,hAPP(c_COMBK(tc_fun(X2227,tc_HOL_Obool),X2227),X2226)))),
    inference(variable_rename,[status(thm)],[fact_funcset__id]) ).

fof(i_0_684,plain,
    ! [X2926,X2927,X2928,X2929,X2930,X2931] : c_Set_Oimage(X2931,X2930,X2929,c_Set_Oimage(X2928,X2931,X2927,X2926)) = c_Set_Oimage(X2928,X2930,hAPP(c_COMBB(X2931,X2930,X2928,X2929),X2927),X2926),
    inference(variable_rename,[status(thm)],[fact_image__image]) ).

fof(i_0_685,plain,
    ! [X2089,X2090,X2091] :
      ( X2091 = X2090
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2089),c_Arrow__Order__Mirabelle_OLin))
      | hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Obelow(X2089,X2091,X2090)),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_below__Lin])]) ).

fof(i_0_686,plain,
    ! [X2431,X2432,X2433,X2434] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2434,X2434)),hAPP(hAPP(c_Product__Type_OPair(X2434,X2434),X2433),X2432)),c_Wellfounded_Omeasure(X2434,X2431)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2431,X2433)),hAPP(X2431,X2432))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2431,X2433)),hAPP(X2431,X2432)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X2434,X2434)),hAPP(hAPP(c_Product__Type_OPair(X2434,X2434),X2433),X2432)),c_Wellfounded_Omeasure(X2434,X2431))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__measure])]) ).

fof(i_0_687,plain,
    ! [X3038,X3039,X3040,X3041,X3042] :
      ( ~ c_Fun_Oinj__on(X3042,X3041,X3040,X3039)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3042,tc_HOL_Obool),X3038),X3039))
      | c_Set_Oimage(X3041,X3042,c_Hilbert__Choice_Oinv__into(X3042,X3041,X3039,X3040),c_Set_Oimage(X3042,X3041,X3040,X3038)) = X3038 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__image__cancel])]) ).

fof(i_0_688,plain,
    ! [X3010,X3011,X3012,X3013,X3014] :
      ( ~ c_Finite__Set_Ofinite(X3014,X3013)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3012,tc_HOL_Obool),X3011),c_Set_Oimage(X3014,X3012,X3010,X3013)))
      | c_Finite__Set_Ofinite(X3012,X3011) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__surj])]) ).

fof(i_0_689,plain,
    ! [X1754,X1755] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1755),c_Arrow__Order__Mirabelle_OLin))
      | hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1755),X1754)),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mkbot__Lin])]) ).

fof(i_0_690,plain,
    ! [X1756,X1757] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1757),c_Arrow__Order__Mirabelle_OLin))
      | hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1757),X1756)),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mktop__Lin])]) ).

fof(i_0_691,plain,
    ! [X3050,X3051,X3052,X3053] :
      ( ~ c_Fun_Oinj__on(X3053,X3052,X3051,c_Orderings_Otop__class_Otop(tc_fun(X3053,tc_HOL_Obool)))
      | c_Set_Oimage(X3052,X3053,c_Hilbert__Choice_Oinv__into(X3053,X3052,c_Orderings_Otop__class_Otop(tc_fun(X3053,tc_HOL_Obool)),X3051),c_Set_Oimage(X3053,X3052,X3051,X3050)) = X3050 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__image__comp])]) ).

fof(i_0_692,plain,
    ! [X3046,X3047,X3048,X3049] :
      ( ~ c_Fun_Oinj__on(X3049,X3048,X3047,c_Orderings_Otop__class_Otop(tc_fun(X3049,tc_HOL_Obool)))
      | c_Set_Oimage(X3048,X3049,c_Hilbert__Choice_Oinv__into(X3049,X3048,c_Orderings_Otop__class_Otop(tc_fun(X3049,tc_HOL_Obool)),X3047),c_Set_Oimage(X3049,X3048,X3047,X3046)) = X3046 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__inv__f__f])]) ).

fof(i_0_693,plain,
    ! [X2963,X2964,X2965,X2966] :
      ( c_Set_Oimage(X2966,X2965,X2964,c_Orderings_Otop__class_Otop(tc_fun(X2966,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X2965,tc_HOL_Obool))
      | hAPP(X2964,hAPP(c_Hilbert__Choice_Oinv__into(X2966,X2965,c_Orderings_Otop__class_Otop(tc_fun(X2966,tc_HOL_Obool)),X2964),X2963)) = X2963 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__f__inv__f])]) ).

fof(i_0_694,plain,
    ! [X2440,X2441,X2442,X2443,X2444] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2444,X2443)),hAPP(X2444,X2442)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X2441,X2441)),hAPP(hAPP(c_Product__Type_OPair(X2441,X2441),X2443),X2442)),c_Wellfounded_Omlex__prod(X2441,X2444,X2440))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mlex__less])]) ).

fof(i_0_695,plain,
    ! [X3114,X3115] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool),X3115),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3114,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3114),c_Finite__Set_Ocard(tc_Nat_Onat,X3115)))))
      | X3115 = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3114,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3114),c_Finite__Set_Ocard(tc_Nat_Onat,X3115))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__card__intvl__is__intvl])]) ).

fof(i_0_696,plain,
    ! [X3116,X3117,X3118,X3119,X3120] :
      ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3120,X3117),X3119))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3120,X3118),X3119))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3120,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(X3120,X3119,X3118)),c_SetInterval_Oord__class_OatLeastLessThan(X3120,X3117,X3116)))
        | ~ class_Orderings_Olinorder(X3120) )
      & ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3120,X3118),X3116))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3120,X3118),X3119))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3120,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(X3120,X3119,X3118)),c_SetInterval_Oord__class_OatLeastLessThan(X3120,X3117,X3116)))
        | ~ class_Orderings_Olinorder(X3120) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__subset__iff])])]) ).

fof(i_0_697,plain,
    ! [X3054,X3055,X3056] :
      ( c_Set_Oimage(X3056,X3055,X3054,c_Orderings_Otop__class_Otop(tc_fun(X3056,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X3055,tc_HOL_Obool))
      | c_Fun_Oinj__on(X3055,X3056,c_Hilbert__Choice_Oinv__into(X3056,X3055,c_Orderings_Otop__class_Otop(tc_fun(X3056,tc_HOL_Obool)),X3054),c_Orderings_Otop__class_Otop(tc_fun(X3055,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__imp__inj__inv])]) ).

fof(i_0_698,plain,
    ! [X3020,X3021,X3022,X3023] : hBOOL(hAPP(hAPP(c_member(X3023),hAPP(X3022,X3021)),c_Set_Oimage(X3020,X3023,X3022,c_Orderings_Otop__class_Otop(tc_fun(X3020,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[fact_rangeI]) ).

fof(i_0_699,plain,
    ! [X3043,X3044,X3045] :
      ( ~ c_Fun_Oinj__on(X3045,X3044,X3043,c_Orderings_Otop__class_Otop(tc_fun(X3045,tc_HOL_Obool)))
      | c_Set_Oimage(X3044,X3045,c_Hilbert__Choice_Oinv__into(X3045,X3044,c_Orderings_Otop__class_Otop(tc_fun(X3045,tc_HOL_Obool)),X3043),c_Orderings_Otop__class_Otop(tc_fun(X3044,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X3045,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__imp__surj__inv])]) ).

fof(i_0_700,plain,
    ! [X2908,X2909,X2910,X2911,X2912] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X2912),X2911),X2910))
      | hBOOL(hAPP(hAPP(c_member(X2909),hAPP(X2908,X2911)),c_Set_Oimage(X2912,X2909,X2908,X2910))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_imageI])]) ).

fof(i_0_701,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____)),
    inference(fof_simplification,[status(thm)],[fact__096_Ib_M_Aa_J_A_126_058_ALab_096]) ).

fof(i_0_702,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lba____)),
    inference(fof_simplification,[status(thm)],[fact__096_Ia_M_Ab_J_A_126_058_ALba_096]) ).

fof(i_0_703,plain,
    ! [X3015,X3016,X3017,X3018,X3019] :
      ( X3019 != hAPP(X3018,X3017)
      | hBOOL(hAPP(hAPP(c_member(X3016),X3019),c_Set_Oimage(X3015,X3016,X3018,c_Orderings_Otop__class_Otop(tc_fun(X3015,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_range__eqI])]) ).

fof(i_0_704,plain,
    ! [X2834,X2835,X2836,X2837,X2838,X2839] :
      ( X2839 != hAPP(X2838,X2837)
      | ~ hBOOL(hAPP(hAPP(c_member(X2836),X2837),X2835))
      | hBOOL(hAPP(hAPP(c_member(X2834),X2839),c_Set_Oimage(X2836,X2834,X2838,X2835))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__eqI])]) ).

fof(i_0_705,plain,
    ! [X2913,X2914,X2915,X2916,X2917,X2918] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X2918),X2917),X2916))
      | X2915 != hAPP(X2914,X2917)
      | hBOOL(hAPP(hAPP(c_member(X2913),X2915),c_Set_Oimage(X2918,X2913,X2914,X2916))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__image__eqI])]) ).

fof(i_0_706,plain,
    ! [X3001,X3002,X3003,X3004,X3005] :
      ( ( c_Set_Oimage(X3005,X3004,X3003,X3002) != c_Set_Oimage(X3005,X3004,X3003,X3001)
        | X3002 = X3001
        | ~ c_Fun_Oinj__on(X3005,X3004,X3003,c_Orderings_Otop__class_Otop(tc_fun(X3005,tc_HOL_Obool))) )
      & ( X3002 != X3001
        | c_Set_Oimage(X3005,X3004,X3003,X3002) = c_Set_Oimage(X3005,X3004,X3003,X3001)
        | ~ c_Fun_Oinj__on(X3005,X3004,X3003,c_Orderings_Otop__class_Otop(tc_fun(X3005,tc_HOL_Obool))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__image__eq__iff])])]) ).

fof(i_0_707,plain,
    ! [X2045,X2046,X2047,X2048] :
      ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2048)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2048),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2048),X2047),X2046)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2048),X2045),X2046)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2048),X2047),X2045)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__right])]) ).

fof(i_0_708,plain,
    ! [X2024,X2025,X2026,X2027] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2027),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2027),X2026),X2025)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2027),X2024),X2025)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2027),X2026),X2024))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2027) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2027),X2026),X2024))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2027),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2027),X2026),X2025)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2027),X2024),X2025)))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2027) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__right])])]) ).

fof(i_0_709,plain,
    ! [X2049,X2050,X2051,X2052] :
      ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2052)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2052),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2052),X2051),X2050)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2052),X2051),X2049)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2052),X2050),X2049)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__left])]) ).

fof(i_0_710,plain,
    ! [X2028,X2029,X2030,X2031] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2031),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2031),X2030),X2029)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2031),X2030),X2028)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2031),X2029),X2028))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2031) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2031),X2029),X2028))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2031),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2031),X2030),X2029)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2031),X2030),X2028)))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2031) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__left])])]) ).

fof(i_0_711,plain,
    ! [X3006,X3007,X3008,X3009] :
      ( ~ c_Finite__Set_Ofinite(X3009,c_Set_Oimage(X3008,X3009,X3007,X3006))
      | ~ c_Fun_Oinj__on(X3008,X3009,X3007,X3006)
      | c_Finite__Set_Ofinite(X3008,X3006) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageD])]) ).

fof(i_0_712,plain,
    ! [X2127,X2128,X2129,X2130] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2130,tc_HOL_Obool)),X2129),X2128))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2130,tc_HOL_Obool)),X2128),X2127))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2130,tc_HOL_Obool)),X2129),X2127)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__trans])]) ).

fof(i_0_713,plain,
    ! [X2020,X2021,X2022,X2023] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2023,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2023),X2022),X2021)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2023),X2020),X2021)))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2023,X2022),X2020))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2023) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2023,X2022),X2020))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2023,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2023),X2022),X2021)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2023),X2020),X2021)))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2023) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__right])])]) ).

fof(i_0_714,plain,
    ! [X1999,X2000,X2001,X2002] :
      ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2002)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2002,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2002),X2001),X2000)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2002),X1999),X2000)))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2002,X2001),X1999)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__right])]) ).

fof(i_0_715,plain,
    ! [X2016,X2017,X2018,X2019] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2019,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2019),X2018),X2017)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2019),X2018),X2016)))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2019,X2017),X2016))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2019) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2019,X2017),X2016))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2019,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2019),X2018),X2017)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2019),X2018),X2016)))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2019) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__left])])]) ).

fof(i_0_716,plain,
    ! [X1995,X1996,X1997,X1998] :
      ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1998)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1998,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1998),X1997),X1996)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1998),X1997),X1995)))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1998,X1996),X1995)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__left])]) ).

fof(i_0_717,plain,
    ! [X2521,X2522,X2523,X2524] :
      ( ( hBOOL(hAPP(hAPP(c_member(X2524),X2523),X2521))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2524,tc_HOL_Obool),c_Set_Oinsert(X2524,X2523,X2522)),X2521)) )
      & ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2524,tc_HOL_Obool),X2522),X2521))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2524,tc_HOL_Obool),c_Set_Oinsert(X2524,X2523,X2522)),X2521)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X2524),X2523),X2521))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2524,tc_HOL_Obool),X2522),X2521))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2524,tc_HOL_Obool),c_Set_Oinsert(X2524,X2523,X2522)),X2521)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__subset])])]) ).

fof(i_0_718,plain,
    ! [X2070,X2071,X2072,X2073] :
      ( ~ c_Fun_Oinj__on(X2073,X2072,X2071,c_Orderings_Otop__class_Otop(tc_fun(X2073,tc_HOL_Obool)))
      | hAPP(c_Hilbert__Choice_Oinv__into(X2073,X2072,c_Orderings_Otop__class_Otop(tc_fun(X2073,tc_HOL_Obool)),X2071),hAPP(X2071,X2070)) = X2070 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__f__f])]) ).

fof(i_0_719,plain,
    ! [X2065,X2066,X2067,X2068,X2069] :
      ( ~ c_Fun_Oinj__on(X2069,X2068,X2067,c_Orderings_Otop__class_Otop(tc_fun(X2069,tc_HOL_Obool)))
      | hAPP(X2067,X2066) != X2065
      | hAPP(c_Hilbert__Choice_Oinv__into(X2069,X2068,c_Orderings_Otop__class_Otop(tc_fun(X2069,tc_HOL_Obool)),X2067),X2065) = X2066 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__f__eq])]) ).

fof(i_0_720,plain,
    ! [X1633,X1634,X1635] :
      ( ( hAPP(hAPP(c_COMBC(X1635,tc_fun(X1635,tc_HOL_Obool),tc_HOL_Obool),c_member(X1635)),X1634) != hAPP(hAPP(c_COMBC(X1635,tc_fun(X1635,tc_HOL_Obool),tc_HOL_Obool),c_member(X1635)),X1633)
        | X1634 = X1633 )
      & ( X1634 != X1633
        | hAPP(hAPP(c_COMBC(X1635,tc_fun(X1635,tc_HOL_Obool),tc_HOL_Obool),c_member(X1635)),X1634) = hAPP(hAPP(c_COMBC(X1635,tc_fun(X1635,tc_HOL_Obool),tc_HOL_Obool),c_member(X1635)),X1633) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__equals__eq])]) ).

fof(i_0_721,plain,
    ! [X2319,X2320,X2321] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2321),X2320)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2321),X2319)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2320),X2319)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2320),X2319))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2321),X2320)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2321),X2319))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__less])]) ).

fof(i_0_722,plain,
    ! [X2080,X2081,X2082,X2083,X2084] :
      ( ~ c_Fun_Oinj__on(X2084,X2083,X2082,X2081)
      | ~ hBOOL(hAPP(hAPP(c_member(X2084),X2080),X2081))
      | hAPP(c_Hilbert__Choice_Oinv__into(X2084,X2083,X2081,X2082),hAPP(X2082,X2080)) = X2080 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__f__f])]) ).

fof(i_0_723,plain,
    ! [X2074,X2075,X2076,X2077,X2078,X2079] :
      ( ~ c_Fun_Oinj__on(X2079,X2078,X2077,X2076)
      | ~ hBOOL(hAPP(hAPP(c_member(X2079),X2075),X2076))
      | hAPP(X2077,X2075) != X2074
      | hAPP(c_Hilbert__Choice_Oinv__into(X2079,X2078,X2076,X2077),X2074) = X2075 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__f__eq])]) ).

fof(i_0_724,plain,
    ! [X2880,X2881,X2882,X2883] :
      ( ~ c_Finite__Set_Ofinite(X2883,X2882)
      | c_Finite__Set_Ocard(X2881,c_Set_Oimage(X2883,X2881,X2880,X2882)) != c_Finite__Set_Ocard(X2883,X2882)
      | c_Fun_Oinj__on(X2883,X2881,X2880,X2882) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__card__imp__inj__on])]) ).

fof(i_0_725,plain,
    ! [X2876,X2877,X2878,X2879] :
      ( ( ~ c_Fun_Oinj__on(X2879,X2877,X2876,X2878)
        | c_Finite__Set_Ocard(X2877,c_Set_Oimage(X2879,X2877,X2876,X2878)) = c_Finite__Set_Ocard(X2879,X2878)
        | ~ c_Finite__Set_Ofinite(X2879,X2878) )
      & ( c_Finite__Set_Ocard(X2877,c_Set_Oimage(X2879,X2877,X2876,X2878)) != c_Finite__Set_Ocard(X2879,X2878)
        | c_Fun_Oinj__on(X2879,X2877,X2876,X2878)
        | ~ c_Finite__Set_Ofinite(X2879,X2878) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__iff__eq__card])])]) ).

fof(i_0_726,plain,
    ! [X2517,X2518,X2519,X2520] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2520,tc_HOL_Obool),X2519),X2518))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2520,tc_HOL_Obool),c_Set_Oinsert(X2520,X2517,X2519)),c_Set_Oinsert(X2520,X2517,X2518))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__mono])]) ).

fof(i_0_727,plain,
    ! [X3150,X3151,X3152,X3153,X3154,X3155] : hAPP(hAPP(c_COMBB(X3155,X3154,X3153,X3152),X3151),X3150) = hAPP(X3152,hAPP(X3151,X3150)),
    inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).

fof(i_0_728,plain,
    ! [X2040,X2041,X2042,X2043,X2044] :
      ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X2044)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2044),X2043),X2042))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2044),X2041),X2040))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2044),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2044),X2043),X2041)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2044),X2042),X2040))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__mono])]) ).

fof(i_0_729,plain,
    ! [X3082,X3083,X3084] : c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X3084),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3083,X3082)) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3083),X3084),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3082),X3084)),
    inference(variable_rename,[status(thm)],[fact_image__add__atLeastLessThan]) ).

fof(i_0_730,plain,
    ! [X2346,X2347,X2348] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2348),X2347)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2348),X2346)))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2347),X2346)) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2347),X2346))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2348),X2347)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2348),X2346))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__le])]) ).

fof(i_0_731,plain,
    ! [X1713,X1714,X1715,X1716,X1717] :
      ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1717)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1717,X1716),X1715))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1717),X1714),X1713))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1717),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1717),X1716),X1714)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1717),X1715),X1713))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__less__mono])]) ).

fof(i_0_732,plain,
    ! [X1708,X1709,X1710,X1711,X1712] :
      ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1712)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1712),X1711),X1710))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1712,X1709),X1708))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1712),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1712),X1711),X1709)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1712),X1710),X1708))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__le__mono])]) ).

fof(i_0_733,plain,
    ! [X2135,X2136,X2137,X2138] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2138,tc_HOL_Obool),X2137),X2136))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2138,tc_HOL_Obool)),X2136),X2135))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2138,tc_HOL_Obool)),X2137),X2135)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__psubset__trans])]) ).

fof(i_0_734,plain,
    ! [X2131,X2132,X2133,X2134] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2134,tc_HOL_Obool)),X2133),X2132))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2134,tc_HOL_Obool),X2132),X2131))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2134,tc_HOL_Obool)),X2133),X2131)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__subset__trans])]) ).

fof(i_0_735,plain,
    ! [X2832,X2833] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2833)),X2832))
        | hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2833),X2832)) )
      & ( ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2833),X2832))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2833)),X2832)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__nat_Osimps_I2_J])]) ).

fof(i_0_736,plain,
    ! [X3024,X3025,X3026,X3027,X3028] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X3028),X3027),X3026))
      | c_Set_Oinsert(X3025,hAPP(X3024,X3027),c_Set_Oimage(X3028,X3025,X3024,X3026)) = c_Set_Oimage(X3028,X3025,X3024,X3026) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__image])]) ).

fof(i_0_737,plain,
    ! [X2399,X2400,X2401] :
      ( ~ c_Finite__Set_Ofinite(X2401,X2400)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2401,tc_HOL_Obool),X2399),X2400))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X2401,X2399)),c_Finite__Set_Ocard(X2401,X2400)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2401,tc_HOL_Obool)),X2399),X2400)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__psubset])]) ).

fof(i_0_738,plain,
    ! [X2003,X2004,X2005,X2006,X2007] :
      ( ~ class_Groups_Oordered__ab__semigroup__add(X2007)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2007,X2006),X2005))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2007,X2004),X2003))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2007,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2007),X2006),X2004)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2007),X2005),X2003))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__mono])]) ).

fof(i_0_739,plain,
    ! [X2623,X2624] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2624),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2624),X2623),X2623)),c_Groups_Ozero__class_Ozero(X2624)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2624),X2623),c_Groups_Ozero__class_Ozero(X2624)))
        | ~ class_Groups_Olinordered__ab__group__add(X2624) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2624),X2623),c_Groups_Ozero__class_Ozero(X2624)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2624),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2624),X2623),X2623)),c_Groups_Ozero__class_Ozero(X2624)))
        | ~ class_Groups_Olinordered__ab__group__add(X2624) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__add__less__zero__iff__single__add__less__zero])])]) ).

fof(i_0_740,plain,
    ! [X2659,X2660] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2660),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2660),X2659),X2659)),c_Groups_Ozero__class_Ozero(X2660)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2660),X2659),c_Groups_Ozero__class_Ozero(X2660)))
        | ~ class_Rings_Olinordered__idom(X2660) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2660),X2659),c_Groups_Ozero__class_Ozero(X2660)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2660),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2660),X2659),X2659)),c_Groups_Ozero__class_Ozero(X2660)))
        | ~ class_Rings_Olinordered__idom(X2660) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_even__less__0__iff])])]) ).

fof(i_0_741,plain,
    ! [X2306,X2307,X2308,X2309] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2309),X2308))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2307),X2306))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2309),X2307)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2308),X2306))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono])]) ).

fof(i_0_742,plain,
    ! [X2949,X2950,X2951,X2952,X2953] : c_Set_Oimage(X2953,X2952,X2951,c_Set_Oinsert(X2953,X2950,X2949)) = c_Set_Oinsert(X2952,hAPP(X2951,X2950),c_Set_Oimage(X2953,X2952,X2951,X2949)),
    inference(variable_rename,[status(thm)],[fact_image__insert]) ).

fof(i_0_743,plain,
    ! [X2865,X2866] :
      ( ~ c_Finite__Set_Ofinite(X2866,c_Orderings_Otop__class_Otop(tc_fun(X2866,tc_HOL_Obool)))
      | c_Set_Oimage(X2866,X2866,X2865,c_Orderings_Otop__class_Otop(tc_fun(X2866,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X2866,tc_HOL_Obool))
      | c_Fun_Oinj__on(X2866,X2866,X2865,c_Orderings_Otop__class_Otop(tc_fun(X2866,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__surj__inj])]) ).

fof(i_0_744,plain,
    ! [X2170,X2171,X2172,X2173,X2174] :
      ( ~ c_Fun_Oinj__on(X2174,X2173,X2172,X2171)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2174,tc_HOL_Obool),X2170),X2171))
      | c_Fun_Oinj__on(X2174,X2173,X2172,X2170) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__inj__on])]) ).

fof(i_0_745,plain,
    ! [X2997,X2998,X2999,X3000] :
      ( ~ c_Fun_Oinj__on(X3000,X2999,X2998,X2997)
      | c_Finite__Set_Ocard(X2999,c_Set_Oimage(X3000,X2999,X2998,X2997)) = c_Finite__Set_Ocard(X3000,X2997) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__image])]) ).

fof(i_0_746,plain,
    ! [X2613,X2614,X2615] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X2615)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2615),X2614),c_Groups_Ozero__class_Ozero(X2615)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2615),X2613),c_Groups_Ozero__class_Ozero(X2615)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2615),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2615),X2614),X2613)),c_Groups_Ozero__class_Ozero(X2615))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__neg])]) ).

fof(i_0_747,plain,
    ! [X2809,X2810,X2811] :
      ( ~ class_Rings_Oring__1(X2811)
      | ~ hBOOL(hAPP(hAPP(c_member(X2811),X2810),c_Int_Oring__1__class_OInts(X2811)))
      | ~ hBOOL(hAPP(hAPP(c_member(X2811),X2809),c_Int_Oring__1__class_OInts(X2811)))
      | hBOOL(hAPP(hAPP(c_member(X2811),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2811),X2810),X2809)),c_Int_Oring__1__class_OInts(X2811))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__add])]) ).

fof(i_0_748,plain,
    ! [X2863,X2864] :
      ( ~ c_Finite__Set_Ofinite(X2864,c_Orderings_Otop__class_Otop(tc_fun(X2864,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(X2864,X2864,X2863,c_Orderings_Otop__class_Otop(tc_fun(X2864,tc_HOL_Obool)))
      | c_Set_Oimage(X2864,X2864,X2863,c_Orderings_Otop__class_Otop(tc_fun(X2864,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X2864,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__inj__surj])]) ).

fof(i_0_749,plain,
    ! [X2032,X2033,X2034,X2035] :
      ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X2035)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2035),X2034),X2033))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2035),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2035),X2034),X2032)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2035),X2033),X2032))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__right__mono])]) ).

fof(i_0_750,plain,
    ! [X2036,X2037,X2038,X2039] :
      ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X2039)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2039),X2038),X2037))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2039),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2039),X2036),X2038)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2039),X2036),X2037))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__left__mono])]) ).

fof(i_0_751,plain,
    ! [X2609,X2610] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2610,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2610),X2609),X2609)),c_Groups_Ozero__class_Ozero(X2610)))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2610,X2609),c_Groups_Ozero__class_Ozero(X2610)))
        | ~ class_Groups_Olinordered__ab__group__add(X2610) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2610,X2609),c_Groups_Ozero__class_Ozero(X2610)))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2610,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2610),X2609),X2609)),c_Groups_Ozero__class_Ozero(X2610)))
        | ~ class_Groups_Olinordered__ab__group__add(X2610) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__add__le__zero__iff__single__add__le__zero])])]) ).

fof(i_0_752,plain,
    ! [X2525,X2526,X2527,X2528] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2528,tc_HOL_Obool),X2526),c_Set_Oinsert(X2528,X2527,X2525)))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2528,tc_HOL_Obool),X2526),X2525))
        | hBOOL(hAPP(hAPP(c_member(X2528),X2527),X2526)) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2528,tc_HOL_Obool),X2526),X2525))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2528,tc_HOL_Obool),X2526),c_Set_Oinsert(X2528,X2527,X2525)))
        | hBOOL(hAPP(hAPP(c_member(X2528),X2527),X2526)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_535])])]) ).

fof(i_0_753,plain,
    ! [X2635,X2636,X2637] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X2637)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2637,X2636),c_Groups_Ozero__class_Ozero(X2637)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2637),X2635),c_Groups_Ozero__class_Ozero(X2637)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2637),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2637),X2636),X2635)),c_Groups_Ozero__class_Ozero(X2637))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__neg])]) ).

fof(i_0_754,plain,
    ! [X2638,X2639,X2640] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X2640)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2640),X2639),c_Groups_Ozero__class_Ozero(X2640)))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2640,X2638),c_Groups_Ozero__class_Ozero(X2640)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2640),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2640),X2639),X2638)),c_Groups_Ozero__class_Ozero(X2640))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__nonpos])]) ).

fof(i_0_755,plain,
    ! [X2253,X2254,X2255,X2256] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2256),X2255))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2254),X2253))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2256),X2254)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2255),X2253))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono])]) ).

fof(i_0_756,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),esk11_0))
    & hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),esk11_0),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_536])])]) ).

fof(i_0_757,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),esk10_0))
    & hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),esk10_0),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_537])])]) ).

fof(i_0_758,plain,
    ! [X2544,X2545,X2546,X2547] :
      ( ( c_Finite__Set_Ofinite(X2547,X2545)
        | ~ c_Finite__Set_Ofinite(tc_sum(X2547,X2546),c_Sum__Type_OPlus(X2547,X2546,X2545,X2544)) )
      & ( c_Finite__Set_Ofinite(X2546,X2544)
        | ~ c_Finite__Set_Ofinite(tc_sum(X2547,X2546),c_Sum__Type_OPlus(X2547,X2546,X2545,X2544)) )
      & ( ~ c_Finite__Set_Ofinite(X2547,X2545)
        | ~ c_Finite__Set_Ofinite(X2546,X2544)
        | c_Finite__Set_Ofinite(tc_sum(X2547,X2546),c_Sum__Type_OPlus(X2547,X2546,X2545,X2544)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Plus__iff])])]) ).

fof(i_0_759,plain,
    ! [X2536,X2537,X2538,X2539] :
      ( ~ c_Finite__Set_Ofinite(tc_sum(X2539,X2538),c_Sum__Type_OPlus(X2539,X2538,X2537,X2536))
      | c_Finite__Set_Ofinite(X2539,X2537) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__PlusD_I1_J])]) ).

fof(i_0_760,plain,
    ! [X2532,X2533,X2534,X2535] :
      ( ~ c_Finite__Set_Ofinite(tc_sum(X2535,X2534),c_Sum__Type_OPlus(X2535,X2534,X2533,X2532))
      | c_Finite__Set_Ofinite(X2534,X2532) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__PlusD_I2_J])]) ).

fof(i_0_761,plain,
    ! [X2012,X2013,X2014,X2015] :
      ( ~ class_Groups_Oordered__ab__semigroup__add(X2015)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2015,X2014),X2013))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2015,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2015),X2014),X2012)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2015),X2013),X2012))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__mono])]) ).

fof(i_0_762,plain,
    ! [X2008,X2009,X2010,X2011] :
      ( ~ class_Groups_Oordered__ab__semigroup__add(X2011)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2011,X2010),X2009))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2011,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2011),X2008),X2010)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2011),X2008),X2009))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__mono])]) ).

fof(i_0_763,plain,
    ! [X2299,X2300,X2301] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2301),X2300)),X2299))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2301),X2299)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__lessD1])]) ).

fof(i_0_764,plain,
    ! [X2592,X2593,X2594] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X2594)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2594,X2593),c_Groups_Ozero__class_Ozero(X2594)))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2594,X2592),c_Groups_Ozero__class_Ozero(X2594)))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2594,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2594),X2593),X2592)),c_Groups_Ozero__class_Ozero(X2594))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__nonpos])]) ).

fof(i_0_765,plain,
    ! [X2100,X2101,X2102,X2103] :
      ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2102,X2103),X2101),X2100))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2102,X2103)),X2101),X2100))
        | ~ class_Orderings_Oord(X2103) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2102,X2103),X2100),X2101))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2102,X2103)),X2101),X2100))
        | ~ class_Orderings_Oord(X2103) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2102,X2103),X2101),X2100))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2102,X2103),X2100),X2101))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2102,X2103)),X2101),X2100))
        | ~ class_Orderings_Oord(X2103) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_538])])]) ).

fof(i_0_766,plain,
    ! [X2143,X2144,X2145,X2146,X2147,X2148] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2148,tc_fun(X2147,tc_HOL_Obool)),X2146),X2145))
      | ~ hBOOL(hAPP(hAPP(X2146,X2144),X2143))
      | hBOOL(hAPP(hAPP(X2145,X2144),X2143)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_predicate2D])]) ).

fof(i_0_767,plain,
    ! [X2152,X2153,X2154,X2155,X2156,X2157] :
      ( ~ hBOOL(hAPP(hAPP(X2157,X2156),X2155))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2154,tc_fun(X2153,tc_HOL_Obool)),X2157),X2152))
      | hBOOL(hAPP(hAPP(X2152,X2156),X2155)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__predicate2D])]) ).

fof(i_0_768,plain,
    ! [X2310,X2311,X2312] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2312),X2311))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2312),X2310)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2311),X2310))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono1])]) ).

fof(i_0_769,plain,
    ! [X2183,X2184,X2185,X2186,X2187,X2188] :
      ( ( hAPP(X2186,X2184) != hAPP(X2186,X2183)
        | X2184 = X2183
        | ~ hBOOL(hAPP(hAPP(c_member(X2188),X2183),X2185))
        | ~ hBOOL(hAPP(hAPP(c_member(X2188),X2184),X2185))
        | ~ c_Fun_Oinj__on(X2188,X2187,X2186,X2185) )
      & ( X2184 != X2183
        | hAPP(X2186,X2184) = hAPP(X2186,X2183)
        | ~ hBOOL(hAPP(hAPP(c_member(X2188),X2183),X2185))
        | ~ hBOOL(hAPP(hAPP(c_member(X2188),X2184),X2185))
        | ~ c_Fun_Oinj__on(X2188,X2187,X2186,X2185) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__iff])])]) ).

fof(i_0_770,plain,
    ! [X2189,X2190,X2191,X2192,X2193,X2194] :
      ( ~ c_Fun_Oinj__on(X2194,X2193,X2192,X2191)
      | X2190 = X2189
      | ~ hBOOL(hAPP(hAPP(c_member(X2194),X2190),X2191))
      | ~ hBOOL(hAPP(hAPP(c_member(X2194),X2189),X2191))
      | hAPP(X2192,X2190) != hAPP(X2192,X2189) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__contraD])]) ).

fof(i_0_771,plain,
    ! [X2177,X2178,X2179,X2180,X2181,X2182] :
      ( ~ c_Fun_Oinj__on(X2182,X2181,X2180,X2179)
      | hAPP(X2180,X2178) != hAPP(X2180,X2177)
      | ~ hBOOL(hAPP(hAPP(c_member(X2182),X2178),X2179))
      | ~ hBOOL(hAPP(hAPP(c_member(X2182),X2177),X2179))
      | X2178 = X2177 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__onD])]) ).

fof(i_0_772,plain,
    ! [X2244,X2245,X2246] :
      ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2246),X2244))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2246),X2245)),X2244)) )
      & ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2245),X2244))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2246),X2245)),X2244)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_539])])]) ).

fof(i_0_773,plain,
    ! [X2247,X2248,X2249] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2249),X2248)),X2247))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2249),X2247)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD1])]) ).

fof(i_0_774,plain,
    ! [X2250,X2251,X2252] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2252),X2251)),X2250))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2251),X2250)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD2])]) ).

fof(i_0_775,plain,
    ! [X2620,X2621,X2622] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X2622)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2622),c_Groups_Ozero__class_Ozero(X2622)),X2621))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2622),c_Groups_Ozero__class_Ozero(X2622)),X2620))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2622),c_Groups_Ozero__class_Ozero(X2622)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2622),X2621),X2620))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__pos])]) ).

fof(i_0_776,plain,
    ! [X3121,X3122,X3123,X3125,X3126,X3127] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk45_2(X3121,X3122)),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3122)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3123),X3122))
        | ~ hBOOL(hAPP(X3121,X3123)) )
      & ( hBOOL(hAPP(X3121,esk45_2(X3121,X3122)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3123),X3122))
        | ~ hBOOL(hAPP(X3121,X3123)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk46_2(X3125,X3126)),X3126))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3127),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3126)))
        | ~ hBOOL(hAPP(X3125,X3127)) )
      & ( hBOOL(hAPP(X3125,esk46_2(X3125,X3126)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3127),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3126)))
        | ~ hBOOL(hAPP(X3125,X3127)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ex__nat__less__eq])])])])])]) ).

fof(i_0_777,plain,
    ! [X2257,X2258,X2259] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2259),X2258))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2259),X2257)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2258),X2257))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono1])]) ).

fof(i_0_778,plain,
    ! [X1726,X1727,X1728,X1729] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1729,tc_HOL_Obool)),X1728),X1727))
      | ~ hBOOL(hAPP(hAPP(c_member(X1729),X1726),X1728))
      | hBOOL(hAPP(hAPP(c_member(X1729),X1726),X1727)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubsetD])]) ).

fof(i_0_779,plain,
    ! [X2402,X2403,X2404] :
      ( ~ c_Finite__Set_Ofinite(X2404,X2403)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2404,tc_HOL_Obool)),X2402),X2403))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X2404,X2402)),c_Finite__Set_Ocard(X2404,X2403))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__card__mono])]) ).

fof(i_0_780,plain,
    ! [X2297,X2298] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X2298),X2297),
    inference(variable_rename,[status(thm)],[fact_inj__on__add__nat]) ).

fof(i_0_781,plain,
    ! [X2783,X2784,X2785,X2786,X2787] :
      ( ~ class_Rings_Ocomm__semiring__1(X2787)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2787),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2787),X2786),X2785)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2787),X2784),X2783)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2787),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2787),X2786),X2784)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2787),X2785),X2783)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J])]) ).

fof(i_0_782,plain,
    ! [X2139,X2140,X2141,X2142] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2142,tc_HOL_Obool),X2141),X2140))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2142,tc_HOL_Obool),X2140),X2139))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2142,tc_HOL_Obool),X2141),X2139)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__trans])]) ).

fof(i_0_783,plain,
    ! [X2649,X2650,X2651] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X2651)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2651,c_Groups_Ozero__class_Ozero(X2651)),X2650))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2651),c_Groups_Ozero__class_Ozero(X2651)),X2649))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2651),c_Groups_Ozero__class_Ozero(X2651)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2651),X2650),X2649))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__pos])]) ).

fof(i_0_784,plain,
    ! [X2652,X2653,X2654] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X2654)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2654),c_Groups_Ozero__class_Ozero(X2654)),X2653))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2654,c_Groups_Ozero__class_Ozero(X2654)),X2652))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2654),c_Groups_Ozero__class_Ozero(X2654)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2654),X2653),X2652))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__nonneg])]) ).

fof(i_0_785,plain,
    ! [X2324,X2325] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2325),X2324)),X2325)),
    inference(variable_rename,[status(thm)],[i_0_540]) ).

fof(i_0_786,plain,
    ! [X2322,X2323] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2323),X2322)),X2322)),
    inference(variable_rename,[status(thm)],[i_0_541]) ).

fof(i_0_787,plain,
    ! [X2550,X2551,X2552,X2553] :
      ( ( ~ c_Finite__Set_Ofinite(X2553,X2552)
        | ~ c_Finite__Set_Ofinite(X2551,X2550)
        | c_Finite__Set_Ocard(tc_sum(X2553,X2551),c_Sum__Type_OPlus(X2553,X2551,X2552,X2550)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Finite__Set_Ocard(X2553,X2552)),c_Finite__Set_Ocard(X2551,X2550)) )
      & ( c_Finite__Set_Ofinite(X2553,X2552)
        | c_Finite__Set_Ocard(tc_sum(X2553,X2551),c_Sum__Type_OPlus(X2553,X2551,X2552,X2550)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( c_Finite__Set_Ofinite(X2551,X2550)
        | c_Finite__Set_Ocard(tc_sum(X2553,X2551),c_Sum__Type_OPlus(X2553,X2551,X2552,X2550)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Plus__conv__if])])]) ).

fof(i_0_788,plain,
    ! [X2454,X2455,X2456,X2457] :
      ( ~ c_Finite__Set_Ofinite(X2457,X2456)
      | ~ c_Finite__Set_Ofinite(X2455,X2454)
      | c_Finite__Set_Ocard(tc_sum(X2457,X2455),c_Sum__Type_OPlus(X2457,X2455,X2456,X2454)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Finite__Set_Ocard(X2457,X2456)),c_Finite__Set_Ocard(X2455,X2454)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Plus])]) ).

fof(i_0_789,plain,
    ! [X2616,X2617,X2618,X2619] :
      ( ~ class_Rings_Olinordered__semidom(X2619)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2619),c_Groups_Ozero__class_Ozero(X2619)),X2618))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2619),X2617),X2616))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2619),X2617),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2619),X2618),X2616))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__add__strict])]) ).

fof(i_0_790,plain,
    ! [X2529,X2530,X2531] :
      ( ~ c_Finite__Set_Ofinite(X2531,X2530)
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2531,X2530)),c_Finite__Set_Ocard(X2531,c_Set_Oinsert(X2531,X2529,X2530)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__insert__le])]) ).

fof(i_0_791,plain,
    ! [X2815,X2816] :
      ( ~ class_Int_Oring__char__0(X2816)
      | ~ hBOOL(hAPP(hAPP(c_member(X2816),X2815),c_Int_Oring__1__class_OInts(X2816)))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2816),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2816),c_Groups_Oone__class_Oone(X2816)),X2815)),X2815) != c_Groups_Ozero__class_Ozero(X2816) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__odd__nonzero])]) ).

fof(i_0_792,plain,
    ! [X2625,X2626] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2626),c_Groups_Ozero__class_Ozero(X2626)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2626),X2625),X2625)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2626),c_Groups_Ozero__class_Ozero(X2626)),X2625))
        | ~ class_Groups_Olinordered__ab__group__add(X2626) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2626),c_Groups_Ozero__class_Ozero(X2626)),X2625))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2626),c_Groups_Ozero__class_Ozero(X2626)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2626),X2625),X2625)))
        | ~ class_Groups_Olinordered__ab__group__add(X2626) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__double__add__iff__zero__less__single__add])])]) ).

fof(i_0_793,plain,
    ! [X2631,X2632] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2632),X2631)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2632))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2631)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2632))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2632),X2631))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2631))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2632),X2631))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__gr__0])])]) ).

fof(i_0_794,plain,
    ! [X2408,X2409,X2410] :
      ( ~ c_Finite__Set_Ofinite(X2410,X2409)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2410,tc_HOL_Obool),X2408),X2409))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2410,X2409)),c_Finite__Set_Ocard(X2410,X2408)))
      | X2408 = X2409 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__seteq])]) ).

fof(i_0_795,plain,
    ! [X2513,X2514,X2515,X2516] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2516,tc_HOL_Obool),X2515),X2514))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2516,tc_HOL_Obool),X2515),c_Set_Oinsert(X2516,X2513,X2514))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__insertI2])]) ).

fof(i_0_796,plain,
    ! [X2641,X2642,X2643,X2644] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X2644)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2644,c_Groups_Ozero__class_Ozero(X2644)),X2643))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2644),X2642),X2641))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2644),X2642),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2644),X2643),X2641))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing2])]) ).

fof(i_0_797,plain,
    ! [X2645,X2646,X2647,X2648] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X2648)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2648),c_Groups_Ozero__class_Ozero(X2648)),X2647))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2648,X2646),X2645))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2648),X2646),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2648),X2647),X2645))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing])]) ).

fof(i_0_798,plain,
    ! [X2606,X2607,X2608] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X2608)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2608,c_Groups_Ozero__class_Ozero(X2608)),X2607))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2608,c_Groups_Ozero__class_Ozero(X2608)),X2606))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2608,c_Groups_Ozero__class_Ozero(X2608)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2608),X2607),X2606))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__nonneg])]) ).

fof(i_0_799,plain,
    ! [X2120,X2121,X2122] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2122,tc_HOL_Obool)),X2121),X2120))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2122,tc_HOL_Obool),X2121),X2120)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__imp__subset])]) ).

fof(i_0_800,plain,
    ! [X2107,X2108,X2109] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2109,tc_HOL_Obool),X2108),X2107))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2109,tc_HOL_Obool)),X2108),X2107))
        | X2108 = X2107 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2109,tc_HOL_Obool)),X2108),X2107))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2109,tc_HOL_Obool),X2108),X2107)) )
      & ( X2108 != X2107
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2109,tc_HOL_Obool),X2108),X2107)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__iff__psubset__eq])])]) ).

fof(i_0_801,plain,
    ! [X2097,X2098,X2099] :
      ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2099,tc_HOL_Obool),X2098),X2097))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2099,tc_HOL_Obool)),X2098),X2097)) )
      & ( X2098 != X2097
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2099,tc_HOL_Obool)),X2098),X2097)) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2099,tc_HOL_Obool),X2098),X2097))
        | X2098 = X2097
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2099,tc_HOL_Obool)),X2098),X2097)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__eq])])]) ).

fof(i_0_802,plain,
    ! [X2492,X2493,X2494,X2495] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X2495),X2494),c_Set_Oinsert(X2495,X2493,X2492)))
        | X2494 = X2493
        | hBOOL(hAPP(hAPP(c_member(X2495),X2494),X2492)) )
      & ( X2494 != X2493
        | hBOOL(hAPP(hAPP(c_member(X2495),X2494),c_Set_Oinsert(X2495,X2493,X2492))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X2495),X2494),X2492))
        | hBOOL(hAPP(hAPP(c_member(X2495),X2494),c_Set_Oinsert(X2495,X2493,X2492))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__iff])])]) ).

fof(i_0_803,plain,
    ! [X2471,X2472,X2473,X2474] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X2474),X2473),c_Set_Oinsert(X2474,X2472,X2471)))
      | X2473 = X2472
      | hBOOL(hAPP(hAPP(c_member(X2474),X2473),X2471)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insertE])]) ).

fof(i_0_804,plain,
    ! [X2611,X2612] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2612,c_Groups_Ozero__class_Ozero(X2612)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2612),X2611),X2611)))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2612,c_Groups_Ozero__class_Ozero(X2612)),X2611))
        | ~ class_Groups_Olinordered__ab__group__add(X2612) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2612,c_Groups_Ozero__class_Ozero(X2612)),X2611))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2612,c_Groups_Ozero__class_Ozero(X2612)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2612),X2611),X2611)))
        | ~ class_Groups_Olinordered__ab__group__add(X2612) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__double__add__iff__zero__le__single__add])])]) ).

fof(i_0_805,plain,
    ! [X2223,X2224,X2225] : c_FuncSet_OPi(X2225,X2224,X2223,hAPP(c_COMBK(tc_fun(X2224,tc_HOL_Obool),X2225),c_Orderings_Otop__class_Otop(tc_fun(X2224,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X2225,X2224),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Pi__UNIV]) ).

fof(i_0_806,plain,
    ! [X2599,X2600,X2601,X2602] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X2602)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2602,c_Groups_Ozero__class_Ozero(X2602)),X2601))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2602,X2600),X2599))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2602,X2600),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2602),X2601),X2599))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing])]) ).

fof(i_0_807,plain,
    ! [X2595,X2596,X2597,X2598] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X2598)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2598,c_Groups_Ozero__class_Ozero(X2598)),X2597))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2598,X2596),X2595))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2598,X2596),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2598),X2595),X2597))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing2])]) ).

fof(i_0_808,plain,
    ! [X2540,X2541,X2542,X2543] :
      ( ~ c_Finite__Set_Ofinite(X2543,X2542)
      | ~ c_Finite__Set_Ofinite(X2541,X2540)
      | c_Finite__Set_Ofinite(tc_sum(X2543,X2541),c_Sum__Type_OPlus(X2543,X2541,X2542,X2540)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Plus])]) ).

fof(i_0_809,plain,
    ! [X3156,X3157,X3158,X3159,X3160,X3161] : hAPP(hAPP(hAPP(c_COMBC(X3161,X3160,X3159),X3158),X3157),X3156) = hAPP(hAPP(X3158,X3156),X3157),
    inference(variable_rename,[status(thm)],[help_c__COMBC__1]) ).

fof(i_0_810,plain,
    ! [X2104,X2105,X2106] :
      ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2104,tc_HOL_Obool),X2106),X2105))
        | X2106 != X2105 )
      & ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2104,tc_HOL_Obool),X2105),X2106))
        | X2106 != X2105 )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2104,tc_HOL_Obool),X2106),X2105))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2104,tc_HOL_Obool),X2105),X2106))
        | X2106 = X2105 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__eq__subset])])]) ).

fof(i_0_811,plain,
    ! [X2092,X2093,X2094] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2094,tc_HOL_Obool),X2093),X2092))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2094,tc_HOL_Obool),X2092),X2093))
      | X2093 = X2092 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityI])]) ).

fof(i_0_812,plain,
    ! [X1738,X1739,X1740,X1741] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X1741),X1740),X1739))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1741,tc_HOL_Obool),X1739),X1738))
      | hBOOL(hAPP(hAPP(c_member(X1741),X1740),X1738)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__rev__mp])]) ).

fof(i_0_813,plain,
    ! [X1742,X1743,X1744,X1745] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1745,tc_HOL_Obool),X1744),X1743))
      | ~ hBOOL(hAPP(hAPP(c_member(X1745),X1742),X1744))
      | hBOOL(hAPP(hAPP(c_member(X1745),X1742),X1743)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__mp])]) ).

fof(i_0_814,plain,
    ! [X1734,X1735,X1736,X1737] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1737,tc_HOL_Obool),X1736),X1735))
      | ~ hBOOL(hAPP(hAPP(c_member(X1737),X1734),X1736))
      | hBOOL(hAPP(hAPP(c_member(X1737),X1734),X1735)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__mono])]) ).

fof(i_0_815,plain,
    ! [X1722,X1723,X1724,X1725] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1725,tc_HOL_Obool),X1724),X1723))
      | ~ hBOOL(hAPP(hAPP(c_member(X1725),X1722),X1724))
      | hBOOL(hAPP(hAPP(c_member(X1725),X1722),X1723)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subsetD])]) ).

fof(i_0_816,plain,
    ! [X1805,X1806,X1807,X1808,X1809] :
      ( ~ class_Orderings_Oord(X1809)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1808,X1809),X1807),X1806))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1809,hAPP(X1807,X1805)),hAPP(X1806,X1805))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funD])]) ).

fof(i_0_817,plain,
    ! [X1767,X1768,X1769,X1770,X1771] :
      ( ~ class_Orderings_Oord(X1771)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1770,X1771),X1769),X1768))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1771,hAPP(X1769,X1767)),hAPP(X1768,X1767))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funE])]) ).

fof(i_0_818,plain,
    ! [X2840,X2841,X2842,X2843] :
      ( ~ c_Finite__Set_Ofinite(X2843,X2842)
      | c_Finite__Set_Ofinite(X2841,c_Set_Oimage(X2843,X2841,X2840,X2842)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageI])]) ).

fof(i_0_819,plain,
    ! [X2405,X2406,X2407] :
      ( ~ c_Finite__Set_Ofinite(X2407,X2406)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2407,tc_HOL_Obool),X2405),X2406))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2407,X2405)),c_Finite__Set_Ocard(X2407,X2406))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__mono])]) ).

fof(i_0_820,plain,
    ! [X2779,X2780,X2781,X2782] :
      ( ~ class_Rings_Ocomm__semiring__1(X2782)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2782),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2782),X2781),X2780)),X2779) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2782),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2782),X2781),X2779)),X2780) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J])]) ).

fof(i_0_821,plain,
    ! [X2195,X2196,X2197,X2198,X2199] :
      ( ( hAPP(X2197,X2196) != hAPP(X2197,X2195)
        | X2196 = X2195
        | ~ c_Fun_Oinj__on(X2199,X2198,X2197,c_Orderings_Otop__class_Otop(tc_fun(X2199,tc_HOL_Obool))) )
      & ( X2196 != X2195
        | hAPP(X2197,X2196) = hAPP(X2197,X2195)
        | ~ c_Fun_Oinj__on(X2199,X2198,X2197,c_Orderings_Otop__class_Otop(tc_fun(X2199,tc_HOL_Obool))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__eq])])]) ).

fof(i_0_822,plain,
    ! [X2200,X2201,X2202,X2203,X2204] :
      ( ~ c_Fun_Oinj__on(X2204,X2203,X2202,c_Orderings_Otop__class_Otop(tc_fun(X2204,tc_HOL_Obool)))
      | hAPP(X2202,X2201) != hAPP(X2202,X2200)
      | X2201 = X2200 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_injD])]) ).

fof(i_0_823,plain,
    ! [X3099,X3100,X3101,X3102,X3103] :
      ( ( X3102 = X3100
        | c_SetInterval_Oord__class_OatLeastLessThan(X3103,X3102,X3101) != c_SetInterval_Oord__class_OatLeastLessThan(X3103,X3100,X3099)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3103),X3100),X3099))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3103),X3102),X3101))
        | ~ class_Orderings_Olinorder(X3103) )
      & ( X3101 = X3099
        | c_SetInterval_Oord__class_OatLeastLessThan(X3103,X3102,X3101) != c_SetInterval_Oord__class_OatLeastLessThan(X3103,X3100,X3099)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3103),X3100),X3099))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3103),X3102),X3101))
        | ~ class_Orderings_Olinorder(X3103) )
      & ( X3102 != X3100
        | X3101 != X3099
        | c_SetInterval_Oord__class_OatLeastLessThan(X3103,X3102,X3101) = c_SetInterval_Oord__class_OatLeastLessThan(X3103,X3100,X3099)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3103),X3100),X3099))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3103),X3102),X3101))
        | ~ class_Orderings_Olinorder(X3103) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__eq__iff])])]) ).

fof(i_0_824,plain,
    ! [X3104,X3105,X3106,X3107,X3108] :
      ( ~ class_Orderings_Olinorder(X3108)
      | c_SetInterval_Oord__class_OatLeastLessThan(X3108,X3107,X3106) != c_SetInterval_Oord__class_OatLeastLessThan(X3108,X3105,X3104)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3108),X3107),X3106))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3108),X3105),X3104))
      | X3107 = X3105 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__inj_I1_J])]) ).

fof(i_0_825,plain,
    ! [X3109,X3110,X3111,X3112,X3113] :
      ( ~ class_Orderings_Olinorder(X3113)
      | c_SetInterval_Oord__class_OatLeastLessThan(X3113,X3112,X3111) != c_SetInterval_Oord__class_OatLeastLessThan(X3113,X3110,X3109)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3113),X3112),X3111))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3113),X3110),X3109))
      | X3111 = X3109 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__inj_I2_J])]) ).

fof(i_0_826,plain,
    ! [X2817,X2818,X2820] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk33_2(X2817,X2818)),X2817))
        | ~ hBOOL(hAPP(X2818,X2817))
        | hBOOL(hAPP(X2818,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2820),esk33_2(X2817,X2818)))
        | ~ hBOOL(hAPP(X2818,X2820))
        | ~ hBOOL(hAPP(X2818,X2817))
        | hBOOL(hAPP(X2818,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
      & ( hBOOL(hAPP(X2818,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk33_2(X2817,X2818)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | ~ hBOOL(hAPP(X2818,X2817))
        | hBOOL(hAPP(X2818,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_542])])])])]) ).

fof(i_0_827,plain,
    ! [X2739,X2740] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2740),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2740),X2739)))),
    inference(variable_rename,[status(thm)],[fact_less__add__Suc1]) ).

fof(i_0_828,plain,
    ! [X2741,X2742] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2742),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2741),X2742)))),
    inference(variable_rename,[status(thm)],[fact_less__add__Suc2]) ).

fof(i_0_829,plain,
    ! [X2484,X2485,X2486,X2487] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X2487),X2486),X2485))
      | hBOOL(hAPP(hAPP(c_member(X2487),X2486),c_Set_Oinsert(X2487,X2484,X2485))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insertI2])]) ).

fof(i_0_830,plain,
    ! [X2467,X2468,X2469,X2470] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X2470),X2469),X2468))
        | hBOOL(hAPP(hAPP(c_member(X2470),X2469),c_Set_Oinsert(X2470,X2467,X2468))) )
      & ( X2469 != X2467
        | hBOOL(hAPP(hAPP(c_member(X2470),X2469),c_Set_Oinsert(X2470,X2467,X2468))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_543])])]) ).

fof(i_0_831,plain,
    ! [X2706,X2707,X2708] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2708),X2707))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2707),X2706))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2708)),X2706)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__trans__Suc])]) ).

fof(i_0_832,plain,
    ! [X2658] :
      ( ~ c_Finite__Set_Ofinite(X2658,c_Orderings_Otop__class_Otop(tc_fun(X2658,tc_HOL_Obool)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Finite__Set_Ocard(X2658,c_Orderings_Otop__class_Otop(tc_fun(X2658,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__card__ge__0])]) ).

fof(i_0_833,plain,
    ( c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,esk39_0,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))
    & c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,esk39_0,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_1230_O_O_060N_125_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096])])]) ).

fof(i_0_834,plain,
    ! [X2717,X2718] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2718)),hAPP(c_Nat_OSuc,X2717)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2718),X2717)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2718),X2717))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2718)),hAPP(c_Nat_OSuc,X2717))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__less__eq])]) ).

fof(i_0_835,plain,
    ! [X2700,X2701] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2701)),hAPP(c_Nat_OSuc,X2700)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2701),X2700)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__less__SucD])]) ).

fof(i_0_836,plain,
    ! [X2661,X2662] :
      ( ~ c_Finite__Set_Ofinite(tc_fun(X2662,X2661),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X2662,X2661),tc_HOL_Obool)))
      | c_Finite__Set_Ocard(X2661,c_Orderings_Otop__class_Otop(tc_fun(X2661,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | c_Finite__Set_Ofinite(X2662,c_Orderings_Otop__class_Otop(tc_fun(X2662,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__fun__UNIVD1])]) ).

fof(i_0_837,plain,
    ! [X1882,X1883,X1884,X1885] :
      ( ~ class_Orderings_Opreorder(X1885)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1885),X1884),X1883))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1885),X1883),X1882))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1885),X1884),X1882)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__trans])]) ).

fof(i_0_838,plain,
    ! [X1886,X1887,X1888,X1889] :
      ( ~ class_Orderings_Oorder(X1889)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1889),X1888),X1887))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1889),X1886),X1888))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1889),X1886),X1887)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I10_J])]) ).

fof(i_0_839,plain,
    ! [X3085,X3086] : c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3086,X3085)) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X3086),hAPP(c_Nat_OSuc,X3085)),
    inference(variable_rename,[status(thm)],[fact_image__Suc__atLeastLessThan]) ).

fof(i_0_840,plain,
    ! [X2603,X2604,X2605] :
      ( ( X2604 = c_Groups_Ozero__class_Ozero(X2605)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2605),X2604),X2603) != c_Groups_Ozero__class_Ozero(X2605)
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2605,c_Groups_Ozero__class_Ozero(X2605)),X2603))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2605,c_Groups_Ozero__class_Ozero(X2605)),X2604))
        | ~ class_Groups_Oordered__comm__monoid__add(X2605) )
      & ( X2603 = c_Groups_Ozero__class_Ozero(X2605)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2605),X2604),X2603) != c_Groups_Ozero__class_Ozero(X2605)
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2605,c_Groups_Ozero__class_Ozero(X2605)),X2603))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2605,c_Groups_Ozero__class_Ozero(X2605)),X2604))
        | ~ class_Groups_Oordered__comm__monoid__add(X2605) )
      & ( X2604 != c_Groups_Ozero__class_Ozero(X2605)
        | X2603 != c_Groups_Ozero__class_Ozero(X2605)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2605),X2604),X2603) = c_Groups_Ozero__class_Ozero(X2605)
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2605,c_Groups_Ozero__class_Ozero(X2605)),X2603))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2605,c_Groups_Ozero__class_Ozero(X2605)),X2604))
        | ~ class_Groups_Oordered__comm__monoid__add(X2605) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__eq__0__iff])])]) ).

fof(i_0_841,plain,
    ! [X2548,X2549] : c_Sum__Type_OPlus(X2549,X2548,c_Orderings_Otop__class_Otop(tc_fun(X2549,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2548,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X2549,X2548),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_UNIV__Plus__UNIV]) ).

fof(i_0_842,plain,
    ! [X2316,X2317,X2318] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2318),X2317))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2318),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2317),X2316))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add1])]) ).

fof(i_0_843,plain,
    ! [X1649,X1650,X1651] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1651),X1650))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1651),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1650),X1649))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I1_J])]) ).

fof(i_0_844,plain,
    ! [X2313,X2314,X2315] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2315),X2314))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2315),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2313),X2314))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add2])]) ).

fof(i_0_845,plain,
    ! [X1646,X1647,X1648] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1648),X1647))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1648),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1646),X1647))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I2_J])]) ).

fof(i_0_846,plain,
    ! [X2729,X2730,X2732,X2733,X2734] :
      ( ( X2730 = hAPP(c_Nat_OSuc,esk31_2(X2729,X2730))
        | X2730 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2730),hAPP(c_Nat_OSuc,X2729))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk31_2(X2729,X2730)),X2729))
        | X2730 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2730),hAPP(c_Nat_OSuc,X2729))) )
      & ( X2733 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2733),hAPP(c_Nat_OSuc,X2732))) )
      & ( X2733 != hAPP(c_Nat_OSuc,X2734)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2734),X2732))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2733),hAPP(c_Nat_OSuc,X2732))) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__0__disj])])])])])]) ).

fof(i_0_847,plain,
    ! [X2775,X2776,X2777,X2778] :
      ( ~ class_Rings_Ocomm__semiring__1(X2778)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2778),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2778),X2777),X2776)),X2775) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2778),X2777),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2778),X2776),X2775)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J])]) ).

fof(i_0_848,plain,
    ! [X1916,X1917,X1918,X1919] :
      ( ~ class_Groups_Oab__semigroup__add(X1919)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1919),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1919),X1918),X1917)),X1916) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1919),X1918),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1919),X1917),X1916)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__semigroup__add__class_Oadd__ac_I1_J])]) ).

fof(i_0_849,plain,
    ! [X2771,X2772,X2773,X2774] :
      ( ~ class_Rings_Ocomm__semiring__1(X2774)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2774),X2773),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2774),X2772),X2771)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2774),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2774),X2773),X2772)),X2771) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J])]) ).

fof(i_0_850,plain,
    ! [X2499,X2500,X2501,X2502] :
      ( ( ~ hBOOL(hAPP(c_Set_Oinsert(X2502,X2501,X2500),X2499))
        | X2501 = X2499
        | hBOOL(hAPP(X2500,X2499)) )
      & ( X2501 != X2499
        | hBOOL(hAPP(c_Set_Oinsert(X2502,X2501,X2500),X2499)) )
      & ( ~ hBOOL(hAPP(X2500,X2499))
        | hBOOL(hAPP(c_Set_Oinsert(X2502,X2501,X2500),X2499)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__code])])]) ).

fof(i_0_851,plain,
    ! [X2655] :
      ( ~ class_Rings_Olinordered__semidom(X2655)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2655),c_Groups_Ozero__class_Ozero(X2655)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2655),c_Groups_Oone__class_Oone(X2655)),c_Groups_Oone__class_Oone(X2655)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__two])]) ).

fof(i_0_852,plain,
    ! [X2686,X2687] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2687)),hAPP(c_Nat_OSuc,X2686)))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2687),X2686)) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2687),X2686))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2687)),hAPP(c_Nat_OSuc,X2686))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__mono])]) ).

fof(i_0_853,plain,
    ! [X1987,X1988,X1989,X1990] :
      ( ~ class_Orderings_Opreorder(X1990)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1990,X1989),X1988))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1990),X1988),X1987))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1990),X1989),X1987)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less__trans])]) ).

fof(i_0_854,plain,
    ! [X1979,X1980,X1981,X1982] :
      ( ~ class_Orderings_Opreorder(X1982)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1982),X1981),X1980))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1982,X1980),X1979))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1982),X1981),X1979)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le__trans])]) ).

fof(i_0_855,plain,
    ! [X1991,X1992,X1993,X1994] :
      ( ~ class_Orderings_Oorder(X1994)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1994,X1993),X1992))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1994),X1991),X1993))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1994),X1991),X1992)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I8_J])]) ).

fof(i_0_856,plain,
    ! [X1983,X1984,X1985,X1986] :
      ( ~ class_Orderings_Oorder(X1986)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1986),X1985),X1984))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1986,X1983),X1985))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1986),X1983),X1984)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I7_J])]) ).

fof(i_0_857,plain,
    ! [X2422,X2423] :
      ( ( c_Finite__Set_Ofinite(X2423,c_Orderings_Otop__class_Otop(tc_fun(X2423,tc_HOL_Obool)))
        | ~ c_Finite__Set_Ofinite(tc_sum(X2423,X2422),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X2423,X2422),tc_HOL_Obool))) )
      & ( c_Finite__Set_Ofinite(X2422,c_Orderings_Otop__class_Otop(tc_fun(X2422,tc_HOL_Obool)))
        | ~ c_Finite__Set_Ofinite(tc_sum(X2423,X2422),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X2423,X2422),tc_HOL_Obool))) )
      & ( ~ c_Finite__Set_Ofinite(X2423,c_Orderings_Otop__class_Otop(tc_fun(X2423,tc_HOL_Obool)))
        | ~ c_Finite__Set_Ofinite(X2422,c_Orderings_Otop__class_Otop(tc_fun(X2422,tc_HOL_Obool)))
        | c_Finite__Set_Ofinite(tc_sum(X2423,X2422),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X2423,X2422),tc_HOL_Obool))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Plus__UNIV__iff])])]) ).

fof(i_0_858,plain,
    ! [X2424,X2425] :
      ( ~ c_Finite__Set_Ofinite(X2425,c_Orderings_Otop__class_Otop(tc_fun(X2425,tc_HOL_Obool)))
      | ~ c_Finite__Set_Ofinite(X2424,c_Orderings_Otop__class_Otop(tc_fun(X2424,tc_HOL_Obool)))
      | c_Finite__Set_Ofinite(tc_prod(X2425,X2424),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X2425,X2424),tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Prod__UNIV])]) ).

fof(i_0_859,plain,
    ! [X2302,X2303,X2304,X2305] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2305),X2304))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2303),X2304) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2305),X2302)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2303),X2302)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__eq__less])]) ).

fof(i_0_860,plain,
    ! [X2510,X2511,X2512] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2512,tc_HOL_Obool),X2511),c_Set_Oinsert(X2512,X2510,X2511))),
    inference(variable_rename,[status(thm)],[fact_subset__insertI]) ).

fof(i_0_861,plain,
    ! [X2488,X2489,X2490,X2491] :
      ( ( c_Set_Oinsert(X2491,X2490,X2489) != c_Set_Oinsert(X2491,X2490,X2488)
        | X2489 = X2488
        | hBOOL(hAPP(hAPP(c_member(X2491),X2490),X2488))
        | hBOOL(hAPP(hAPP(c_member(X2491),X2490),X2489)) )
      & ( X2489 != X2488
        | c_Set_Oinsert(X2491,X2490,X2489) = c_Set_Oinsert(X2491,X2490,X2488)
        | hBOOL(hAPP(hAPP(c_member(X2491),X2490),X2488))
        | hBOOL(hAPP(hAPP(c_member(X2491),X2490),X2489)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_544])])]) ).

fof(i_0_862,plain,
    ! [X2702,X2703] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2703)),X2702))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2703),X2702)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__lessD])]) ).

fof(i_0_863,plain,
    ! [X2682,X2683] :
      ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2683),X2682))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2682)),X2683)) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2682)),X2683))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2683),X2682)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_545])]) ).

fof(i_0_864,plain,
    ! [X2666,X2667] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2667),X2666))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2667)),hAPP(c_Nat_OSuc,X2666))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mono])]) ).

fof(i_0_865,plain,
    ! [X2349,X2350,X2351] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2351),X2350))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2351),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2350),X2349))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add1])]) ).

fof(i_0_866,plain,
    ! [X1640,X1641,X1642] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1642),X1641))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1642),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1641),X1640))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I3_J])]) ).

fof(i_0_867,plain,
    ! [X2352,X2353,X2354] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2354),X2353))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2354),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2352),X2353))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add2])]) ).

fof(i_0_868,plain,
    ! [X1643,X1644,X1645] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1645),X1644))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1645),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1643),X1644))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I4_J])]) ).

fof(i_0_869,plain,
    ! [X2429,X2430] :
      ( ~ c_Finite__Set_Ofinite(tc_fun(X2430,X2429),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X2430,X2429),tc_HOL_Obool)))
      | c_Finite__Set_Ofinite(X2429,c_Orderings_Otop__class_Otop(tc_fun(X2429,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__fun__UNIVD2])]) ).

fof(i_0_870,plain,
    ! [X2721,X2722] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2722),X2721))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2721),hAPP(c_Nat_OSuc,X2722))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2721),hAPP(c_Nat_OSuc,X2722)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2722),X2721)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_546])]) ).

fof(i_0_871,plain,
    ! [X2278,X2279,X2280] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2280),X2279)),X2278) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2280),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2279),X2278)),
    inference(variable_rename,[status(thm)],[fact_nat__add__assoc]) ).

fof(i_0_872,plain,
    ! [X2761,X2762] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2762)),X2761))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2762),X2761)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__lessD])]) ).

fof(i_0_873,plain,
    ! [X2753,X2754] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2754)),X2753))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2754),X2753)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2754),X2753))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2754)),X2753)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__eq])]) ).

fof(i_0_874,plain,
    ! [X2749,X2750] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2750),X2749))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2750)),X2749)) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2750)),X2749))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2750),X2749)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__Suc__le])]) ).

fof(i_0_875,plain,
    ! [X2123,X2124,X2125,X2126] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2126,tc_HOL_Obool),X2125),X2124))
      | ~ hBOOL(hAPP(X2125,X2123))
      | hBOOL(hAPP(X2124,X2123)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_predicate1D])]) ).

fof(i_0_876,plain,
    ! [X2110,X2111,X2112,X2113] :
      ( ~ hBOOL(hAPP(X2113,X2112))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2111,tc_HOL_Obool),X2113),X2110))
      | hBOOL(hAPP(X2110,X2112)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__predicate1D])]) ).

fof(i_0_877,plain,
    ! [X1779,X1780,X1781,X1782] :
      ( ~ class_Orderings_Opreorder(X1782)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1782,X1781),X1780))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1782,X1780),X1779))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1782,X1781),X1779)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__trans])]) ).

fof(i_0_878,plain,
    ! [X1772,X1773,X1774,X1775] :
      ( ~ class_Orderings_Oorder(X1775)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1775,X1774),X1773))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1775,X1772),X1774))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1775,X1772),X1773)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I6_J])]) ).

fof(i_0_879,plain,
    ! [X2709,X2710] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2710),X2709))
      | hAPP(c_Nat_OSuc,X2710) = X2709
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2710)),X2709)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__lessI])]) ).

fof(i_0_880,plain,
    ! [X1863,X1864,X1865] :
      ( ~ class_Orderings_Oorder(X1865)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1865),X1864),X1863))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1865),X1863),X1864)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_547])]) ).

fof(i_0_881,plain,
    ! [X1830,X1831,X1832] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1832),X1831),X1830))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1832),X1830),X1831))
        | X1831 = X1830
        | ~ class_Orderings_Olinorder(X1832) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1832),X1830),X1831))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1832),X1831),X1830))
        | ~ class_Orderings_Olinorder(X1832) )
      & ( X1831 != X1830
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1832),X1831),X1830))
        | ~ class_Orderings_Olinorder(X1832) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_548])])]) ).

fof(i_0_882,plain,
    ! [X1890,X1891,X1892] :
      ( ~ class_Orderings_Opreorder(X1892)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1892),X1891),X1890))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1892),X1890),X1891)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_549])]) ).

fof(i_0_883,plain,
    ! [X1860,X1861,X1862] :
      ( ~ class_Orderings_Opreorder(X1862)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1862),X1861),X1860))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1862),X1860),X1861)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_550])]) ).

fof(i_0_884,plain,
    ! [X1851,X1852,X1853] :
      ( ~ class_Orderings_Opreorder(X1853)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1853),X1852),X1851))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1853),X1851),X1852)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_551])]) ).

fof(i_0_885,plain,
    ! [X1848,X1849,X1850] :
      ( ~ class_Orderings_Opreorder(X1850)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1850),X1849),X1848))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1850),X1848),X1849)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_552])]) ).

fof(i_0_886,plain,
    ! [X1706,X1707] :
      ( ~ class_Rings_Olinordered__semidom(X1707)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1707),X1706),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1707),X1706),c_Groups_Oone__class_Oone(X1707)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__one])]) ).

fof(i_0_887,plain,
    ! [X2759,X2760] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2759),hAPP(c_Nat_OSuc,X2760)))
        | X2759 = X2760
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2760),X2759)) )
      & ( X2759 != X2760
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2759),hAPP(c_Nat_OSuc,X2760)))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2760),X2759)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__less__Suc__eq])])]) ).

fof(i_0_888,plain,
    ! [X2692,X2693] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2693)),X2692))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2693),X2692)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__leD])]) ).

fof(i_0_889,plain,
    ! [X2458,X2459,X2460] :
      ( ~ c_Finite__Set_Ofinite(X2460,X2459)
      | hBOOL(hAPP(hAPP(c_member(X2460),X2458),X2459))
      | c_Finite__Set_Ocard(X2460,c_Set_Oinsert(X2460,X2458,X2459)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Finite__Set_Ocard(X2460,X2459)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_553])]) ).

fof(i_0_890,plain,
    ! [X1940,X1941,X1942] :
      ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1942,X1941),X1940))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1942),X1941),X1940))
        | ~ class_Orderings_Opreorder(X1942) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1942,X1940),X1941))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1942),X1941),X1940))
        | ~ class_Orderings_Opreorder(X1942) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1942,X1941),X1940))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1942,X1940),X1941))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1942),X1941),X1940))
        | ~ class_Orderings_Opreorder(X1942) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_554])])]) ).

fof(i_0_891,plain,
    ! [X2791,X2792,X2793] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X2793),X2791),X2792))
        | c_Finite__Set_Ocard(X2793,c_Set_Oinsert(X2793,X2791,X2792)) = c_Finite__Set_Ocard(X2793,X2792)
        | ~ c_Finite__Set_Ofinite(X2793,X2792) )
      & ( hBOOL(hAPP(hAPP(c_member(X2793),X2791),X2792))
        | c_Finite__Set_Ocard(X2793,c_Set_Oinsert(X2793,X2791,X2792)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X2793,X2792))
        | ~ c_Finite__Set_Ofinite(X2793,X2792) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_555])])]) ).

fof(i_0_892,plain,
    ! [X3087,X3089,X3090,X3091] :
      ( ( ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X3087)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3089),X3087))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3089),esk41_1(X3087))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk42_2(X3090,X3091)),X3090))
        | c_Finite__Set_Ofinite(tc_Nat_Onat,X3090) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk42_2(X3090,X3091)),X3091))
        | c_Finite__Set_Ofinite(tc_Nat_Onat,X3090) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__nat__set__iff__bounded])])])])])]) ).

fof(i_0_893,plain,
    ! [X2503,X2504,X2505,X2506] : c_Set_Oinsert(X2506,X2505,c_Set_Oinsert(X2506,X2504,X2503)) = c_Set_Oinsert(X2506,X2504,c_Set_Oinsert(X2506,X2505,X2503)),
    inference(variable_rename,[status(thm)],[fact_insert__commute]) ).

fof(i_0_894,plain,
    ! [X2496,X2497,X2498] : hBOOL(hAPP(hAPP(c_member(X2498),X2497),c_Set_Oinsert(X2498,X2497,X2496))),
    inference(variable_rename,[status(thm)],[fact_insertI1]) ).

fof(i_0_895,plain,
    ! [X2719,X2720] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2720),hAPP(c_Nat_OSuc,X2719)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2720),X2719))
        | X2720 = X2719 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2720),X2719))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2720),hAPP(c_Nat_OSuc,X2719))) )
      & ( X2720 != X2719
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2720),hAPP(c_Nat_OSuc,X2719))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq])])]) ).

fof(i_0_896,plain,
    ! [X2715,X2716] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2716),hAPP(c_Nat_OSuc,X2715)))
        | X2716 = X2715
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2716),X2715)) )
      & ( X2716 != X2715
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2716),hAPP(c_Nat_OSuc,X2715)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2716),X2715)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_556])])]) ).

fof(i_0_897,plain,
    ! [X2713,X2714] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2714),X2713))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2714),hAPP(c_Nat_OSuc,X2713)))
      | X2713 = X2714 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_557])]) ).

fof(i_0_898,plain,
    ! [X2704,X2705] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2705),hAPP(c_Nat_OSuc,X2704)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2705),X2704))
      | X2705 = X2704 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_558])]) ).

fof(i_0_899,plain,
    ! [X2757,X2758] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2758),X2757))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2758)),X2757)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__leI])]) ).

fof(i_0_900,plain,
    ! [X2767,X2768,X2769,X2770] :
      ( ~ class_Rings_Ocomm__semiring__1(X2770)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2770),X2769),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2770),X2768),X2767)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2770),X2768),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2770),X2769),X2767)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J])]) ).

fof(i_0_901,plain,
    ! [X2292,X2293,X2294] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2294),X2293))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2293),X2292))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2294),X2292)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__trans])]) ).

fof(i_0_902,plain,
    ! [X2418,X2419,X2420] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2420,tc_HOL_Obool),X2419),X2418))
      | ~ c_Finite__Set_Ofinite(X2420,X2418)
      | c_Finite__Set_Ofinite(X2420,X2419) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__subset])]) ).

fof(i_0_903,plain,
    ! [X2415,X2416,X2417] :
      ( ~ c_Finite__Set_Ofinite(X2417,X2416)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2417,tc_HOL_Obool),X2415),X2416))
      | c_Finite__Set_Ofinite(X2417,X2415) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__finite__subset])]) ).

fof(i_0_904,plain,
    ! [X1967,X1968,X1969] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1969),X1968),X1967))
        | X1968 = X1967
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1969,X1968),X1967))
        | ~ class_Orderings_Olinorder(X1969) )
      & ( X1968 != X1967
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1969),X1968),X1967))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1969,X1968),X1967))
        | ~ class_Orderings_Olinorder(X1969) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_559])])]) ).

fof(i_0_905,plain,
    ! [X1961,X1962,X1963] :
      ( ~ class_Orderings_Olinorder(X1963)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1963,X1962),X1961))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1963),X1961),X1962)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_560])]) ).

fof(i_0_906,plain,
    ! [X1928,X1929,X1930] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1930),X1929),X1928))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1930,X1928),X1929))
        | ~ class_Orderings_Olinorder(X1930) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1930,X1928),X1929))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1930),X1929),X1928))
        | ~ class_Orderings_Olinorder(X1930) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_561])])]) ).

fof(i_0_907,plain,
    ! [X1931,X1932,X1933] :
      ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1933,X1932),X1931))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1933),X1931),X1932))
        | ~ class_Orderings_Olinorder(X1933) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1933),X1931),X1932))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1933,X1932),X1931))
        | ~ class_Orderings_Olinorder(X1933) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_562])])]) ).

fof(i_0_908,plain,
    ! [X2743,X2744,X2746,X2747,X2748] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2744),X2743))
        | X2743 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2744),esk32_2(X2743,X2744))) )
      & ( X2746 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2747),X2748))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2747),X2746)) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__iff__Suc__add])])])])]) ).

fof(i_0_909,plain,
    ! [X2751,X2752] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2752),hAPP(c_Nat_OSuc,X2751)))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2752),X2751)) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2752),X2751))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2752),hAPP(c_Nat_OSuc,X2751))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__le])]) ).

fof(i_0_910,plain,
    ! [X3093,X3095,X3096,X3097] :
      ( ( ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X3093)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3095),X3093))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3095),esk43_1(X3093))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk44_2(X3096,X3097)),X3096))
        | c_Finite__Set_Ofinite(tc_Nat_Onat,X3096) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk44_2(X3096,X3097)),X3097))
        | c_Finite__Set_Ofinite(tc_Nat_Onat,X3096) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__nat__set__iff__bounded__le])])])])])]) ).

fof(i_0_911,plain,
    ! [X2788,X2789,X2790] :
      ( ~ c_Finite__Set_Ofinite(X2790,X2789)
      | hBOOL(hAPP(hAPP(c_member(X2790),X2788),X2789))
      | c_Finite__Set_Ocard(X2790,c_Set_Oinsert(X2790,X2788,X2789)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X2790,X2789)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_563])]) ).

fof(i_0_912,plain,
    ! [X2711,X2712] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2712),X2711))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2712),hAPP(c_Nat_OSuc,X2711))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__SucI])]) ).

fof(i_0_913,plain,
    ! [X2813,X2814] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2814),X2813),X2813) != c_Groups_Ozero__class_Ozero(X2814)
        | X2813 = c_Groups_Ozero__class_Ozero(X2814)
        | ~ hBOOL(hAPP(hAPP(c_member(X2814),X2813),c_Int_Oring__1__class_OInts(X2814)))
        | ~ class_Int_Oring__char__0(X2814) )
      & ( X2813 != c_Groups_Ozero__class_Ozero(X2814)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2814),X2813),X2813) = c_Groups_Ozero__class_Ozero(X2814)
        | ~ hBOOL(hAPP(hAPP(c_member(X2814),X2813),c_Int_Oring__1__class_OInts(X2814)))
        | ~ class_Int_Oring__char__0(X2814) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__double__eq__0__iff])])]) ).

fof(i_0_914,plain,
    ! [X2892,X2893,X2894,X2895] : c_Nat_Onat_Onat__case(X2895,X2894,X2893,hAPP(c_Nat_OSuc,X2892)) = hAPP(X2893,X2892),
    inference(variable_rename,[status(thm)],[fact_nat__case__Suc]) ).

fof(i_0_915,plain,
    ! [X2690,X2691] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2691),hAPP(c_Nat_OSuc,X2690)))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2691),X2690))
      | X2691 = hAPP(c_Nat_OSuc,X2690) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_564])]) ).

fof(i_0_916,plain,
    ! [X2684,X2685] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2685),hAPP(c_Nat_OSuc,X2684)))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2685),X2684))
        | X2685 = hAPP(c_Nat_OSuc,X2684) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2685),X2684))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2685),hAPP(c_Nat_OSuc,X2684))) )
      & ( X2685 != hAPP(c_Nat_OSuc,X2684)
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2685),hAPP(c_Nat_OSuc,X2684))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__Suc__eq])])]) ).

fof(i_0_917,plain,
    ! [X1746,X1747] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1747,tc_HOL_Obool),X1746),c_Orderings_Otop__class_Otop(tc_fun(X1747,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_subset__UNIV]) ).

fof(i_0_918,plain,
    ! [X2260,X2261,X2262] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2261),X2262))
        | hBOOL(hAPP(hAPP(X2260,X2261),X2262))
        | X2262 = X2261
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2262),X2261)) )
      & ( ~ hBOOL(hAPP(hAPP(X2260,X2261),X2262))
        | hBOOL(hAPP(hAPP(X2260,X2261),X2262))
        | X2262 = X2261
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2262),X2261)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2261),X2262))
        | hBOOL(hAPP(hAPP(X2260,X2261),X2262))
        | ~ hBOOL(hAPP(hAPP(X2260,X2261),X2262))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2262),X2261)) )
      & ( ~ hBOOL(hAPP(hAPP(X2260,X2261),X2262))
        | hBOOL(hAPP(hAPP(X2260,X2261),X2262))
        | ~ hBOOL(hAPP(hAPP(X2260,X2261),X2262))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2262),X2261)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2261),X2262))
        | hBOOL(hAPP(hAPP(X2260,X2261),X2262))
        | X2262 = X2261
        | ~ hBOOL(hAPP(hAPP(X2260,X2261),X2262)) )
      & ( ~ hBOOL(hAPP(hAPP(X2260,X2261),X2262))
        | hBOOL(hAPP(hAPP(X2260,X2261),X2262))
        | X2262 = X2261
        | ~ hBOOL(hAPP(hAPP(X2260,X2261),X2262)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2261),X2262))
        | hBOOL(hAPP(hAPP(X2260,X2261),X2262))
        | ~ hBOOL(hAPP(hAPP(X2260,X2261),X2262))
        | ~ hBOOL(hAPP(hAPP(X2260,X2261),X2262)) )
      & ( ~ hBOOL(hAPP(hAPP(X2260,X2261),X2262))
        | hBOOL(hAPP(hAPP(X2260,X2261),X2262))
        | ~ hBOOL(hAPP(hAPP(X2260,X2261),X2262))
        | ~ hBOOL(hAPP(hAPP(X2260,X2261),X2262)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__cases])])]) ).

fof(i_0_919,plain,
    ! [X2275,X2276,X2277] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2277),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2276),X2275)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2276),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2277),X2275)),
    inference(variable_rename,[status(thm)],[fact_nat__add__left__commute]) ).

fof(i_0_920,plain,
    ! [X1813,X1814,X1815] :
      ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1815,X1814),X1813))
        | X1814 != X1813
        | ~ class_Orderings_Oorder(X1815) )
      & ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1815,X1813),X1814))
        | X1814 != X1813
        | ~ class_Orderings_Oorder(X1815) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1815,X1814),X1813))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1815,X1813),X1814))
        | X1814 = X1813
        | ~ class_Orderings_Oorder(X1815) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__iff])])]) ).

fof(i_0_921,plain,
    ! [X1802,X1803,X1804] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1804,X1802),X1803))
        | X1802 = X1803
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1804,X1803),X1802))
        | ~ class_Orderings_Oorder(X1804) )
      & ( X1802 != X1803
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1804,X1802),X1803))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1804,X1803),X1802))
        | ~ class_Orderings_Oorder(X1804) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym__conv])])]) ).

fof(i_0_922,plain,
    ! [X1783,X1784,X1785] :
      ( ~ class_Orderings_Oorder(X1785)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1785,X1784),X1783))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1785,X1783),X1784))
      | X1784 = X1783 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym])]) ).

fof(i_0_923,plain,
    ! [X1776,X1777,X1778] :
      ( ~ class_Orderings_Oorder(X1778)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1778,X1777),X1776))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1778,X1776),X1777))
      | X1776 = X1777 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I5_J])]) ).

fof(i_0_924,plain,
    ! [X2656,X2657] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Finite__Set_Ocard(X2657,X2656)))
      | c_Finite__Set_Ofinite(X2657,X2656) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__ge__0__finite])]) ).

fof(i_0_925,plain,
    ! [X2681] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2681)),X2681)),
    inference(variable_rename,[status(thm)],[i_0_565]) ).

fof(i_0_926,plain,
    ! [X2755,X2756] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2756),X2755))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2756),hAPP(c_Nat_OSuc,X2755))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__less__Suc])]) ).

fof(i_0_927,plain,
    ! [X2427,X2428] :
      ( ~ c_Finite__Set_Ofinite(X2428,c_Orderings_Otop__class_Otop(tc_fun(X2428,tc_HOL_Obool)))
      | c_Finite__Set_Ocard(X2428,X2427) != c_Finite__Set_Ocard(X2428,c_Orderings_Otop__class_Otop(tc_fun(X2428,tc_HOL_Obool)))
      | X2427 = c_Orderings_Otop__class_Otop(tc_fun(X2428,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__eq__UNIV__imp__eq__UNIV])]) ).

fof(i_0_928,plain,
    ! [X1943,X1944,X1945] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1945,X1944),X1943))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1945),X1944),X1943))
        | X1944 = X1943
        | ~ class_Orderings_Oorder(X1945) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1945),X1944),X1943))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1945,X1944),X1943))
        | ~ class_Orderings_Oorder(X1945) )
      & ( X1944 != X1943
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1945,X1944),X1943))
        | ~ class_Orderings_Oorder(X1945) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less])])]) ).

fof(i_0_929,plain,
    ! [X1937,X1938,X1939] :
      ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1939,X1938),X1937))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1939),X1938),X1937))
        | ~ class_Orderings_Oorder(X1939) )
      & ( X1938 != X1937
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1939),X1938),X1937))
        | ~ class_Orderings_Oorder(X1939) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1939,X1938),X1937))
        | X1938 = X1937
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1939),X1938),X1937))
        | ~ class_Orderings_Oorder(X1939) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le])])]) ).

fof(i_0_930,plain,
    ! [X1964,X1965,X1966] :
      ( ~ class_Orderings_Opreorder(X1966)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1966),X1965),X1964))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1966,X1965),X1964)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__le])]) ).

fof(i_0_931,plain,
    ! [X2338,X2339] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2339),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2339),X2338))),
    inference(variable_rename,[status(thm)],[fact_le__add1]) ).

fof(i_0_932,plain,
    ! [X2336,X2337] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2337),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2336),X2337))),
    inference(variable_rename,[status(thm)],[fact_le__add2]) ).

fof(i_0_933,plain,
    ! [X2924,X2925] : c_Set_Oimage(X2925,X2925,c_COMBI(X2925),X2924) = X2924,
    inference(variable_rename,[status(thm)],[fact_image__ident]) ).

fof(i_0_934,plain,
    ! [X2175,X2176] : c_Fun_Oinj__on(X2176,X2176,c_COMBI(X2176),X2175),
    inference(variable_rename,[status(thm)],[fact_inj__on__id2]) ).

fof(i_0_935,plain,
    ! [X2889,X2890,X2891] : c_Nat_Onat_Onat__case(X2891,X2890,X2889,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2890,
    inference(variable_rename,[status(thm)],[fact_nat__case__0]) ).

fof(i_0_936,plain,
    ! [X1976,X1977,X1978] :
      ( ~ class_Orderings_Oorder(X1978)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1978,X1977),X1976))
      | X1976 = X1977
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1978),X1977),X1976)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I11_J])]) ).

fof(i_0_937,plain,
    ! [X1973,X1974,X1975] :
      ( ~ class_Orderings_Oorder(X1975)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1975,X1974),X1973))
      | X1974 = X1973
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1975),X1974),X1973)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__neq__trans])]) ).

fof(i_0_938,plain,
    ! [X1970,X1971,X1972] :
      ( ~ class_Orderings_Oorder(X1972)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1972,X1971),X1970))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1972),X1971),X1970))
      | X1971 = X1970 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__imp__less__or__eq])]) ).

fof(i_0_939,plain,
    ! [X1955,X1956,X1957] :
      ( ~ class_Orderings_Oorder(X1957)
      | X1956 = X1955
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1957,X1956),X1955))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1957),X1956),X1955)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__neq__le__trans])]) ).

fof(i_0_940,plain,
    ! [X1952,X1953,X1954] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1954,X1953),X1952))
        | X1953 = X1952
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1954),X1953),X1952))
        | ~ class_Orderings_Olinorder(X1954) )
      & ( X1953 != X1952
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1954,X1953),X1952))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1954),X1953),X1952))
        | ~ class_Orderings_Olinorder(X1954) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_566])])]) ).

fof(i_0_941,plain,
    ! [X1958,X1959,X1960] :
      ( ~ class_Orderings_Oorder(X1960)
      | X1959 = X1958
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1960,X1958),X1959))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1960),X1958),X1959)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I12_J])]) ).

fof(i_0_942,plain,
    ! [X2728] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2728),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
        | X2728 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X2728 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2728),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc0])]) ).

fof(i_0_943,plain,
    ! [X2723] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X2723),
    inference(variable_rename,[status(thm)],[fact_inj__Suc]) ).

fof(i_0_944,plain,
    ! [X2295,X2296] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2296),X2295))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2295),X2296))
      | X2296 = X2295 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__antisym])]) ).

fof(i_0_945,plain,
    ! [X1666,X1667,X1668] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X1668),X1667),hAPP(c_fequal,X1666)))
        | X1667 = X1666 )
      & ( X1667 != X1666
        | hBOOL(hAPP(hAPP(c_member(X1668),X1667),hAPP(c_fequal,X1666))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__mem])]) ).

fof(i_0_946,plain,
    ! [X2688,X2689] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2689),X2688))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2689),hAPP(c_Nat_OSuc,X2688))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__SucI])]) ).

fof(i_0_947,plain,
    ! [X2630] :
      ( ~ class_Rings_Olinordered__semidom(X2630)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2630),c_Groups_Oone__class_Oone(X2630)),c_Groups_Ozero__class_Ozero(X2630))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_567])]) ).

fof(i_0_948,plain,
    ! [X2334,X2335] :
      ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2335),X2334))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2335),X2334)) )
      & ( X2335 != X2334
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2335),X2334)) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2335),X2334))
        | X2335 = X2334
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2335),X2334)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__le])])]) ).

fof(i_0_949,plain,
    ! [X2332,X2333] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2333),X2332))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2333),X2332))
        | X2333 = X2332 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2333),X2332))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2333),X2332)) )
      & ( X2333 != X2332
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2333),X2332)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__eq__less__or__eq])])]) ).

fof(i_0_950,plain,
    ! [X2330,X2331] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2331),X2330))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2331),X2330)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__le__nat])]) ).

fof(i_0_951,plain,
    ! [X2326,X2327] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2327),X2326))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2327),X2326)) )
      & ( X2327 != X2326
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2327),X2326)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__or__eq__imp__le])])]) ).

fof(i_0_952,plain,
    ! [X1652,X1653] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1653),X1652))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1653),X1652)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I5_J])]) ).

fof(i_0_953,plain,
    ! [X2481,X2482,X2483] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X2483),X2482),X2481))
      | c_Set_Oinsert(X2483,X2482,X2481) = X2481 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__absorb])]) ).

fof(i_0_954,plain,
    ! [X1827,X1828,X1829] :
      ( ( X1828 = X1827
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1829),X1828),X1827))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1829),X1827),X1828))
        | ~ class_Orderings_Olinorder(X1829) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1829),X1828),X1827))
        | X1828 != X1827
        | ~ class_Orderings_Olinorder(X1829) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1829),X1827),X1828))
        | X1828 != X1827
        | ~ class_Orderings_Olinorder(X1829) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__neq__iff])])]) ).

fof(i_0_955,plain,
    ! [X1842,X1843,X1844] :
      ( ~ class_Rings_Olinordered__idom(X1844)
      | X1843 = X1842
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1844),X1843),X1842))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1844),X1842),X1843)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_568])]) ).

fof(i_0_956,plain,
    ! [X1893,X1894,X1895] :
      ( ~ class_Orderings_Olinorder(X1895)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1895),X1894),X1893))
      | X1894 = X1893
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1895),X1893),X1894)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_569])]) ).

fof(i_0_957,plain,
    ! [X1839,X1840,X1841] :
      ( ~ class_Orderings_Olinorder(X1841)
      | X1840 = X1839
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1841),X1840),X1839))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1841),X1839),X1840)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_570])]) ).

fof(i_0_958,plain,
    ! [X1836,X1837,X1838] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1838),X1836),X1837))
        | X1836 = X1837
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1838),X1837),X1836))
        | ~ class_Orderings_Olinorder(X1838) )
      & ( X1836 != X1837
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1838),X1836),X1837))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1838),X1837),X1836))
        | ~ class_Orderings_Olinorder(X1838) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_571])])]) ).

fof(i_0_959,plain,
    ! [X1833,X1834,X1835] :
      ( ~ class_Orderings_Olinorder(X1835)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1835),X1834),X1833))
      | X1834 = X1833
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1835),X1833),X1834)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__less__linear])]) ).

fof(i_0_960,plain,
    ! [X2421] :
      ( ( ~ c_Finite__Set_Ofinite(tc_Option_Ooption(X2421),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X2421),tc_HOL_Obool)))
        | c_Finite__Set_Ofinite(X2421,c_Orderings_Otop__class_Otop(tc_fun(X2421,tc_HOL_Obool))) )
      & ( ~ c_Finite__Set_Ofinite(X2421,c_Orderings_Otop__class_Otop(tc_fun(X2421,tc_HOL_Obool)))
        | c_Finite__Set_Ofinite(tc_Option_Ooption(X2421),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X2421),tc_HOL_Obool))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__option__UNIV])]) ).

fof(i_0_961,plain,
    ! [X2328,X2329] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2329),X2328))
      | X2329 = X2328
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2329),X2328)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__neq__implies__less])]) ).

fof(i_0_962,plain,
    ! [X2507,X2508,X2509] : c_Set_Oinsert(X2509,X2508,c_Set_Oinsert(X2509,X2508,X2507)) = c_Set_Oinsert(X2509,X2508,X2507),
    inference(variable_rename,[status(thm)],[fact_insert__absorb2]) ).

fof(i_0_963,plain,
    ! [X2386,X2387] : hBOOL(hAPP(hAPP(c_member(X2387),X2386),c_Orderings_Otop__class_Otop(tc_fun(X2387,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_iso__tuple__UNIV__I]) ).

fof(i_0_964,plain,
    ! [X1638,X1639] : hBOOL(hAPP(hAPP(c_member(X1639),X1638),c_Orderings_Otop__class_Otop(tc_fun(X1639,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_UNIV__I]) ).

fof(i_0_965,plain,
    ! [X2478,X2479,X2480] :
      ( ( ~ c_Finite__Set_Ofinite(X2480,c_Set_Oinsert(X2480,X2479,X2478))
        | c_Finite__Set_Ofinite(X2480,X2478) )
      & ( ~ c_Finite__Set_Ofinite(X2480,X2478)
        | c_Finite__Set_Ofinite(X2480,c_Set_Oinsert(X2480,X2479,X2478)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__insert])]) ).

fof(i_0_966,plain,
    ! [X1669,X1670,X1671] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X1671),X1670),X1669))
        | hBOOL(hAPP(X1669,X1670)) )
      & ( ~ hBOOL(hAPP(X1669,X1670))
        | hBOOL(hAPP(hAPP(c_member(X1671),X1670),X1669)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__def])]) ).

fof(i_0_967,plain,
    ! [X1949,X1950,X1951] :
      ( ~ class_Orderings_Olinorder(X1951)
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1951,X1950),X1949))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1951),X1949),X1950)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_572])]) ).

fof(i_0_968,plain,
    ! [X1934,X1935,X1936] :
      ( ~ class_Orderings_Olinorder(X1936)
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1936,X1935),X1934))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1936),X1934),X1935)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__le__less__linear])]) ).

fof(i_0_969,plain,
    ! [X1946,X1947,X1948] :
      ( ~ class_Orderings_Olinorder(X1948)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1948),X1947),X1946))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1948,X1946),X1947)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_573])]) ).

fof(i_0_970,plain,
    ! [X2677,X2678] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2678)),X2677) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2678),X2677)),
    inference(variable_rename,[status(thm)],[fact_add__Suc]) ).

fof(i_0_971,plain,
    ! [X2628] :
      ( ~ class_Rings_Olinordered__semidom(X2628)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2628,c_Groups_Oone__class_Oone(X2628)),c_Groups_Ozero__class_Ozero(X2628))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_574])]) ).

fof(i_0_972,plain,
    ! [X2340,X2341,X2343,X2344,X2345] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2341),X2340))
        | X2340 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2341),esk18_2(X2340,X2341)) )
      & ( X2343 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2344),X2345)
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2344),X2343)) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__add])])])])]) ).

fof(i_0_973,plain,
    ! [X2270,X2271] :
      ( ( X2271 = X2270
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2271),X2270))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2270),X2271)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2271),X2270))
        | X2271 != X2270 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2270),X2271))
        | X2271 != X2270 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__neq__iff])])]) ).

fof(i_0_974,plain,
    ! [X2268,X2269] :
      ( X2269 = X2268
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2269),X2268))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2268),X2269)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_575])]) ).

fof(i_0_975,plain,
    ! [X2724,X2726,X2727] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2724))
        | X2724 = hAPP(c_Nat_OSuc,esk30_1(X2724)) )
      & ( X2726 != hAPP(c_Nat_OSuc,X2727)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2726)) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr0__conv__Suc])])])])]) ).

fof(i_0_976,plain,
    ! [X1857,X1858,X1859] :
      ( ~ class_Orderings_Oorder(X1859)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1859),X1858),X1857))
      | X1857 != X1858 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq2])]) ).

fof(i_0_977,plain,
    ! [X1854,X1855,X1856] :
      ( ~ class_Orderings_Oorder(X1856)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1856),X1855),X1854))
      | X1855 != X1854 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq])]) ).

fof(i_0_978,plain,
    ! [X1845,X1846,X1847] :
      ( ~ class_Orderings_Oorder(X1847)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1847),X1846),X1845))
      | X1846 != X1845 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__neq])]) ).

fof(i_0_979,plain,
    ! [X2149,X2150,X2151] :
      ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2149,tc_HOL_Obool),X2151),X2150))
        | X2151 != X2150 )
      & ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2149,tc_HOL_Obool),X2150),X2151))
        | X2151 != X2150 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_576])])]) ).

fof(i_0_980,plain,
    ! [X2114,X2115,X2116] :
      ( X2116 != X2115
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2114,tc_HOL_Obool),X2116),X2115)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityD1])]) ).

fof(i_0_981,plain,
    ! [X2117,X2118,X2119] :
      ( X2119 != X2118
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2117,tc_HOL_Obool),X2118),X2119)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityD2])]) ).

fof(i_0_982,plain,
    ! [X1825,X1826] :
      ( ~ class_Orderings_Opreorder(X1826)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1826),X1825),X1825)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_577])]) ).

fof(i_0_983,plain,
    ! [X2095,X2096] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2096,tc_HOL_Obool),X2095),X2095)),
    inference(variable_rename,[status(thm)],[fact_subset__refl]) ).

fof(i_0_984,plain,
    ! [X2590] :
      ( ( X2590 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2590)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2590))
        | X2590 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neq0__conv])]) ).

fof(i_0_985,plain,
    ! [X1908,X1909,X1910,X1911] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1911),X1910),X1909) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1911),X1908),X1909)
        | X1910 = X1908
        | ~ class_Groups_Ocancel__semigroup__add(X1911) )
      & ( X1910 != X1908
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1911),X1910),X1909) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1911),X1908),X1909)
        | ~ class_Groups_Ocancel__semigroup__add(X1911) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__cancel])])]) ).

fof(i_0_986,plain,
    ! [X1896,X1897,X1898,X1899] :
      ( ~ class_Groups_Ocancel__semigroup__add(X1899)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1899),X1898),X1897) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1899),X1896),X1897)
      | X1898 = X1896 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__imp__eq])]) ).

fof(i_0_987,plain,
    ! [X1900,X1901,X1902,X1903] :
      ( ~ class_Groups_Ocancel__ab__semigroup__add(X1903)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1903),X1902),X1901) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1903),X1902),X1900)
      | X1901 = X1900 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__imp__eq])]) ).

fof(i_0_988,plain,
    ! [X1912,X1913,X1914,X1915] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1915),X1914),X1913) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1915),X1914),X1912)
        | X1913 = X1912
        | ~ class_Groups_Ocancel__semigroup__add(X1915) )
      & ( X1913 != X1912
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1915),X1914),X1913) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1915),X1914),X1912)
        | ~ class_Groups_Ocancel__semigroup__add(X1915) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__cancel])])]) ).

fof(i_0_989,plain,
    ! [X1904,X1905,X1906,X1907] :
      ( ~ class_Groups_Ocancel__semigroup__add(X1907)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1907),X1906),X1905) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1907),X1906),X1904)
      | X1905 = X1904 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__imp__eq])]) ).

fof(i_0_990,plain,
    ! [X1816,X1817,X1818] :
      ( ~ class_Orderings_Olinorder(X1818)
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1818,X1817),X1816))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1818,X1816),X1817)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__linear])]) ).

fof(i_0_991,plain,
    ! [X1764,X1765,X1766] :
      ( ~ class_Orderings_Olinorder(X1766)
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1766,X1765),X1764))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1766,X1764),X1765)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_578])]) ).

fof(i_0_992,plain,
    ! [X2675,X2676] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2676),hAPP(c_Nat_OSuc,X2675)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2676),X2675)),
    inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).

fof(i_0_993,plain,
    ! [X2679,X2680] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2680)),X2679) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2680),hAPP(c_Nat_OSuc,X2679)),
    inference(variable_rename,[status(thm)],[fact_add__Suc__shift]) ).

fof(i_0_994,plain,
    ! [X2591] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2591),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[i_0_579]) ).

fof(i_0_995,plain,
    ! [X2589] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2589),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[i_0_580]) ).

fof(i_0_996,plain,
    ! [X2562] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2562),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[i_0_581]) ).

fof(i_0_997,plain,
    ! [X2804] : c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2804)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_Nat_Onat,X2804)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[fact_nat_Osize_I4_J]) ).

fof(i_0_998,plain,
    ! [X2587,X2588] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2588),X2587))
      | X2587 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr__implies__not0])]) ).

fof(i_0_999,plain,
    ! [X2288,X2289] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2289),X2288))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2288),X2289)) ),
    inference(variable_rename,[status(thm)],[fact_nat__le__linear]) ).

fof(i_0_1000,plain,
    ! [X2668] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X2668))),
    inference(variable_rename,[status(thm)],[fact_zero__less__Suc]) ).

fof(i_0_1001,plain,
    ! [X2265,X2266] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2266),X2265))
      | X2265 != X2266 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl2])]) ).

fof(i_0_1002,plain,
    ! [X2263,X2264] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2264),X2263))
      | X2264 != X2263 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl3])]) ).

fof(i_0_1003,plain,
    ! [X2629] :
      ( ~ class_Rings_Olinordered__semidom(X2629)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2629),c_Groups_Ozero__class_Ozero(X2629)),c_Groups_Oone__class_Oone(X2629))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__one])]) ).

fof(i_0_1004,plain,
    ! [X2808] :
      ( ~ class_Rings_Oring__1(X2808)
      | hBOOL(hAPP(hAPP(c_member(X2808),c_Groups_Ozero__class_Ozero(X2808)),c_Int_Oring__1__class_OInts(X2808))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__0])]) ).

fof(i_0_1005,plain,
    ! [X2812] :
      ( ~ class_Rings_Oring__1(X2812)
      | hBOOL(hAPP(hAPP(c_member(X2812),c_Groups_Oone__class_Oone(X2812)),c_Int_Oring__1__class_OInts(X2812))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__1])]) ).

fof(i_0_1006,plain,
    ! [X2272] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2272),X2272)),
    inference(variable_rename,[status(thm)],[i_0_582]) ).

fof(i_0_1007,plain,
    ! [X2267] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2267),X2267)),
    inference(variable_rename,[status(thm)],[i_0_583]) ).

fof(i_0_1008,plain,
    ! [X2284,X2285,X2286] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2286),X2285) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2284),X2285)
        | X2286 = X2284 )
      & ( X2286 != X2284
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2286),X2285) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2284),X2285) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__right__cancel])]) ).

fof(i_0_1009,plain,
    ! [X2281,X2282,X2283] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2283),X2282) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2283),X2281)
        | X2282 = X2281 )
      & ( X2282 != X2281
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2283),X2282) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2283),X2281) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel])]) ).

fof(i_0_1010,plain,
    ! [X2475,X2476,X2477] :
      ( ~ c_Finite__Set_Ofinite(X2477,X2476)
      | c_Finite__Set_Ofinite(X2477,c_Set_Oinsert(X2477,X2475,X2476)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite_OinsertI])]) ).

fof(i_0_1011,plain,
    ! [X2665] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2665),hAPP(c_Nat_OSuc,X2665))),
    inference(variable_rename,[status(thm)],[fact_lessI]) ).

fof(i_0_1012,plain,
    ! [X1636,X1637] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1637,tc_HOL_Obool)),X1636)),
    inference(variable_rename,[status(thm)],[fact_top1I]) ).

fof(i_0_1013,plain,
    ! [X2578] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2578),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | X2578 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X2578 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2578),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__0__eq])]) ).

fof(i_0_1014,plain,
    ! [X2735,X2736] :
      ( ( X2736 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X2736 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2736),X2735) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X2735 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X2736 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2736),X2735) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X2736 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X2735 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2736),X2735) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X2735 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X2735 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2736),X2735) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X2736 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X2735 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2736),X2735) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X2736 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X2735 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2736),X2735) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__is__1])])]) ).

fof(i_0_1015,plain,
    ! [X2737,X2738] :
      ( ( X2738 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X2738 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2738),X2737) )
      & ( X2737 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X2738 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2738),X2737) )
      & ( X2738 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X2737 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2738),X2737) )
      & ( X2737 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X2737 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2738),X2737) )
      & ( X2738 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X2737 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2738),X2737) )
      & ( X2738 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X2737 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2738),X2737) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__is__add])])]) ).

fof(i_0_1016,plain,
    ! [X1597,X1598] :
      ( hAPP(X1598,esk1_2(X1597,X1598)) != hAPP(X1597,esk1_2(X1597,X1598))
      | X1598 = X1597 ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])]) ).

fof(i_0_1017,plain,
    ! [X2627] :
      ( ~ class_Rings_Olinordered__semidom(X2627)
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2627,c_Groups_Ozero__class_Ozero(X2627)),c_Groups_Oone__class_Oone(X2627))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__one])]) ).

fof(i_0_1018,plain,
    ! [X3168,X3169] :
      ( ~ hBOOL(hAPP(hAPP(c_fequal,X3169),X3168))
      | X3169 = X3168 ),
    inference(variable_rename,[status(thm)],[i_0_584]) ).

fof(i_0_1019,plain,
    ! [X3080,X3081] : c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3081,X3080)),
    inference(variable_rename,[status(thm)],[fact_finite__atLeastLessThan]) ).

fof(i_0_1020,plain,
    ! [X2803] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X2803)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(X2803)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[fact_nat_Osize_I2_J]) ).

fof(i_0_1021,plain,
    ! [X2764,X2765,X2766] :
      ( ~ class_Rings_Ocomm__semiring__1(X2766)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2766),X2765),X2764) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2766),X2764),X2765) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])]) ).

fof(i_0_1022,plain,
    ! [X2586] :
      ( X2586 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2586)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr0I])]) ).

fof(i_0_1023,plain,
    ! [X2053,X2054] :
      ( ~ class_Orderings_Otop(X2054)
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2054,X2053),c_Orderings_Otop__class_Otop(X2054))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_top__greatest])]) ).

fof(i_0_1024,plain,
    ! [X2794,X2795] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2795),X2794),X2794) != c_Groups_Ozero__class_Ozero(X2795)
        | X2794 = c_Groups_Ozero__class_Ozero(X2795)
        | ~ class_Groups_Olinordered__ab__group__add(X2795) )
      & ( X2794 != c_Groups_Ozero__class_Ozero(X2795)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2795),X2794),X2794) = c_Groups_Ozero__class_Ozero(X2795)
        | ~ class_Groups_Olinordered__ab__group__add(X2795) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__eq__0__iff])])]) ).

fof(i_0_1025,plain,
    ! [X2568,X2569] :
      ( ( c_Groups_Ozero__class_Ozero(X2569) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2569),X2568),X2568)
        | X2568 = c_Groups_Ozero__class_Ozero(X2569)
        | ~ class_Groups_Olinordered__ab__group__add(X2569) )
      & ( X2568 != c_Groups_Ozero__class_Ozero(X2569)
        | c_Groups_Ozero__class_Ozero(X2569) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2569),X2568),X2568)
        | ~ class_Groups_Olinordered__ab__group__add(X2569) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__zero__sym])])]) ).

fof(i_0_1026,plain,
    ! [X2796,X2797,X2798] :
      ( ( X2797 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2798),X2797),X2796)
        | X2796 = c_Groups_Ozero__class_Ozero(X2798)
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2798) )
      & ( X2796 != c_Groups_Ozero__class_Ozero(X2798)
        | X2797 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2798),X2797),X2796)
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2798) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__iff])])]) ).

fof(i_0_1027,plain,
    ! [X1810,X1811,X1812] :
      ( ~ class_Orderings_Opreorder(X1812)
      | X1811 != X1810
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1812,X1811),X1810)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__refl])]) ).

fof(i_0_1028,plain,
    ! [X3146,X3147,X3148,X3149] : hAPP(hAPP(c_COMBK(X3149,X3148),X3147),X3146) = X3147,
    inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).

fof(i_0_1029,plain,
    ! [X2273,X2274] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2274),X2273) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2273),X2274),
    inference(variable_rename,[status(thm)],[fact_nat__add__commute]) ).

fof(i_0_1030,plain,
    ! [X1720,X1721] :
      ( ~ class_Orderings_Opreorder(X1721)
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1721,X1720),X1720)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__refl])]) ).

fof(i_0_1031,plain,
    ! [X2579] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2579)),
    inference(variable_rename,[status(thm)],[fact_less__eq__nat_Osimps_I1_J]) ).

fof(i_0_1032,plain,
    ! [X2563] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2563)),
    inference(variable_rename,[status(thm)],[fact_le0]) ).

fof(i_0_1033,plain,
    ! [X2055,X2056,X2057] :
      ( ~ class_Orderings_Otop(X2057)
      | hAPP(c_Orderings_Otop__class_Otop(tc_fun(X2056,X2057)),X2055) = c_Orderings_Otop__class_Otop(X2057) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_top__apply])]) ).

fof(i_0_1034,plain,
    ! [X2582,X2583] :
      ( ( X2583 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2583),X2582) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X2582 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2583),X2582) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X2583 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X2582 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2583),X2582) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__is__0])])]) ).

fof(i_0_1035,plain,
    ! [X2290,X2291] :
      ( X2291 != X2290
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2291),X2290)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__imp__le])]) ).

fof(i_0_1036,plain,
    ! [X3170,X3171] :
      ( X3171 != X3170
      | hBOOL(hAPP(hAPP(c_fequal,X3171),X3170)) ),
    inference(variable_rename,[status(thm)],[help_c__fequal__2]) ).

fof(i_0_1037,plain,
    ! [X2580,X2581] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2581),X2580) != X2581
      | X2580 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__self__zero])]) ).

fof(i_0_1038,plain,
    ! [X2287] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2287),X2287)),
    inference(variable_rename,[status(thm)],[fact_le__refl]) ).

fof(i_0_1039,plain,
    ! [X2426] :
      ( ~ class_Finite__Set_Ofinite(X2426)
      | c_Finite__Set_Ofinite(X2426,c_Orderings_Otop__class_Otop(tc_fun(X2426,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV])]) ).

fof(i_0_1040,plain,
    ! [X2663,X2664] :
      ( ~ class_Rings_Ocomm__semiring__1(X2664)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2664),c_Groups_Ozero__class_Ozero(X2664)),X2663) = X2663 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J])]) ).

fof(i_0_1041,plain,
    ! [X2566,X2567] :
      ( ~ class_Groups_Ocomm__monoid__add(X2567)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2567),c_Groups_Ozero__class_Ozero(X2567)),X2566) = X2566 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0])]) ).

fof(i_0_1042,plain,
    ! [X2564,X2565] :
      ( ~ class_Groups_Omonoid__add(X2565)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2565),c_Groups_Ozero__class_Ozero(X2565)),X2564) = X2564 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__left])]) ).

fof(i_0_1043,plain,
    ! [X2799,X2800] :
      ( ~ class_Rings_Ocomm__semiring__1(X2800)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2800),X2799),c_Groups_Ozero__class_Ozero(X2800)) = X2799 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J])]) ).

fof(i_0_1044,plain,
    ! [X2572,X2573] :
      ( ~ class_Groups_Ocomm__monoid__add(X2573)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2573),X2572),c_Groups_Ozero__class_Ozero(X2573)) = X2572 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add_Ocomm__neutral])]) ).

fof(i_0_1045,plain,
    ! [X2570,X2571] :
      ( ~ class_Groups_Omonoid__add(X2571)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2571),X2570),c_Groups_Ozero__class_Ozero(X2571)) = X2570 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__right])]) ).

fof(i_0_1046,plain,
    ! [X2802] : hAPP(c_Nat_OSuc,X2802) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2802),
    inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1__left]) ).

fof(i_0_1047,plain,
    ! [X2801] : hAPP(c_Nat_OSuc,X2801) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2801),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1]) ).

fof(i_0_1048,plain,
    ! [X2585] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2585) = X2585,
    inference(variable_rename,[status(thm)],[fact_plus__nat_Oadd__0]) ).

fof(i_0_1049,plain,
    ! [X2763] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2763) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2763)),
    inference(variable_rename,[status(thm)],[fact_less__eq__Suc__le__raw]) ).

fof(i_0_1050,plain,
    ! [X2584] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2584),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2584,
    inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).

fof(i_0_1051,plain,
    ! [X3139,X3140] :
      ( ~ class_Finite__Set_Ofinite(X3140)
      | ~ class_Finite__Set_Ofinite(X3139)
      | class_Finite__Set_Ofinite(tc_sum(X3140,X3139)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_sum__Finite__Set_Ofinite])]) ).

fof(i_0_1052,plain,
    ! [X3131,X3132] :
      ( ~ class_Finite__Set_Ofinite(X3132)
      | ~ class_Finite__Set_Ofinite(X3131)
      | class_Finite__Set_Ofinite(tc_fun(X3132,X3131)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Finite__Set_Ofinite])]) ).

fof(i_0_1053,plain,
    ! [X3142,X3143] :
      ( ~ class_Finite__Set_Ofinite(X3143)
      | ~ class_Finite__Set_Ofinite(X3142)
      | class_Finite__Set_Ofinite(tc_prod(X3143,X3142)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_prod__Finite__Set_Ofinite])]) ).

fof(i_0_1054,plain,
    ! [X2696,X2697] :
      ( ( hAPP(c_Nat_OSuc,X2697) != hAPP(c_Nat_OSuc,X2696)
        | X2697 = X2696 )
      & ( X2697 != X2696
        | hAPP(c_Nat_OSuc,X2697) = hAPP(c_Nat_OSuc,X2696) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat_Oinject])]) ).

fof(i_0_1055,plain,
    ! [X2694,X2695] :
      ( hAPP(c_Nat_OSuc,X2695) != hAPP(c_Nat_OSuc,X2694)
      | X2695 = X2694 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__inject])]) ).

fof(i_0_1056,plain,
    ! [X3135,X3136] :
      ( ~ class_Orderings_Otop(X3136)
      | class_Orderings_Otop(tc_fun(X3135,X3136)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Otop])]) ).

fof(i_0_1057,plain,
    ! [X3133,X3134] :
      ( ~ class_Orderings_Oorder(X3134)
      | class_Orderings_Oorder(tc_fun(X3133,X3134)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oorder])]) ).

fof(i_0_1058,plain,
    ! [X3137,X3138] :
      ( ~ class_Orderings_Oord(X3138)
      | class_Orderings_Oord(tc_fun(X3137,X3138)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oord])]) ).

fof(i_0_1059,plain,
    ! [X3129,X3130] :
      ( ~ class_Orderings_Opreorder(X3130)
      | class_Orderings_Opreorder(tc_fun(X3129,X3130)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Opreorder])]) ).

fof(i_0_1060,plain,
    ! [X2633,X2634] :
      ( c_Finite__Set_Ofinite(X2634,X2633)
      | c_Finite__Set_Ocard(X2634,X2633) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_585])]) ).

fof(i_0_1061,plain,
    ! [X2674] : hAPP(c_Nat_OSuc,X2674) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_Suc__neq__Zero]) ).

fof(i_0_1062,plain,
    ! [X2672] : hAPP(c_Nat_OSuc,X2672) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_nat_Osimps_I3_J]) ).

fof(i_0_1063,plain,
    ! [X2671] : hAPP(c_Nat_OSuc,X2671) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_Suc__not__Zero]) ).

fof(i_0_1064,plain,
    ! [X2673] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X2673),
    inference(variable_rename,[status(thm)],[fact_Zero__neq__Suc]) ).

fof(i_0_1065,plain,
    ! [X2670] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X2670),
    inference(variable_rename,[status(thm)],[fact_nat_Osimps_I2_J]) ).

fof(i_0_1066,plain,
    ! [X2669] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X2669),
    inference(variable_rename,[status(thm)],[fact_Zero__not__Suc]) ).

fof(i_0_1067,plain,
    ! [X2413,X2414] :
      ( ~ class_Finite__Set_Ofinite(X2414)
      | c_Finite__Set_Ofinite(X2414,X2413) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__code])]) ).

fof(i_0_1068,plain,
    ! [X2411,X2412] :
      ( ~ class_Finite__Set_Ofinite(X2412)
      | c_Finite__Set_Ofinite(X2412,X2411) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite])]) ).

fof(i_0_1069,plain,
    ! [X2698] : hAPP(c_Nat_OSuc,X2698) != X2698,
    inference(variable_rename,[status(thm)],[fact_Suc__n__not__n]) ).

fof(i_0_1070,plain,
    ! [X2699] : X2699 != hAPP(c_Nat_OSuc,X2699),
    inference(variable_rename,[status(thm)],[fact_n__not__Suc__n]) ).

fof(i_0_1071,plain,
    ! [X3144,X3145] : hAPP(c_COMBI(X3145),X3144) = X3144,
    inference(variable_rename,[status(thm)],[help_c__COMBI__1]) ).

fof(i_0_1072,plain,
    ! [X2575] :
      ( ~ class_Rings_Ozero__neq__one(X2575)
      | c_Groups_Ozero__class_Ozero(X2575) != c_Groups_Oone__class_Oone(X2575) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__neq__one])]) ).

fof(i_0_1073,plain,
    ! [X2574] :
      ( ~ class_Rings_Ozero__neq__one(X2574)
      | c_Groups_Oone__class_Oone(X2574) != c_Groups_Ozero__class_Ozero(X2574) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__neq__zero])]) ).

fof(i_0_1074,plain,
    ! [X3141] :
      ( ~ class_Finite__Set_Ofinite(X3141)
      | class_Finite__Set_Ofinite(tc_Option_Ooption(X3141)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Option__Ooption__Finite__Set_Ofinite])]) ).

fof(i_0_1075,plain,
    ! [X2807] : c_Nat_Osize__class_Osize(tc_Nat_Onat,X2807) = X2807,
    inference(variable_rename,[status(thm)],[fact_nat__size]) ).

fof(i_0_1076,plain,
    ~ hBOOL(c_fFalse),
    inference(fof_simplification,[status(thm)],[help_c__fFalse__1]) ).

cnf(i_0_1077,plain,
    ( v_e____ = v_d____
    | v_b____ = v_a____
    | epred1_0
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____)))),c_Arrow__Order__Mirabelle_OProf))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____)),c_Arrow__Order__Mirabelle_OProf)) ),
    inference(split_conjunct,[status(thm)],[i_0_586]),
    [final] ).

cnf(i_0_1078,negated_conjecture,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____)))) ),
    inference(split_conjunct,[status(thm)],[i_0_587]),
    [final] ).

cnf(i_0_1079,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____)))))) ),
    inference(split_conjunct,[status(thm)],[i_0_588]),
    [final] ).

cnf(i_0_1080,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_524]),
    [final] ).

cnf(i_0_1081,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_524]),
    [final] ).

cnf(i_0_1082,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_524]),
    [final] ).

cnf(i_0_1083,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_524]),
    [final] ).

cnf(i_0_1084,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
    | hAPP(v_h____,esk47_0) != v_n____
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_524]),
    [final] ).

cnf(i_0_1085,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
    | hAPP(v_h____,esk47_0) = v_n____
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_524]),
    [final] ).

cnf(i_0_1086,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
    | hAPP(v_h____,esk47_0) != v_n____
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_524]),
    [final] ).

cnf(i_0_1087,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | hAPP(v_h____,esk47_0) != v_n____
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_524]),
    [final] ).

cnf(i_0_1088,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
    | ~ epred1_0
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____)))))) ),
    inference(cn,[status(thm)],[i_0_589]),
    [final] ).

cnf(i_0_1089,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
    | hAPP(v_h____,esk47_0) = v_n____
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_524]),
    [final] ).

cnf(i_0_1090,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
    | hAPP(v_h____,esk47_0) != v_n____
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_524]),
    [final] ).

cnf(i_0_1091,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | hAPP(v_h____,esk47_0) = v_n____
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_524]),
    [final] ).

cnf(i_0_1092,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_524]),
    [final] ).

cnf(i_0_1093,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
    | hAPP(v_h____,esk47_0) = v_n____
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_524]),
    [final] ).

cnf(i_0_1094,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
    | hAPP(v_h____,esk47_0) != v_n____
    | ~ epred1_0
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____)))))) ),
    inference(cn,[status(thm)],[i_0_590]),
    [final] ).

cnf(i_0_1095,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
    | ~ epred1_0
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____)))))) ),
    inference(cn,[status(thm)],[i_0_591]),
    [final] ).

cnf(i_0_1096,plain,
    ( hAPP(v_h____,esk47_0) = v_n____
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
    | ~ epred1_0
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____)))))) ),
    inference(cn,[status(thm)],[i_0_592]),
    [final] ).

cnf(i_0_1097,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
    | hAPP(v_h____,esk47_0) != v_n____
    | ~ epred1_0
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____)))))) ),
    inference(cn,[status(thm)],[i_0_593]),
    [final] ).

cnf(i_0_1098,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
    | ~ epred1_0
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____)))))) ),
    inference(cn,[status(thm)],[i_0_594]),
    [final] ).

cnf(i_0_1099,plain,
    ( hAPP(v_h____,esk47_0) = v_n____
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
    | ~ epred1_0
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____)))))) ),
    inference(cn,[status(thm)],[i_0_595]),
    [final] ).

cnf(i_0_1100,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))) ),
    inference(split_conjunct,[status(thm)],[i_0_588]),
    [final] ).

cnf(i_0_1101,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_524]),
    [final] ).

cnf(i_0_1102,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_524]),
    [final] ).

cnf(i_0_1103,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_524]),
    [final] ).

cnf(i_0_1104,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_524]),
    [final] ).

cnf(i_0_1105,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
    | hAPP(v_h____,esk47_0) != v_n____
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_524]),
    [final] ).

cnf(i_0_1106,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | hAPP(v_h____,esk47_0) = v_n____
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_524]),
    [final] ).

cnf(i_0_1107,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
    | hAPP(v_h____,esk47_0) != v_n____
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_524]),
    [final] ).

cnf(i_0_1108,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | hAPP(v_h____,esk47_0) != v_n____
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_524]),
    [final] ).

cnf(i_0_1109,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | ~ epred1_0
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____)))) ),
    inference(cn,[status(thm)],[i_0_596]),
    [final] ).

cnf(i_0_1110,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | hAPP(v_h____,esk47_0) = v_n____
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_524]),
    [final] ).

cnf(i_0_1111,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
    | hAPP(v_h____,esk47_0) != v_n____
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_524]),
    [final] ).

cnf(i_0_1112,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | hAPP(v_h____,esk47_0) = v_n____
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_524]),
    [final] ).

cnf(i_0_1113,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_524]),
    [final] ).

cnf(i_0_1114,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | hAPP(v_h____,esk47_0) = v_n____
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_524]),
    [final] ).

cnf(i_0_1115,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | hAPP(v_h____,esk47_0) != v_n____
    | ~ epred1_0
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____)))) ),
    inference(cn,[status(thm)],[i_0_597]),
    [final] ).

cnf(i_0_1116,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | ~ epred1_0
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____)))) ),
    inference(cn,[status(thm)],[i_0_598]),
    [final] ).

cnf(i_0_1117,plain,
    ( hAPP(v_h____,esk47_0) = v_n____
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | ~ epred1_0
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____)))) ),
    inference(cn,[status(thm)],[i_0_599]),
    [final] ).

cnf(i_0_1118,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | hAPP(v_h____,esk47_0) != v_n____
    | ~ epred1_0
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____)))) ),
    inference(cn,[status(thm)],[i_0_600]),
    [final] ).

cnf(i_0_1119,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk47_0)),v_e____)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | ~ epred1_0
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____)))) ),
    inference(cn,[status(thm)],[i_0_601]),
    [final] ).

cnf(i_0_1120,plain,
    ( hAPP(v_h____,esk47_0) = v_n____
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | ~ epred1_0
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____)))) ),
    inference(cn,[status(thm)],[i_0_602]),
    [final] ).

cnf(i_0_1121,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_F,v_P____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____)))))) ),
    inference(split_conjunct,[status(thm)],[i_0_603]),
    [final] ).

cnf(i_0_1122,negated_conjecture,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____)))) ),
    inference(split_conjunct,[status(thm)],[i_0_587]),
    [final] ).

cnf(i_0_1123,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_F,v_P____))) ),
    inference(split_conjunct,[status(thm)],[i_0_603]),
    [final] ).

cnf(i_0_1124,plain,
    hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____)))),c_Arrow__Order__Mirabelle_OProf)),
    inference(split_conjunct,[status(thm)],[fact__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_058_AProf_096]),
    [final] ).

cnf(i_0_1125,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____)))))),
    inference(split_conjunct,[status(thm)],[fact__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ae_096]),
    [final] ).

cnf(i_0_1126,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk8_0),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))),
    inference(split_conjunct,[status(thm)],[i_0_604]),
    [final] ).

cnf(i_0_1127,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk7_0),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))),
    inference(split_conjunct,[status(thm)],[i_0_605]),
    [final] ).

cnf(i_0_1128,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))),
    inference(split_conjunct,[status(thm)],[fact_n_I3_J]),
    [final] ).

cnf(i_0_1129,plain,
    hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),X1))),v_Lab____)),v_Lba____)),c_Arrow__Order__Mirabelle_OProf)),
    inference(split_conjunct,[status(thm)],[i_0_606]),
    [final] ).

cnf(i_0_1130,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),X1))),v_Lab____)),v_Lba____))))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),esk8_0)) ),
    inference(split_conjunct,[status(thm)],[i_0_604]),
    [final] ).

cnf(i_0_1131,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),X1))),v_Lab____)),v_Lba____))))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),esk7_0)) ),
    inference(split_conjunct,[status(thm)],[i_0_605]),
    [final] ).

cnf(i_0_1132,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),X1))),v_Lab____)),v_Lba____))))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),v_n____)) ),
    inference(split_conjunct,[status(thm)],[i_0_607]),
    [final] ).

cnf(i_0_1133,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X3),X4))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1,c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1,c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2,c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1,c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1,c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2,c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_608]),
    [final] ).

cnf(i_0_1134,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1,c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1,c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2,c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1,c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1,c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2,c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X4)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_608]),
    [final] ).

cnf(i_0_1135,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X5)),hAPP(v_F,X6)))
    | X5 = X1
    | X4 = X2
    | X1 = X2
    | X4 = X5
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X5)),hAPP(X6,esk6_6(X3,X6,X2,X1,X5,X4))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk6_6(X3,X6,X2,X1,X5,X4))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X6),c_Arrow__Order__Mirabelle_OProf)) ),
    inference(split_conjunct,[status(thm)],[i_0_609]),
    [final] ).

cnf(i_0_1136,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X5)),hAPP(v_F,X6)))
    | X2 = X4
    | X1 = X5
    | X4 = X5
    | X1 = X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk6_6(X6,X3,X5,X4,X2,X1))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X5)),hAPP(X6,esk6_6(X6,X3,X5,X4,X2,X1))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X6),c_Arrow__Order__Mirabelle_OProf))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf)) ),
    inference(split_conjunct,[status(thm)],[i_0_609]),
    [final] ).

cnf(i_0_1137,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X6),X5)),hAPP(v_F,X4)))
    | X2 = X6
    | X1 = X5
    | X6 = X5
    | X1 = X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk5_6(X4,X3,X5,X6,X2,X1))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X6),X5)),hAPP(X4,esk5_6(X4,X3,X5,X6,X2,X1))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X4),c_Arrow__Order__Mirabelle_OProf))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf)) ),
    inference(split_conjunct,[status(thm)],[i_0_610]),
    [final] ).

cnf(i_0_1138,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X5)),hAPP(v_F,X6)))
    | X1 = X2
    | X4 = X5
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X5)),hAPP(X6,esk3_6(X3,X6,X2,X1,X5,X4))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk3_6(X3,X6,X2,X1,X5,X4))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X6),c_Arrow__Order__Mirabelle_OProf)) ),
    inference(split_conjunct,[status(thm)],[i_0_611]),
    [final] ).

cnf(i_0_1139,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X5)),hAPP(v_F,X6)))
    | X4 = X5
    | X1 = X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk3_6(X6,X3,X5,X4,X2,X1))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X5)),hAPP(X6,esk3_6(X6,X3,X5,X4,X2,X1))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X6),c_Arrow__Order__Mirabelle_OProf))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf)) ),
    inference(split_conjunct,[status(thm)],[i_0_611]),
    [final] ).

cnf(i_0_1140,plain,
    ( X3 = X4
    | hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1,c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1,c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2,c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3) != hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1,c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1,c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2,c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_612]),
    [final] ).

cnf(i_0_1141,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X5)),hAPP(v_F,X6)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X5)),hAPP(X6,esk6_6(X3,X6,X2,X1,X5,X4))))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk6_6(X3,X6,X2,X1,X5,X4))))
    | X5 = X1
    | X4 = X2
    | X1 = X2
    | X4 = X5
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X6),c_Arrow__Order__Mirabelle_OProf)) ),
    inference(split_conjunct,[status(thm)],[i_0_609]),
    [final] ).

cnf(i_0_1142,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X5)),hAPP(v_F,X6)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk6_6(X6,X3,X5,X4,X2,X1))))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X5)),hAPP(X6,esk6_6(X6,X3,X5,X4,X2,X1))))
    | X2 = X4
    | X1 = X5
    | X4 = X5
    | X1 = X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X6),c_Arrow__Order__Mirabelle_OProf))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf)) ),
    inference(split_conjunct,[status(thm)],[i_0_609]),
    [final] ).

cnf(i_0_1143,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk5_6(X4,X3,X5,X6,X2,X1))))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X6),X5)),hAPP(X4,esk5_6(X4,X3,X5,X6,X2,X1))))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X6),X5)),hAPP(v_F,X4)))
    | X2 = X6
    | X1 = X5
    | X6 = X5
    | X1 = X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X4),c_Arrow__Order__Mirabelle_OProf))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf)) ),
    inference(split_conjunct,[status(thm)],[i_0_610]),
    [final] ).

cnf(i_0_1144,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X5)),hAPP(v_F,X6)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X5)),hAPP(X6,esk3_6(X3,X6,X2,X1,X5,X4))))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk3_6(X3,X6,X2,X1,X5,X4))))
    | X1 = X2
    | X4 = X5
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X6),c_Arrow__Order__Mirabelle_OProf)) ),
    inference(split_conjunct,[status(thm)],[i_0_611]),
    [final] ).

cnf(i_0_1145,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X5)),hAPP(v_F,X6)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk3_6(X6,X3,X5,X4,X2,X1))))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X5)),hAPP(X6,esk3_6(X6,X3,X5,X4,X2,X1))))
    | X4 = X5
    | X1 = X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X6),c_Arrow__Order__Mirabelle_OProf))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf)) ),
    inference(split_conjunct,[status(thm)],[i_0_611]),
    [final] ).

cnf(i_0_1146,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X5,X1),tc_HOL_Obool),c_FuncSet_OPi(X5,X1,X4,X2)),c_FuncSet_OPi(X5,X1,X4,X3)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),hAPP(X2,esk28_5(X3,X2,X1,X4,X5))),hAPP(X3,esk28_5(X3,X2,X1,X4,X5)))) ),
    inference(split_conjunct,[status(thm)],[i_0_613]),
    [final] ).

cnf(i_0_1147,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X1)),X2),c_FuncSet_OPi(X5,X1,X4,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,esk29_5(X3,X2,X1,X4,X5))),hAPP(X3,esk29_5(X3,X2,X1,X4,X5)))) ),
    inference(split_conjunct,[status(thm)],[i_0_614]),
    [final] ).

cnf(i_0_1148,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,X5)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X4,esk19_5(X3,X4,X5,X1,X2))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X5,esk19_5(X3,X4,X5,X1,X2))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X5),c_Arrow__Order__Mirabelle_OProf))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X4),c_Arrow__Order__Mirabelle_OProf))
    | ~ c_Arrow__Order__Mirabelle_OIIA(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_615]),
    [final] ).

cnf(i_0_1149,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,X5)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X5,esk19_5(X3,X5,X4,X1,X2))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X4,esk19_5(X3,X5,X4,X1,X2))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X4),c_Arrow__Order__Mirabelle_OProf))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X5),c_Arrow__Order__Mirabelle_OProf))
    | ~ c_Arrow__Order__Mirabelle_OIIA(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_615]),
    [final] ).

cnf(i_0_1150,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X4)),hAPP(v_F,X5)))
    | X1 = X4
    | X2 = X4
    | X1 = X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk4_5(X5,X3,X4,X2,X1))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X4)),hAPP(X5,esk4_5(X5,X3,X4,X2,X1))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X5),c_Arrow__Order__Mirabelle_OProf))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf)) ),
    inference(split_conjunct,[status(thm)],[i_0_616]),
    [final] ).

cnf(i_0_1151,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X1)),hAPP(v_F,X5)))
    | X4 = X2
    | X1 = X2
    | X4 = X1
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X1)),hAPP(X5,esk4_5(X3,X5,X2,X1,X4))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk4_5(X3,X5,X2,X1,X4))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X5),c_Arrow__Order__Mirabelle_OProf)) ),
    inference(split_conjunct,[status(thm)],[i_0_616]),
    [final] ).

cnf(i_0_1152,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,X5)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X4,esk19_5(X3,X4,X5,X1,X2))))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X5,esk19_5(X3,X4,X5,X1,X2))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X5),c_Arrow__Order__Mirabelle_OProf))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X4),c_Arrow__Order__Mirabelle_OProf))
    | ~ c_Arrow__Order__Mirabelle_OIIA(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_615]),
    [final] ).

cnf(i_0_1153,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,X5)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X5,esk19_5(X3,X5,X4,X1,X2))))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X4,esk19_5(X3,X5,X4,X1,X2))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X4),c_Arrow__Order__Mirabelle_OProf))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X5),c_Arrow__Order__Mirabelle_OProf))
    | ~ c_Arrow__Order__Mirabelle_OIIA(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_615]),
    [final] ).

cnf(i_0_1154,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X4)),hAPP(v_F,X5)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk4_5(X5,X3,X4,X2,X1))))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X4)),hAPP(X5,esk4_5(X5,X3,X4,X2,X1))))
    | X1 = X4
    | X2 = X4
    | X1 = X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X5),c_Arrow__Order__Mirabelle_OProf))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf)) ),
    inference(split_conjunct,[status(thm)],[i_0_616]),
    [final] ).

cnf(i_0_1155,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X1)),hAPP(v_F,X5)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X1)),hAPP(X5,esk4_5(X3,X5,X2,X1,X4))))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk4_5(X3,X5,X2,X1,X4))))
    | X4 = X2
    | X1 = X2
    | X4 = X1
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X5),c_Arrow__Order__Mirabelle_OProf)) ),
    inference(split_conjunct,[status(thm)],[i_0_616]),
    [final] ).

cnf(i_0_1156,plain,
    ( c_Arrow__Order__Mirabelle_Odictator(X2,X1)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk15_2(X1,X2)),esk16_2(X1,X2))),hAPP(X2,esk14_2(X1,X2))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin)))) ),
    inference(split_conjunct,[status(thm)],[i_0_617]),
    [final] ).

cnf(i_0_1157,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk15_2(X1,X2)),esk16_2(X1,X2))),hAPP(esk14_2(X1,X2),X1)))
    | c_Arrow__Order__Mirabelle_Odictator(X2,X1)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin)))) ),
    inference(split_conjunct,[status(thm)],[i_0_617]),
    [final] ).

cnf(i_0_1158,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk14_2(X1,X2)),c_Arrow__Order__Mirabelle_OProf))
    | c_Arrow__Order__Mirabelle_Odictator(X2,X1)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin)))) ),
    inference(split_conjunct,[status(thm)],[i_0_617]),
    [final] ).

cnf(i_0_1159,plain,
    ( c_Arrow__Order__Mirabelle_Odictator(X2,X1)
    | esk15_2(X1,X2) != esk16_2(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin)))) ),
    inference(split_conjunct,[status(thm)],[i_0_617]),
    [final] ).

cnf(i_0_1160,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X7)),X8))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X1),tc_prod(X5,X1))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X1),tc_prod(X5,X1)),hAPP(hAPP(c_Product__Type_OPair(X5,X1),X6),X2)),hAPP(hAPP(c_Product__Type_OPair(X5,X1),X7),X3))),c_Wellfounded_Olex__prod(X5,X1,X8,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_618]),
    [final] ).

cnf(i_0_1161,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X1)),hAPP(v_F,X4)))
    | X2 = X1
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X1)),hAPP(X4,esk2_4(X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk2_4(X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X4),c_Arrow__Order__Mirabelle_OProf)) ),
    inference(split_conjunct,[status(thm)],[i_0_619]),
    [final] ).

cnf(i_0_1162,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X1)),hAPP(v_F,X4)))
    | X1 = X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk2_4(X4,X3,X2,X1))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X1)),hAPP(X4,esk2_4(X4,X3,X2,X1))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X4),c_Arrow__Order__Mirabelle_OProf))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf)) ),
    inference(split_conjunct,[status(thm)],[i_0_619]),
    [final] ).

cnf(i_0_1163,plain,
    ( hAPP(X6,X7) = c_Finite__Set_Ofold__image(X1,X2,X3,X5,X4,X7)
    | ~ c_Finite__Set_Ofolding__image__simple(X1,X2,X3,X4,X5,X6)
    | ~ c_Finite__Set_Ofinite(X2,X7) ),
    inference(split_conjunct,[status(thm)],[i_0_620]),
    [final] ).

cnf(i_0_1164,plain,
    ( X1 = X2
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3,X5),tc_prod(X3,X5))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3,X5),tc_prod(X3,X5)),hAPP(hAPP(c_Product__Type_OPair(X3,X5),X1),X6)),hAPP(hAPP(c_Product__Type_OPair(X3,X5),X2),X7))),c_Wellfounded_Olex__prod(X3,X5,X4,X8))) ),
    inference(split_conjunct,[status(thm)],[i_0_618]),
    [final] ).

cnf(i_0_1165,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk28_5(X2,X3,X4,X5,X1)),X5))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,X4),tc_HOL_Obool),c_FuncSet_OPi(X1,X4,X5,X3)),c_FuncSet_OPi(X1,X4,X5,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_613]),
    [final] ).

cnf(i_0_1166,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X1)),hAPP(v_F,X4)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X1)),hAPP(X4,esk2_4(X3,X4,X1,X2))))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk2_4(X3,X4,X1,X2))))
    | X2 = X1
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X4),c_Arrow__Order__Mirabelle_OProf)) ),
    inference(split_conjunct,[status(thm)],[i_0_619]),
    [final] ).

cnf(i_0_1167,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X1)),hAPP(v_F,X4)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk2_4(X4,X3,X2,X1))))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X1)),hAPP(X4,esk2_4(X4,X3,X2,X1))))
    | X1 = X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X4),c_Arrow__Order__Mirabelle_OProf))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf)) ),
    inference(split_conjunct,[status(thm)],[i_0_619]),
    [final] ).

cnf(i_0_1168,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),esk37_5(X2,X3,X1,X4,X5)),X2))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X4),c_Set_Oimage(X1,X5,X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_621]),
    [final] ).

cnf(i_0_1169,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk29_5(X2,X3,X4,X5,X1)),X5))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X4)),X3),c_FuncSet_OPi(X1,X4,X5,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_614]),
    [final] ).

cnf(i_0_1170,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X7,X3),tc_prod(X7,X3))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X7,X3),tc_prod(X7,X3)),hAPP(hAPP(c_Product__Type_OPair(X7,X3),X2),X4)),hAPP(hAPP(c_Product__Type_OPair(X7,X3),X2),X5))),c_Recdef_Osame__fst(X7,X3,X1,X6)))
    | ~ hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X4),X5)),hAPP(X6,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_622]),
    [final] ).

cnf(i_0_1171,plain,
    hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_F),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin)))),
    inference(split_conjunct,[status(thm)],[fact_assms_I1_J]),
    [final] ).

cnf(i_0_1172,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X7,X3),tc_prod(X7,X3))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X7,X3),tc_prod(X7,X3)),hAPP(hAPP(c_Product__Type_OPair(X7,X3),X1),X4)),hAPP(hAPP(c_Product__Type_OPair(X7,X3),X2),X5))),c_Wellfounded_Olex__prod(X7,X3,X8,X6)))
    | X1 != X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X4),X5)),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_618]),
    [final] ).

cnf(i_0_1173,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X5),tc_prod(X1,X5))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X5),tc_prod(X1,X5)),hAPP(hAPP(c_Product__Type_OPair(X1,X5),X2),X6)),hAPP(hAPP(c_Product__Type_OPair(X1,X5),X3),X7))),c_Wellfounded_Olex__prod(X1,X5,X4,X8)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_618]),
    [final] ).

cnf(i_0_1174,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X1),X2),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk9_4(X3,X2,X4,X1))),hAPP(X3,esk9_4(X3,X2,X4,X1))))
    | ~ class_Orderings_Oord(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_623]),
    [final] ).

cnf(i_0_1175,plain,
    ( hBOOL(hAPP(hAPP(c_member(X2),X8),X7))
    | hAPP(X6,c_Set_Oinsert(X2,X8,X7)) = hAPP(hAPP(X3,hAPP(X5,X8)),hAPP(X6,X7))
    | ~ c_Finite__Set_Ofolding__image__simple(X1,X2,X3,X4,X5,X6)
    | ~ c_Finite__Set_Ofinite(X2,X7) ),
    inference(split_conjunct,[status(thm)],[i_0_624]),
    [final] ).

cnf(i_0_1176,plain,
    ( c_Finite__Set_Ocard(X1,X4) = c_Finite__Set_Ocard(X2,X5)
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),c_Set_Oimage(X1,X2,X3,X4)),X5))
    | ~ c_Fun_Oinj__on(X2,X1,X6,X5)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X2,X1,X6,X5)),X4))
    | ~ c_Finite__Set_Ofinite(X1,X4)
    | ~ c_Finite__Set_Ofinite(X2,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_625]),
    [final] ).

cnf(i_0_1177,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),hAPP(X1,X2)))
    | ~ c_Arrow__Order__Mirabelle_Ounanimity(X1)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2),c_Arrow__Order__Mirabelle_OProf))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),hAPP(X2,esk24_4(X1,X2,X3,X4)))) ),
    inference(split_conjunct,[status(thm)],[i_0_626]),
    [final] ).

cnf(i_0_1178,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lab____))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1)),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1)),v_c____),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1)),v_e____))) ),
    inference(split_conjunct,[status(thm)],[i_0_627]),
    [final] ).

cnf(i_0_1179,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lba____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1)),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1)),v_c____),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1)),v_e____))) ),
    inference(split_conjunct,[status(thm)],[i_0_627]),
    [final] ).

cnf(i_0_1180,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1)),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1)),v_c____),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1)),v_e____))) ),
    inference(split_conjunct,[status(thm)],[i_0_531]),
    [final] ).

cnf(i_0_1181,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1)),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1)),v_c____),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1)),v_e____))) ),
    inference(split_conjunct,[status(thm)],[i_0_531]),
    [final] ).

cnf(i_0_1182,plain,
    ( c_Finite__Set_Ocard(X1,X4) = c_Finite__Set_Ocard(X2,X5)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X1,X2,X4,hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X5))))
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2,X1)),X6),c_FuncSet_OPi(X2,X1,X5,hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X2),X4))))
    | ~ c_Fun_Oinj__on(X2,X1,X6,X5)
    | ~ c_Finite__Set_Ofinite(X1,X4)
    | ~ c_Finite__Set_Ofinite(X2,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_628]),
    [final] ).

cnf(i_0_1183,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_629]),
    [final] ).

cnf(i_0_1184,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,X1)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1)),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1)),v_c____),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1)),v_e____))) ),
    inference(split_conjunct,[status(thm)],[i_0_630]),
    [final] ).

cnf(i_0_1185,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X1,c_Set_Oimage(X2,X1,X3,X4))),c_Finite__Set_Ocard(X2,X4)))
    | ~ c_Fun_Oinj__on(X2,X1,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_631]),
    [final] ).

cnf(i_0_1186,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X2,X1,esk40_4(X3,X1,X4,X2),X4)),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2,X4)),c_Finite__Set_Ocard(X1,X3)))
    | ~ c_Finite__Set_Ofinite(X1,X3)
    | ~ c_Finite__Set_Ofinite(X2,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_632]),
    [final] ).

cnf(i_0_1187,plain,
    ( X1 = X2
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X3),X4),X5)))
    | X4 = X5
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X4)),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(split_conjunct,[status(thm)],[i_0_633]),
    [final] ).

cnf(i_0_1188,plain,
    ( X1 = X2
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),c_Arrow__Order__Mirabelle_Obelow(X3,X5,X4)))
    | X5 = X4
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X4)),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(split_conjunct,[status(thm)],[i_0_634]),
    [final] ).

cnf(i_0_1189,plain,
    ( c_Finite__Set_Ocard(X1,X2) = c_Finite__Set_Ofold__image(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | ~ c_Finite__Set_Ofinite(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_635]),
    [final] ).

cnf(i_0_1190,plain,
    ( c_Finite__Set_Ocard(X1,X2) = c_Finite__Set_Ofold__image(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | ~ c_Finite__Set_Ofinite(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_636]),
    [final] ).

cnf(i_0_1191,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lab____))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1)),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1)),v_c____),v_e____))) ),
    inference(split_conjunct,[status(thm)],[i_0_627]),
    [final] ).

cnf(i_0_1192,plain,
    ( hBOOL(hAPP(hAPP(c_member(X3),hAPP(c_Hilbert__Choice_Oinv__into(X3,X1,X5,X4),X2)),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oimage(X3,X1,X4,X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_637]),
    [final] ).

cnf(i_0_1193,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lab____))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | hAPP(v_h____,X1) != v_n____
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1)),v_c____),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1)),v_e____))) ),
    inference(split_conjunct,[status(thm)],[i_0_627]),
    [final] ).

cnf(i_0_1194,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lba____))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1)),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1)),v_c____),v_e____))) ),
    inference(split_conjunct,[status(thm)],[i_0_627]),
    [final] ).

cnf(i_0_1195,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,hAPP(c_Hilbert__Choice_Oinv__into(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)),v_h____),v_n____)))),
    inference(split_conjunct,[status(thm)],[fact__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_096]),
    [final] ).

cnf(i_0_1196,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X4),X5))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X2,X1,X3,X4)),c_Set_Oimage(X2,X1,X3,X5)))
    | ~ c_Fun_Oinj__on(X2,X1,X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_638]),
    [final] ).

cnf(i_0_1197,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lba____))
    | hAPP(v_h____,X1) != v_n____
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1)),v_c____),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1)),v_e____))) ),
    inference(split_conjunct,[status(thm)],[i_0_627]),
    [final] ).

cnf(i_0_1198,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | hAPP(v_h____,X1) != v_n____
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1)),v_c____),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1)),v_e____))) ),
    inference(split_conjunct,[status(thm)],[i_0_531]),
    [final] ).

cnf(i_0_1199,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),X3)),c_Wellfounded_Ofinite__psubset(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_639]),
    [final] ).

cnf(i_0_1200,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,X1)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1)),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1)),v_c____),v_e____))) ),
    inference(split_conjunct,[status(thm)],[i_0_630]),
    [final] ).

cnf(i_0_1201,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | hAPP(v_h____,X1) != v_n____
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1)),v_c____),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1)),v_e____))) ),
    inference(split_conjunct,[status(thm)],[i_0_531]),
    [final] ).

cnf(i_0_1202,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1)),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1)),v_c____),v_e____))) ),
    inference(cn,[status(thm)],[i_0_640]),
    [final] ).

cnf(i_0_1203,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),c_Set_Oimage(X1,X2,X3,X4)),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X1,X2,X4,hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X5)))) ),
    inference(split_conjunct,[status(thm)],[i_0_641]),
    [final] ).

cnf(i_0_1204,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,X1)))
    | hAPP(v_h____,X1) != v_n____
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1)),v_c____),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1)),v_e____))) ),
    inference(split_conjunct,[status(thm)],[i_0_630]),
    [final] ).

cnf(i_0_1205,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lab____))
    | hAPP(v_h____,X1) = v_n____
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1)),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1)),v_e____))) ),
    inference(split_conjunct,[status(thm)],[i_0_627]),
    [final] ).

cnf(i_0_1206,plain,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3),X2)),c_Wellfounded_Ofinite__psubset(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_639]),
    [final] ).

cnf(i_0_1207,plain,
    ( X5 = X6
    | hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),X5) != hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),X6)
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X5),c_Set_Oimage(X1,X2,X4,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X6),c_Set_Oimage(X1,X2,X4,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_642]),
    [final] ).

cnf(i_0_1208,plain,
    ( X3 = X1
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X5),X4),X2)))
    | X4 = X2
    | X1 != X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X1)),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X5),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(split_conjunct,[status(thm)],[i_0_633]),
    [final] ).

cnf(i_0_1209,plain,
    ( X1 = X2
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X3),X4),X5)))
    | X4 = X5
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3))
    | X1 != X4
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(split_conjunct,[status(thm)],[i_0_633]),
    [final] ).

cnf(i_0_1210,plain,
    ( X1 = X5
    | X1 = X2
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X3),X4),X5)))
    | X4 = X5
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X4)),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(split_conjunct,[status(thm)],[i_0_633]),
    [final] ).

cnf(i_0_1211,plain,
    ( X2 = X4
    | X1 = X2
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X3),X5),X4)))
    | X5 = X4
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X5),X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(split_conjunct,[status(thm)],[i_0_633]),
    [final] ).

cnf(i_0_1212,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lba____))
    | hAPP(v_h____,X1) = v_n____
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1)),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1)),v_e____))) ),
    inference(split_conjunct,[status(thm)],[i_0_627]),
    [final] ).

cnf(i_0_1213,plain,
    ( X1 = X4
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X4)),c_Arrow__Order__Mirabelle_Obelow(X5,X2,X3)))
    | X2 = X3
    | X1 != X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X5),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(split_conjunct,[status(thm)],[i_0_634]),
    [final] ).

cnf(i_0_1214,plain,
    ( X1 = X2
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),c_Arrow__Order__Mirabelle_Obelow(X3,X5,X4)))
    | X5 = X4
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3))
    | X2 != X4
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X4)),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(split_conjunct,[status(thm)],[i_0_634]),
    [final] ).

cnf(i_0_1215,plain,
    ( X1 = X4
    | X1 = X2
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X5)))
    | X4 = X5
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X5)),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(split_conjunct,[status(thm)],[i_0_634]),
    [final] ).

cnf(i_0_1216,plain,
    ( X2 = X5
    | X1 = X2
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),c_Arrow__Order__Mirabelle_Obelow(X3,X5,X4)))
    | X5 = X4
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(split_conjunct,[status(thm)],[i_0_634]),
    [final] ).

cnf(i_0_1217,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
    | hAPP(v_h____,X1) = v_n____
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1)),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1)),v_e____))) ),
    inference(split_conjunct,[status(thm)],[i_0_531]),
    [final] ).

cnf(i_0_1218,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | hAPP(v_h____,X1) = v_n____
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1)),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1)),v_e____))) ),
    inference(split_conjunct,[status(thm)],[i_0_531]),
    [final] ).

cnf(i_0_1219,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_629]),
    [final] ).

cnf(i_0_1220,plain,
    ( hAPP(v_h____,X1) = v_n____
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,X1)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1)),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1)),v_e____))) ),
    inference(split_conjunct,[status(thm)],[i_0_630]),
    [final] ).

cnf(i_0_1221,plain,
    ( X1 = c_Set_Oimage(X2,X3,X4,esk37_5(X5,X4,X2,X1,X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1),c_Set_Oimage(X2,X3,X4,X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_621]),
    [final] ).

cnf(i_0_1222,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1)),v_c____),v_e____)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | hAPP(v_h____,X1) != v_n____
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____)) ),
    inference(split_conjunct,[status(thm)],[i_0_531]),
    [final] ).

cnf(i_0_1223,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1)),v_c____),v_e____)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | hAPP(v_h____,X1) != v_n____
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lba____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lab____)) ),
    inference(split_conjunct,[status(thm)],[i_0_627]),
    [final] ).

cnf(i_0_1224,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),X2)),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1)))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_643]),
    [final] ).

cnf(i_0_1225,plain,
    ( X1 = hAPP(X2,esk35_5(X1,X2,X3,X4,X5))
    | hBOOL(hAPP(hAPP(c_member(X3),X1),c_Set_Oimage(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))))
    | X1 != hAPP(X2,X5)
    | ~ c_Fun_Oinj__on(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_644]),
    [final] ).

cnf(i_0_1226,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X3,c_Set_Oimage(X1,X3,X4,X2))),c_Finite__Set_Ocard(X1,X2)))
    | ~ c_Finite__Set_Ofinite(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_645]),
    [final] ).

cnf(i_0_1227,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1)),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____)) ),
    inference(split_conjunct,[status(thm)],[i_0_531]),
    [final] ).

cnf(i_0_1228,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1)),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lba____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lab____)) ),
    inference(split_conjunct,[status(thm)],[i_0_627]),
    [final] ).

cnf(i_0_1229,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool)),c_Set_Oimage(X1,X2,X3,X5)),c_Set_Oimage(X1,X2,X3,X4)))
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X5),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_646]),
    [final] ).

cnf(i_0_1230,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lab____))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | hAPP(v_h____,X1) != v_n____
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1)),v_c____),v_e____))) ),
    inference(split_conjunct,[status(thm)],[i_0_627]),
    [final] ).

cnf(i_0_1231,plain,
    ( hAPP(v_h____,X1) = v_n____
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1)),v_e____)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____)) ),
    inference(split_conjunct,[status(thm)],[i_0_531]),
    [final] ).

cnf(i_0_1232,plain,
    ( hAPP(v_h____,X1) = v_n____
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1)),v_e____)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lba____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lab____)) ),
    inference(split_conjunct,[status(thm)],[i_0_627]),
    [final] ).

cnf(i_0_1233,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X1,X4)),c_Finite__Set_Ocard(X2,X5)))
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),c_Set_Oimage(X1,X2,X3,X4)),X5))
    | ~ c_Finite__Set_Ofinite(X2,X5)
    | ~ c_Finite__Set_Ofinite(X1,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_632]),
    [final] ).

cnf(i_0_1234,plain,
    ( c_Set_Oimage(X1,X1,X3,X2) = X2
    | ~ c_Finite__Set_Ofinite(X1,X2)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X1,X1,X3,X2)),X2))
    | ~ c_Fun_Oinj__on(X1,X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_647]),
    [final] ).

cnf(i_0_1235,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X1,X4)),c_Finite__Set_Ocard(X2,X5)))
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),c_Set_Oimage(X1,X2,X3,X4)),X5))
    | ~ c_Finite__Set_Ofinite(X2,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_648]),
    [final] ).

cnf(i_0_1236,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Set_Oimage(X1,X4,X5,X2)),c_Set_Oimage(X1,X4,X5,X3)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
    | ~ c_Fun_Oinj__on(X1,X4,X5,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_638]),
    [final] ).

cnf(i_0_1237,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lba____))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | hAPP(v_h____,X1) != v_n____
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1)),v_c____),v_e____))) ),
    inference(split_conjunct,[status(thm)],[i_0_627]),
    [final] ).

cnf(i_0_1238,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk36_4(X2,X3,X1,X4)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X5),X4),c_Set_Oimage(X1,X5,X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_649]),
    [final] ).

cnf(i_0_1239,plain,
    ( X3 = X4
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),X5))
    | X3 = X2
    | X4 = X2
    | X1 != X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X5),X4),X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X5),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(split_conjunct,[status(thm)],[i_0_633]),
    [final] ).

cnf(i_0_1240,plain,
    ( X1 = X2
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),X4))
    | X3 = X2
    | X5 = X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X4),X5),X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X4),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(split_conjunct,[status(thm)],[i_0_633]),
    [final] ).

cnf(i_0_1241,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),X5))
    | X3 = X2
    | X1 != X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X4)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X5),X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X5),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(split_conjunct,[status(thm)],[i_0_633]),
    [final] ).

cnf(i_0_1242,plain,
    ( X2 = X1
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X1)),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(split_conjunct,[status(thm)],[i_0_650]),
    [final] ).

cnf(i_0_1243,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),X1))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_651]),
    [final] ).

cnf(i_0_1244,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X1,X4)),c_Finite__Set_Ocard(X2,X5)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X1,X2,X4,hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X5))))
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ c_Finite__Set_Ofinite(X2,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_652]),
    [final] ).

cnf(i_0_1245,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),X3)),c_Wellfounded_Ofinite__psubset(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ c_Finite__Set_Ofinite(X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_639]),
    [final] ).

cnf(i_0_1246,plain,
    ( hBOOL(hAPP(hAPP(c_member(X3),X1),c_Set_Oimage(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))))
    | esk35_5(X1,X2,X3,X4,X5) != X5
    | X1 != hAPP(X2,X5)
    | ~ c_Fun_Oinj__on(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_644]),
    [final] ).

cnf(i_0_1247,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1)),v_c____),v_e____)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | hAPP(v_h____,X1) != v_n____
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lab____)) ),
    inference(split_conjunct,[status(thm)],[i_0_627]),
    [final] ).

cnf(i_0_1248,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,X4),tc_HOL_Obool),c_FuncSet_OPi(X1,X4,X3,X5)),c_FuncSet_OPi(X1,X4,X2,X5)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_653]),
    [final] ).

cnf(i_0_1249,plain,
    ( X3 = X1
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X5),X4),X2)))
    | X4 = X2
    | X1 != X2
    | X3 != X4
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X1)),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X5),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(split_conjunct,[status(thm)],[i_0_633]),
    [final] ).

cnf(i_0_1250,plain,
    ( X3 = X2
    | X3 = X1
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X5),X4),X2)))
    | X4 = X2
    | X1 != X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X5),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(split_conjunct,[status(thm)],[i_0_633]),
    [final] ).

cnf(i_0_1251,plain,
    ( X1 = X5
    | X1 = X2
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X3),X4),X5)))
    | X4 = X5
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3))
    | X1 != X4
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(split_conjunct,[status(thm)],[i_0_633]),
    [final] ).

cnf(i_0_1252,plain,
    ( X2 = X4
    | X1 = X4
    | X1 = X2
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X3),X5),X4)))
    | X5 = X4
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(split_conjunct,[status(thm)],[i_0_633]),
    [final] ).

cnf(i_0_1253,plain,
    ( X1 = X4
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X4)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X5),X3),X2)))
    | X3 = X2
    | X1 != X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X5),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(split_conjunct,[status(thm)],[i_0_633]),
    [final] ).

cnf(i_0_1254,plain,
    ( X3 = X4
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X3)),X5))
    | X3 = X2
    | X2 = X4
    | X1 != X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),c_Arrow__Order__Mirabelle_Obelow(X5,X2,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X5),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(split_conjunct,[status(thm)],[i_0_634]),
    [final] ).

cnf(i_0_1255,plain,
    ( c_Finite__Set_Ofinite(X4,c_Set_Oimage(X2,X4,hAPP(c_COMBB(X1,X4,X2,X5),X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))
    | ~ c_Finite__Set_Ofinite(X1,c_Set_Oimage(X2,X1,X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_654]),
    [final] ).

cnf(i_0_1256,plain,
    ( X1 = X2
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),X4))
    | X3 = X2
    | X2 = X5
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),c_Arrow__Order__Mirabelle_Obelow(X4,X2,X5)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X4),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(split_conjunct,[status(thm)],[i_0_634]),
    [final] ).

cnf(i_0_1257,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),X5))
    | X2 = X4
    | X1 != X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),c_Arrow__Order__Mirabelle_Obelow(X5,X2,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X5),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(split_conjunct,[status(thm)],[i_0_634]),
    [final] ).

cnf(i_0_1258,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lab____))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1)),v_e____))) ),
    inference(split_conjunct,[status(thm)],[i_0_627]),
    [final] ).

cnf(i_0_1259,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,X1)))
    | hAPP(v_h____,X1) != v_n____
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1)),v_c____),v_e____))) ),
    inference(split_conjunct,[status(thm)],[i_0_630]),
    [final] ).

cnf(i_0_1260,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi),X1)),c_Arrow__Order__Mirabelle_OProf))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(split_conjunct,[status(thm)],[i_0_655]),
    [final] ).

cnf(i_0_1261,plain,
    ( c_Arrow__Order__Mirabelle_OIIA(X1)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk22_1(X1)),esk23_1(X1))),hAPP(X1,esk20_1(X1))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk22_1(X1)),esk23_1(X1))),hAPP(X1,esk21_1(X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_615]),
    [final] ).

cnf(i_0_1262,plain,
    ( hBOOL(hAPP(hAPP(c_member(X2),hAPP(X3,X6)),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X1,X2,X4,hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X5))))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_656]),
    [final] ).

cnf(i_0_1263,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | hAPP(v_h____,X1) != v_n____
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1)),v_c____),v_e____))) ),
    inference(cn,[status(thm)],[i_0_657]),
    [final] ).

cnf(i_0_1264,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lab____))
    | hAPP(v_h____,X1) = v_n____
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1)),v_e____))) ),
    inference(split_conjunct,[status(thm)],[i_0_627]),
    [final] ).

cnf(i_0_1265,plain,
    ( X1 = X3
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),c_Arrow__Order__Mirabelle_Obelow(X5,X2,X4)))
    | X2 = X4
    | X1 != X2
    | X3 != X4
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X4)),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X5),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(split_conjunct,[status(thm)],[i_0_634]),
    [final] ).

cnf(i_0_1266,plain,
    ( X4 = X2
    | X1 = X4
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X4)),c_Arrow__Order__Mirabelle_Obelow(X5,X2,X3)))
    | X2 = X3
    | X1 != X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X5),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(split_conjunct,[status(thm)],[i_0_634]),
    [final] ).

cnf(i_0_1267,plain,
    ( X2 = X5
    | X1 = X2
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),c_Arrow__Order__Mirabelle_Obelow(X3,X5,X4)))
    | X5 = X4
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3))
    | X2 != X4
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(split_conjunct,[status(thm)],[i_0_634]),
    [final] ).

cnf(i_0_1268,plain,
    ( X1 = X4
    | X2 = X4
    | X1 = X2
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X5)))
    | X4 = X5
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(split_conjunct,[status(thm)],[i_0_634]),
    [final] ).

cnf(i_0_1269,plain,
    ( X3 = X1
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),c_Arrow__Order__Mirabelle_Obelow(X5,X2,X4)))
    | X2 = X4
    | X1 != X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X5),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(split_conjunct,[status(thm)],[i_0_634]),
    [final] ).

cnf(i_0_1270,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1)),v_c____),v_e____)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | hAPP(v_h____,X1) != v_n____
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lba____)) ),
    inference(split_conjunct,[status(thm)],[i_0_627]),
    [final] ).

cnf(i_0_1271,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Set_Oimage(X1,X4,X5,X2)),c_Set_Oimage(X1,X4,X5,X3)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_658]),
    [final] ).

cnf(i_0_1272,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1)),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lab____)) ),
    inference(split_conjunct,[status(thm)],[i_0_627]),
    [final] ).

cnf(i_0_1273,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lba____))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1)),v_e____))) ),
    inference(split_conjunct,[status(thm)],[i_0_627]),
    [final] ).

cnf(i_0_1274,plain,
    ( hAPP(v_h____,X1) = v_n____
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1)),v_e____)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lab____)) ),
    inference(split_conjunct,[status(thm)],[i_0_627]),
    [final] ).

cnf(i_0_1275,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lba____))
    | hAPP(v_h____,X1) = v_n____
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1)),v_e____))) ),
    inference(split_conjunct,[status(thm)],[i_0_627]),
    [final] ).

cnf(i_0_1276,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_Wellfounded_Omlex__prod(X4,X1,X5)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X1,X2)),hAPP(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_659]),
    [final] ).

cnf(i_0_1277,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1)),v_e____)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lba____)) ),
    inference(split_conjunct,[status(thm)],[i_0_627]),
    [final] ).

cnf(i_0_1278,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1)),v_c____),v_e____)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | hAPP(v_h____,X1) != v_n____
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_630]),
    [final] ).

cnf(i_0_1279,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1)),v_c____),v_e____)))
    | hAPP(v_h____,X1) != v_n____
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____)) ),
    inference(cn,[status(thm)],[i_0_660]),
    [final] ).

cnf(i_0_1280,plain,
    ( hAPP(v_h____,X1) = v_n____
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1)),v_e____)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lba____)) ),
    inference(split_conjunct,[status(thm)],[i_0_627]),
    [final] ).

cnf(i_0_1281,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1)),v_e____))) ),
    inference(split_conjunct,[status(thm)],[i_0_630]),
    [final] ).

cnf(i_0_1282,plain,
    ( X1 = hAPP(X2,esk34_4(X1,X2,X3,X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X3),X1),c_Set_Oimage(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))))
    | ~ c_Fun_Oinj__on(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_644]),
    [final] ).

cnf(i_0_1283,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1)),v_e____))) ),
    inference(cn,[status(thm)],[i_0_661]),
    [final] ).

cnf(i_0_1284,plain,
    ( hAPP(v_h____,X1) = v_n____
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,X1)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1)),v_e____))) ),
    inference(split_conjunct,[status(thm)],[i_0_630]),
    [final] ).

cnf(i_0_1285,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),X2)),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1)))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_643]),
    [final] ).

cnf(i_0_1286,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X5)),X3))
    | ~ c_FunDef_Oin__rel(X1,X2,X3,X4,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_662]),
    [final] ).

cnf(i_0_1287,plain,
    ( hAPP(v_h____,X1) = v_n____
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1)),v_e____))) ),
    inference(cn,[status(thm)],[i_0_663]),
    [final] ).

cnf(i_0_1288,plain,
    ( X4 = X5
    | X1 != X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X3),X4),X5)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(split_conjunct,[status(thm)],[i_0_633]),
    [final] ).

cnf(i_0_1289,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1)),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_630]),
    [final] ).

cnf(i_0_1290,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk22_1(X1)),esk23_1(X1))),hAPP(esk21_1(X1),X2)))
    | c_Arrow__Order__Mirabelle_OIIA(X1)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk22_1(X1)),esk23_1(X1))),hAPP(esk20_1(X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_615]),
    [final] ).

cnf(i_0_1291,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk22_1(X1)),esk23_1(X1))),hAPP(esk20_1(X1),X2)))
    | c_Arrow__Order__Mirabelle_OIIA(X1)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk22_1(X1)),esk23_1(X1))),hAPP(esk21_1(X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_615]),
    [final] ).

cnf(i_0_1292,plain,
    ( c_FunDef_Oin__rel(X1,X2,X5,X3,X4)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_662]),
    [final] ).

cnf(i_0_1293,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1)),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____)) ),
    inference(cn,[status(thm)],[i_0_664]),
    [final] ).

cnf(i_0_1294,plain,
    ( hAPP(v_h____,X1) = v_n____
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1)),v_e____)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_630]),
    [final] ).

cnf(i_0_1295,plain,
    ( X3 = esk34_4(X1,X2,X4,X5)
    | X1 != hAPP(X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_member(X4),X1),c_Set_Oimage(X5,X4,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))))
    | ~ c_Fun_Oinj__on(X5,X4,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_644]),
    [final] ).

cnf(i_0_1296,plain,
    ( hAPP(X4,hAPP(c_Hilbert__Choice_Oinv__into(X3,X1,X5,X4),X2)) = X2
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oimage(X3,X1,X4,X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_665]),
    [final] ).

cnf(i_0_1297,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X1)),X3))
    | X1 = X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(split_conjunct,[status(thm)],[i_0_650]),
    [final] ).

cnf(i_0_1298,plain,
    ( hAPP(v_h____,X1) = v_n____
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1)),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____)) ),
    inference(cn,[status(thm)],[i_0_666]),
    [final] ).

cnf(i_0_1299,plain,
    ( X4 = X5
    | X1 != X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X5)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(split_conjunct,[status(thm)],[i_0_634]),
    [final] ).

cnf(i_0_1300,plain,
    ( c_Set_Oimage(X2,X3,X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))
    | hAPP(X1,hAPP(c_Hilbert__Choice_Oinv__into(X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),X1),esk38_3(X1,X3,X2))) != esk38_3(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_667]),
    [final] ).

cnf(i_0_1301,plain,
    ( c_Fun_Oinj__on(X1,X3,c_Hilbert__Choice_Oinv__into(X3,X1,X5,X4),X2)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Set_Oimage(X3,X1,X4,X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_668]),
    [final] ).

cnf(i_0_1302,plain,
    ( X1 = X2
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X4),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_669]),
    [final] ).

cnf(i_0_1303,plain,
    ( X1 = X2
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X4),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_670]),
    [final] ).

cnf(i_0_1304,plain,
    hAPP(c_COMBS(X1,X2,X3,X4,X5),X6) = hAPP(hAPP(X4,X6),hAPP(X5,X6)),
    inference(split_conjunct,[status(thm)],[i_0_671]),
    [final] ).

cnf(i_0_1305,plain,
    ( hBOOL(hAPP(hAPP(c_member(X2),hAPP(X3,X6)),hAPP(X5,X6)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X1,X2,X4,X5)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_672]),
    [final] ).

cnf(i_0_1306,plain,
    ( hBOOL(hAPP(hAPP(c_member(X2),hAPP(X3,X6)),hAPP(X5,X6)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X1,X2,X4,X5)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_673]),
    [final] ).

cnf(i_0_1307,plain,
    ( hBOOL(hAPP(hAPP(c_member(X4),X3),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),c_Set_Oimage(X4,X1,X2,X5)))
    | ~ c_Fun_Oinj__on(X4,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_674]),
    [final] ).

cnf(i_0_1308,plain,
    ( c_Set_Oimage(X1,X2,X3,c_Set_Oimage(X2,X1,c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3),X4)) = X4
    | c_Set_Oimage(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_675]),
    [final] ).

cnf(i_0_1309,plain,
    ( X1 = X2
    | X1 = X4
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_670]),
    [final] ).

cnf(i_0_1310,plain,
    ( X1 = X2
    | X2 = X4
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_669]),
    [final] ).

cnf(i_0_1311,plain,
    ( X1 = X4
    | X2 = X4
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_669]),
    [final] ).

cnf(i_0_1312,plain,
    ( X2 = X4
    | X1 = X4
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_670]),
    [final] ).

cnf(i_0_1313,plain,
    ( c_Set_Oimage(X1,X2,X3,c_Set_Oimage(X2,X1,c_Hilbert__Choice_Oinv__into(X1,X2,X4,X3),X6)) = X6
    | c_Set_Oimage(X1,X2,X3,X4) != X5
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X6),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_676]),
    [final] ).

cnf(i_0_1314,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk13_4(X2,X3,X4,X1)),X2))
    | c_Fun_Oinj__on(X1,X4,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_677]),
    [final] ).

cnf(i_0_1315,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk12_4(X2,X3,X4,X1)),X2))
    | c_Fun_Oinj__on(X1,X4,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_677]),
    [final] ).

cnf(i_0_1316,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk22_1(X1)),esk23_1(X1))),hAPP(X1,esk20_1(X1))))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk22_1(X1)),esk23_1(X1))),hAPP(X1,esk21_1(X1))))
    | c_Arrow__Order__Mirabelle_OIIA(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_615]),
    [final] ).

cnf(i_0_1317,plain,
    ( X1 = X2
    | hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X3),X1),X2)),c_Arrow__Order__Mirabelle_OLin))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(split_conjunct,[status(thm)],[i_0_678]),
    [final] ).

cnf(i_0_1318,plain,
    ( X1 = hAPP(X2,esk36_4(X3,X2,X4,X1))
    | ~ hBOOL(hAPP(hAPP(c_member(X5),X1),c_Set_Oimage(X4,X5,X2,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_649]),
    [final] ).

cnf(i_0_1319,plain,
    ( X3 = X2
    | X3 = X1
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X5),X4),X2)))
    | X4 = X2
    | X1 != X2
    | X3 != X4
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X5),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(split_conjunct,[status(thm)],[i_0_633]),
    [final] ).

cnf(i_0_1320,plain,
    c_Set_Oimage(X1,X2,hAPP(c_COMBB(X3,X2,X1,X4),X5),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = c_Set_Oimage(X3,X2,X4,c_Set_Oimage(X1,X3,X5,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[i_0_679]),
    [final] ).

cnf(i_0_1321,plain,
    ( c_Fun_Oinj__on(X1,X1,X3,X2)
    | ~ c_Finite__Set_Ofinite(X1,X2)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Set_Oimage(X1,X1,X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_680]),
    [final] ).

cnf(i_0_1322,plain,
    ( hAPP(X1,X3) = hAPP(X3,X2)
    | ~ c_Arrow__Order__Mirabelle_Odictator(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf)) ),
    inference(split_conjunct,[status(thm)],[i_0_681]),
    [final] ).

cnf(i_0_1323,plain,
    ( X3 = X2
    | X1 = X3
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),c_Arrow__Order__Mirabelle_Obelow(X5,X2,X4)))
    | X2 = X4
    | X1 != X2
    | X3 != X4
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X5),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(split_conjunct,[status(thm)],[i_0_634]),
    [final] ).

cnf(i_0_1324,plain,
    ( c_Fun_Oinj__on(X1,tc_fun(X4,X2),hAPP(c_COMBB(X2,tc_fun(X4,X2),X1,c_COMBK(X2,X4)),X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_682]),
    [final] ).

cnf(i_0_1325,plain,
    hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X1)),c_COMBI(X1)),c_FuncSet_OPi(X1,X1,X2,hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X2)))),
    inference(split_conjunct,[status(thm)],[i_0_683]),
    [final] ).

cnf(i_0_1326,plain,
    c_Set_Oimage(X1,X2,X3,c_Set_Oimage(X4,X1,X5,X6)) = c_Set_Oimage(X4,X2,hAPP(c_COMBB(X1,X2,X4,X3),X5),X6),
    inference(split_conjunct,[status(thm)],[i_0_684]),
    [final] ).

cnf(i_0_1327,plain,
    ( X1 = X2
    | hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)),c_Arrow__Order__Mirabelle_OLin))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(split_conjunct,[status(thm)],[i_0_685]),
    [final] ).

cnf(i_0_1328,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X4,X2)),hAPP(X4,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Wellfounded_Omeasure(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_686]),
    [final] ).

cnf(i_0_1329,plain,
    ( c_Set_Oimage(X2,X1,c_Hilbert__Choice_Oinv__into(X1,X2,X4,X3),c_Set_Oimage(X1,X2,X3,X5)) = X5
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X5),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_687]),
    [final] ).

cnf(i_0_1330,plain,
    ( c_Finite__Set_Ofinite(X3,X4)
    | ~ c_Finite__Set_Ofinite(X1,X2)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X4),c_Set_Oimage(X1,X3,X5,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_688]),
    [final] ).

cnf(i_0_1331,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1),X2)),c_Arrow__Order__Mirabelle_OLin))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(split_conjunct,[status(thm)],[i_0_689]),
    [final] ).

cnf(i_0_1332,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1),X2)),c_Arrow__Order__Mirabelle_OLin))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(split_conjunct,[status(thm)],[i_0_690]),
    [final] ).

cnf(i_0_1333,plain,
    ( hBOOL(hAPP(hAPP(c_member(X4),hAPP(X5,X2)),c_Set_Oimage(X1,X4,X5,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ c_Fun_Oinj__on(X1,X4,X5,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_674]),
    [final] ).

cnf(i_0_1334,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X4),c_Set_Oimage(X1,X5,X6,X3)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
    | X4 != c_Set_Oimage(X1,X5,X6,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_621]),
    [final] ).

cnf(i_0_1335,plain,
    ( c_Set_Oimage(X2,X1,c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3),c_Set_Oimage(X1,X2,X3,X4)) = X4
    | ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_691]),
    [final] ).

cnf(i_0_1336,plain,
    ( c_Set_Oimage(X2,X1,c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3),c_Set_Oimage(X1,X2,X3,X4)) = X4
    | ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_692]),
    [final] ).

cnf(i_0_1337,plain,
    ( c_Arrow__Order__Mirabelle_Ounanimity(X1)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk26_1(X1)),esk27_1(X1))),hAPP(X1,esk25_1(X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_626]),
    [final] ).

cnf(i_0_1338,plain,
    ( hAPP(X3,hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3),X4)) = X4
    | c_Set_Oimage(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_667]),
    [final] ).

cnf(i_0_1339,plain,
    ( hAPP(X3,hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3),X4)) = X4
    | c_Set_Oimage(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_693]),
    [final] ).

cnf(i_0_1340,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_Wellfounded_Omlex__prod(X4,X1,X5)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1,X2)),hAPP(X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_694]),
    [final] ).

cnf(i_0_1341,plain,
    ( X1 != X2
    | X1 != X3
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X4),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_669]),
    [final] ).

cnf(i_0_1342,plain,
    ( X1 != X2
    | X3 != X1
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X4),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_670]),
    [final] ).

cnf(i_0_1343,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X4),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_670]),
    [final] ).

cnf(i_0_1344,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X4),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_669]),
    [final] ).

cnf(i_0_1345,plain,
    ( X1 = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),c_Finite__Set_Ocard(tc_Nat_Onat,X1)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool),X1),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),c_Finite__Set_Ocard(tc_Nat_Onat,X1))))) ),
    inference(split_conjunct,[status(thm)],[i_0_695]),
    [final] ).

cnf(i_0_1346,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_Wellfounded_Omeasure(X4,X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1,X2)),hAPP(X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_686]),
    [final] ).

cnf(i_0_1347,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(X1,X4,X2)),c_SetInterval_Oord__class_OatLeastLessThan(X1,X5,X3)))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_696]),
    [final] ).

cnf(i_0_1348,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(X1,X3,X4)),c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X5)))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_696]),
    [final] ).

cnf(i_0_1349,plain,
    ( c_Fun_Oinj__on(X2,X1,c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))
    | c_Set_Oimage(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_697]),
    [final] ).

cnf(i_0_1350,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk17_2(X1,X2)),c_Arrow__Order__Mirabelle_OProf))
    | c_Arrow__Order__Mirabelle_Odictator(X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_681]),
    [final] ).

cnf(i_0_1351,plain,
    hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),c_Set_Oimage(X4,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))),
    inference(split_conjunct,[status(thm)],[i_0_698]),
    [final] ).

cnf(i_0_1352,plain,
    ( c_Set_Oimage(X2,X1,c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))
    | ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_699]),
    [final] ).

cnf(i_0_1353,plain,
    ( hBOOL(hAPP(hAPP(c_member(X4),hAPP(X5,X2)),c_Set_Oimage(X1,X4,X5,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_700]),
    [final] ).

cnf(i_0_1354,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____)),
    inference(split_conjunct,[status(thm)],[i_0_701]),
    [final] ).

cnf(i_0_1355,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lba____)),
    inference(split_conjunct,[status(thm)],[i_0_702]),
    [final] ).

cnf(i_0_1356,plain,
    ( hBOOL(hAPP(hAPP(c_member(X4),X1),c_Set_Oimage(X5,X4,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))))
    | X1 != hAPP(X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_703]),
    [final] ).

cnf(i_0_1357,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk25_1(X1)),c_Arrow__Order__Mirabelle_OProf))
    | c_Arrow__Order__Mirabelle_Ounanimity(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_626]),
    [final] ).

cnf(i_0_1358,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk21_1(X1)),c_Arrow__Order__Mirabelle_OProf))
    | c_Arrow__Order__Mirabelle_OIIA(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_615]),
    [final] ).

cnf(i_0_1359,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk20_1(X1)),c_Arrow__Order__Mirabelle_OProf))
    | c_Arrow__Order__Mirabelle_OIIA(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_615]),
    [final] ).

cnf(i_0_1360,plain,
    ( hBOOL(hAPP(hAPP(c_member(X6),X1),c_Set_Oimage(X4,X6,X2,X5)))
    | X1 != hAPP(X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_member(X4),X3),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_704]),
    [final] ).

cnf(i_0_1361,plain,
    ( hBOOL(hAPP(hAPP(c_member(X6),X4),c_Set_Oimage(X1,X6,X5,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | X4 != hAPP(X5,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_705]),
    [final] ).

cnf(i_0_1362,plain,
    ( hBOOL(hAPP(hAPP(c_member(X6),X4),c_Set_Oimage(X1,X6,X5,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | X4 != hAPP(X5,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_649]),
    [final] ).

cnf(i_0_1363,plain,
    hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_P____),c_Arrow__Order__Mirabelle_OProf)),
    inference(split_conjunct,[status(thm)],[fact__096P_A_058_AProf_096]),
    [final] ).

cnf(i_0_1364,plain,
    ( hAPP(X1,esk12_4(X2,X1,X3,X4)) = hAPP(X1,esk13_4(X2,X1,X3,X4))
    | c_Fun_Oinj__on(X4,X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_677]),
    [final] ).

cnf(i_0_1365,plain,
    ( X4 = X5
    | c_Set_Oimage(X1,X2,X3,X4) != c_Set_Oimage(X1,X2,X3,X5)
    | ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_706]),
    [final] ).

cnf(i_0_1366,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_707]),
    [final] ).

cnf(i_0_1367,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_708]),
    [final] ).

cnf(i_0_1368,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_709]),
    [final] ).

cnf(i_0_1369,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_710]),
    [final] ).

cnf(i_0_1370,plain,
    ( c_Finite__Set_Ofinite(X2,X4)
    | ~ c_Finite__Set_Ofinite(X1,c_Set_Oimage(X2,X1,X3,X4))
    | ~ c_Fun_Oinj__on(X2,X1,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_711]),
    [final] ).

cnf(i_0_1371,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_712]),
    [final] ).

cnf(i_0_1372,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_713]),
    [final] ).

cnf(i_0_1373,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_714]),
    [final] ).

cnf(i_0_1374,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_715]),
    [final] ).

cnf(i_0_1375,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_716]),
    [final] ).

cnf(i_0_1376,plain,
    ( c_Fun_Oinj__on(X1,X2,esk40_4(X3,X2,X4,X1),X4)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X1,X4)),c_Finite__Set_Ocard(X2,X3)))
    | ~ c_Finite__Set_Ofinite(X2,X3)
    | ~ c_Finite__Set_Ofinite(X1,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_632]),
    [final] ).

cnf(i_0_1377,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk26_1(X1)),esk27_1(X1))),hAPP(esk25_1(X1),X2)))
    | c_Arrow__Order__Mirabelle_Ounanimity(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_626]),
    [final] ).

cnf(i_0_1378,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1,X4,X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_717]),
    [final] ).

cnf(i_0_1379,plain,
    ( hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(X3,X4)) = X4
    | ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_718]),
    [final] ).

cnf(i_0_1380,plain,
    ( hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3),X5) = X4
    | ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
    | hAPP(X3,X4) != X5 ),
    inference(split_conjunct,[status(thm)],[i_0_719]),
    [final] ).

cnf(i_0_1381,plain,
    ( X2 = X3
    | hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2) != hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_720]),
    [final] ).

cnf(i_0_1382,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_721]),
    [final] ).

cnf(i_0_1383,plain,
    ( hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X4,X3),hAPP(X3,X5)) = X5
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_722]),
    [final] ).

cnf(i_0_1384,plain,
    ( hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X4,X3),X6) = X5
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X4))
    | hAPP(X3,X5) != X6 ),
    inference(split_conjunct,[status(thm)],[i_0_723]),
    [final] ).

cnf(i_0_1385,plain,
    ( c_Fun_Oinj__on(X1,X3,X4,X2)
    | ~ c_Finite__Set_Ofinite(X1,X2)
    | c_Finite__Set_Ocard(X3,c_Set_Oimage(X1,X3,X4,X2)) != c_Finite__Set_Ocard(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_724]),
    [final] ).

cnf(i_0_1386,plain,
    ( c_Fun_Oinj__on(X2,X1,X3,X4)
    | c_Finite__Set_Ocard(X1,c_Set_Oimage(X2,X1,X3,X4)) != c_Finite__Set_Ocard(X2,X4)
    | ~ c_Finite__Set_Ofinite(X2,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_725]),
    [final] ).

cnf(i_0_1387,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1,X4,X2)),c_Set_Oinsert(X1,X4,X3)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_726]),
    [final] ).

cnf(i_0_1388,plain,
    hAPP(hAPP(c_COMBB(X1,X2,X3,X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
    inference(split_conjunct,[status(thm)],[i_0_727]),
    [final] ).

cnf(i_0_1389,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X5)))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_728]),
    [final] ).

cnf(i_0_1390,plain,
    c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X1),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2,X3)) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),
    inference(split_conjunct,[status(thm)],[i_0_729]),
    [final] ).

cnf(i_0_1391,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1,X2,X4)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_717]),
    [final] ).

cnf(i_0_1392,plain,
    ( X1 = X3
    | X3 = X2
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X4),X2)))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_669]),
    [final] ).

cnf(i_0_1393,plain,
    ( X3 = X1
    | X3 = X2
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X4),X2)))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_670]),
    [final] ).

cnf(i_0_1394,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_730]),
    [final] ).

cnf(i_0_1395,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1,X2,X4)),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_717]),
    [final] ).

cnf(i_0_1396,plain,
    ( c_Fun_Oinj__on(X4,X3,X2,X1)
    | esk12_4(X1,X2,X3,X4) != esk13_4(X1,X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_677]),
    [final] ).

cnf(i_0_1397,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X5)))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_731]),
    [final] ).

cnf(i_0_1398,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X5)))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_732]),
    [final] ).

cnf(i_0_1399,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X4))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_733]),
    [final] ).

cnf(i_0_1400,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_734]),
    [final] ).

cnf(i_0_1401,plain,
    c_Arrow__Order__Mirabelle_OProf = c_FuncSet_OPi(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)),hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_OLin)),
    inference(split_conjunct,[status(thm)],[fact_Prof__def]),
    [final] ).

cnf(i_0_1402,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2))
    | ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_735]),
    [final] ).

cnf(i_0_1403,plain,
    ( c_Set_Oinsert(X4,hAPP(X5,X2),c_Set_Oimage(X1,X4,X5,X3)) = c_Set_Oimage(X1,X4,X5,X3)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_736]),
    [final] ).

cnf(i_0_1404,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X3),X2))
    | ~ c_Finite__Set_Ofinite(X1,X2)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X1,X3)),c_Finite__Set_Ocard(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_737]),
    [final] ).

cnf(i_0_1405,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X5)))
    | ~ class_Groups_Oordered__ab__semigroup__add(X1)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_738]),
    [final] ).

cnf(i_0_1406,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_739]),
    [final] ).

cnf(i_0_1407,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_740]),
    [final] ).

cnf(i_0_1408,plain,
    ( c_Finite__Set_Ocard(X2,c_Set_Oimage(X1,X2,X3,X4)) = c_Finite__Set_Ocard(X1,X4)
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ c_Finite__Set_Ofinite(X1,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_725]),
    [final] ).

cnf(i_0_1409,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_741]),
    [final] ).

cnf(i_0_1410,plain,
    c_Set_Oimage(X1,X2,X3,c_Set_Oinsert(X1,X4,X5)) = c_Set_Oinsert(X2,hAPP(X3,X4),c_Set_Oimage(X1,X2,X3,X5)),
    inference(split_conjunct,[status(thm)],[i_0_742]),
    [final] ).

cnf(i_0_1411,plain,
    ( c_Fun_Oinj__on(X1,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
    | ~ c_Finite__Set_Ofinite(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
    | c_Set_Oimage(X1,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_743]),
    [final] ).

cnf(i_0_1412,plain,
    ( c_Fun_Oinj__on(X1,X2,X3,X5)
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X5),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_744]),
    [final] ).

cnf(i_0_1413,plain,
    ( c_Finite__Set_Ocard(X2,c_Set_Oimage(X1,X2,X3,X4)) = c_Finite__Set_Ocard(X1,X4)
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_745]),
    [final] ).

cnf(i_0_1414,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_746]),
    [final] ).

cnf(i_0_1415,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Int_Oring__1__class_OInts(X1)))
    | ~ class_Rings_Oring__1(X1)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),c_Int_Oring__1__class_OInts(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_747]),
    [final] ).

cnf(i_0_1416,plain,
    ( c_Set_Oimage(X1,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))
    | ~ c_Finite__Set_Ofinite(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(X1,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_748]),
    [final] ).

cnf(i_0_1417,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_708]),
    [final] ).

cnf(i_0_1418,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_749]),
    [final] ).

cnf(i_0_1419,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_710]),
    [final] ).

cnf(i_0_1420,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_750]),
    [final] ).

cnf(i_0_1421,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_751]),
    [final] ).

cnf(i_0_1422,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X4))
    | hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Set_Oinsert(X1,X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_752]),
    [final] ).

cnf(i_0_1423,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_753]),
    [final] ).

cnf(i_0_1424,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_754]),
    [final] ).

cnf(i_0_1425,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_755]),
    [final] ).

cnf(i_0_1426,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),esk11_0)),
    inference(split_conjunct,[status(thm)],[i_0_756]),
    [final] ).

cnf(i_0_1427,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____)),
    inference(split_conjunct,[status(thm)],[fact__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096]),
    [final] ).

cnf(i_0_1428,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),esk10_0)),
    inference(split_conjunct,[status(thm)],[i_0_757]),
    [final] ).

cnf(i_0_1429,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lab____)),
    inference(split_conjunct,[status(thm)],[fact__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096]),
    [final] ).

cnf(i_0_1430,plain,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Finite__Set_Ofinite(tc_sum(X1,X3),c_Sum__Type_OPlus(X1,X3,X2,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_758]),
    [final] ).

cnf(i_0_1431,plain,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Finite__Set_Ofinite(tc_sum(X3,X1),c_Sum__Type_OPlus(X3,X1,X4,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_758]),
    [final] ).

cnf(i_0_1432,plain,
    ( c_Finite__Set_Ofinite(X1,X3)
    | ~ c_Finite__Set_Ofinite(tc_sum(X1,X2),c_Sum__Type_OPlus(X1,X2,X3,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_759]),
    [final] ).

cnf(i_0_1433,plain,
    ( c_Finite__Set_Ofinite(X2,X4)
    | ~ c_Finite__Set_Ofinite(tc_sum(X1,X2),c_Sum__Type_OPlus(X1,X2,X3,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_760]),
    [final] ).

cnf(i_0_1434,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
    | ~ class_Groups_Oordered__ab__semigroup__add(X1)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_761]),
    [final] ).

cnf(i_0_1435,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_713]),
    [final] ).

cnf(i_0_1436,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
    | ~ class_Groups_Oordered__ab__semigroup__add(X1)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_762]),
    [final] ).

cnf(i_0_1437,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_715]),
    [final] ).

cnf(i_0_1438,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_763]),
    [final] ).

cnf(i_0_1439,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_764]),
    [final] ).

cnf(i_0_1440,plain,
    ( hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_735]),
    [final] ).

cnf(i_0_1441,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2),X4),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,X2)),X3),X4))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2),X3),X4))
    | ~ class_Orderings_Oord(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_765]),
    [final] ).

cnf(i_0_1442,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,X2)),X4),X3))
    | ~ class_Orderings_Oord(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_765]),
    [final] ).

cnf(i_0_1443,plain,
    ( hBOOL(hAPP(hAPP(X4,X5),X6))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4))
    | ~ hBOOL(hAPP(hAPP(X3,X5),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_766]),
    [final] ).

cnf(i_0_1444,plain,
    ( hBOOL(hAPP(hAPP(X6,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_fun(X5,tc_HOL_Obool)),X1),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_767]),
    [final] ).

cnf(i_0_1445,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_768]),
    [final] ).

cnf(i_0_1446,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_721]),
    [final] ).

cnf(i_0_1447,plain,
    ( X2 = X3
    | hAPP(X1,X2) != hAPP(X1,X3)
    | ~ hBOOL(hAPP(hAPP(c_member(X4),X3),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(X4),X2),X5))
    | ~ c_Fun_Oinj__on(X4,X6,X1,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_769]),
    [final] ).

cnf(i_0_1448,plain,
    ( X5 = X6
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X4))
    | hAPP(X3,X5) != hAPP(X3,X6) ),
    inference(split_conjunct,[status(thm)],[i_0_770]),
    [final] ).

cnf(i_0_1449,plain,
    ( X5 = X6
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | hAPP(X3,X5) != hAPP(X3,X6)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_771]),
    [final] ).

cnf(i_0_1450,plain,
    ( X5 = X6
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X4))
    | hAPP(X3,X5) != hAPP(X3,X6) ),
    inference(split_conjunct,[status(thm)],[i_0_677]),
    [final] ).

cnf(i_0_1451,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Set_Oinsert(X1,X4,X3)))
    | hBOOL(hAPP(hAPP(c_member(X1),X4),X2))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_752]),
    [final] ).

cnf(i_0_1452,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_772]),
    [final] ).

cnf(i_0_1453,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_772]),
    [final] ).

cnf(i_0_1454,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_773]),
    [final] ).

cnf(i_0_1455,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_774]),
    [final] ).

cnf(i_0_1456,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)))
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_775]),
    [final] ).

cnf(i_0_1457,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk46_2(X1,X2)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)))
    | ~ hBOOL(hAPP(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_776]),
    [final] ).

cnf(i_0_1458,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_777]),
    [final] ).

cnf(i_0_1459,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_730]),
    [final] ).

cnf(i_0_1460,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_778]),
    [final] ).

cnf(i_0_1461,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X1,X3)),c_Finite__Set_Ocard(X1,X2)))
    | ~ c_Finite__Set_Ofinite(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_779]),
    [final] ).

cnf(i_0_1462,plain,
    c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X1),X2),
    inference(split_conjunct,[status(thm)],[i_0_780]),
    [final] ).

cnf(i_0_1463,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X5))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_781]),
    [final] ).

cnf(i_0_1464,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_739]),
    [final] ).

cnf(i_0_1465,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_740]),
    [final] ).

cnf(i_0_1466,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X4))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_782]),
    [final] ).

cnf(i_0_1467,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)))
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_783]),
    [final] ).

cnf(i_0_1468,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)))
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_784]),
    [final] ).

cnf(i_0_1469,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X1)),
    inference(split_conjunct,[status(thm)],[i_0_785]),
    [final] ).

cnf(i_0_1470,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X2)),
    inference(split_conjunct,[status(thm)],[i_0_786]),
    [final] ).

cnf(i_0_1471,plain,
    ( c_Finite__Set_Ocard(tc_sum(X1,X3),c_Sum__Type_OPlus(X1,X3,X2,X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Finite__Set_Ocard(X1,X2)),c_Finite__Set_Ocard(X3,X4))
    | ~ c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Finite__Set_Ofinite(X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_787]),
    [final] ).

cnf(i_0_1472,plain,
    ( c_Finite__Set_Ocard(tc_sum(X1,X3),c_Sum__Type_OPlus(X1,X3,X2,X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Finite__Set_Ocard(X1,X2)),c_Finite__Set_Ocard(X3,X4))
    | ~ c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Finite__Set_Ofinite(X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_788]),
    [final] ).

cnf(i_0_1473,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_789]),
    [final] ).

cnf(i_0_1474,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,X2)),X3),X4))
    | ~ class_Orderings_Oord(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_765]),
    [final] ).

cnf(i_0_1475,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X1,X2)),c_Finite__Set_Ocard(X1,c_Set_Oinsert(X1,X3,X2))))
    | ~ c_Finite__Set_Ofinite(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_790]),
    [final] ).

cnf(i_0_1476,plain,
    ( ~ class_Int_Oring__char__0(X1)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1)))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),X2)),X2) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_791]),
    [final] ).

cnf(i_0_1477,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)))
    | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_792]),
    [final] ).

cnf(i_0_1478,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_793]),
    [final] ).

cnf(i_0_1479,plain,
    ( X3 = X2
    | ~ c_Finite__Set_Ofinite(X1,X2)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3),X2))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X1,X2)),c_Finite__Set_Ocard(X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_794]),
    [final] ).

cnf(i_0_1480,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Set_Oinsert(X1,X4,X3)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_795]),
    [final] ).

cnf(i_0_1481,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_751]),
    [final] ).

cnf(i_0_1482,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_796]),
    [final] ).

cnf(i_0_1483,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_797]),
    [final] ).

cnf(i_0_1484,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)))
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_798]),
    [final] ).

cnf(i_0_1485,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_799]),
    [final] ).

cnf(i_0_1486,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_800]),
    [final] ).

cnf(i_0_1487,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_801]),
    [final] ).

cnf(i_0_1488,plain,
    ( hBOOL(hAPP(X1,esk46_2(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)))
    | ~ hBOOL(hAPP(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_776]),
    [final] ).

cnf(i_0_1489,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk45_2(X1,X2)),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2))
    | ~ hBOOL(hAPP(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_776]),
    [final] ).

cnf(i_0_1490,plain,
    ( X2 = X3
    | hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_802]),
    [final] ).

cnf(i_0_1491,plain,
    ( X2 = X3
    | hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_803]),
    [final] ).

cnf(i_0_1492,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)))
    | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_804]),
    [final] ).

cnf(i_0_1493,plain,
    c_FuncSet_OPi(X1,X2,X3,hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X1,X2),tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_805]),
    [final] ).

cnf(i_0_1494,plain,
    hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),esk11_0),c_Arrow__Order__Mirabelle_OLin)),
    inference(split_conjunct,[status(thm)],[i_0_756]),
    [final] ).

cnf(i_0_1495,plain,
    hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),esk10_0),c_Arrow__Order__Mirabelle_OLin)),
    inference(split_conjunct,[status(thm)],[i_0_757]),
    [final] ).

cnf(i_0_1496,plain,
    hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_Lba____),c_Arrow__Order__Mirabelle_OLin)),
    inference(split_conjunct,[status(thm)],[fact__096Lba_A_058_ALin_096]),
    [final] ).

cnf(i_0_1497,plain,
    hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_Lab____),c_Arrow__Order__Mirabelle_OLin)),
    inference(split_conjunct,[status(thm)],[fact__096Lab_A_058_ALin_096]),
    [final] ).

cnf(i_0_1498,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_806]),
    [final] ).

cnf(i_0_1499,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2)))
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_807]),
    [final] ).

cnf(i_0_1500,plain,
    ( c_Finite__Set_Ofinite(tc_sum(X1,X3),c_Sum__Type_OPlus(X1,X3,X2,X4))
    | ~ c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Finite__Set_Ofinite(X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_758]),
    [final] ).

cnf(i_0_1501,plain,
    ( c_Finite__Set_Ofinite(tc_sum(X1,X3),c_Sum__Type_OPlus(X1,X3,X2,X4))
    | ~ c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Finite__Set_Ofinite(X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_808]),
    [final] ).

cnf(i_0_1502,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | X2 = X3
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_800]),
    [final] ).

cnf(i_0_1503,plain,
    ( X2 = X3
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_801]),
    [final] ).

cnf(i_0_1504,plain,
    hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
    inference(split_conjunct,[status(thm)],[i_0_809]),
    [final] ).

cnf(i_0_1505,plain,
    ( c_Finite__Set_Ofinite(X1,X2)
    | c_Finite__Set_Ocard(tc_sum(X1,X3),c_Sum__Type_OPlus(X1,X3,X2,X4)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_787]),
    [final] ).

cnf(i_0_1506,plain,
    ( c_Finite__Set_Ofinite(X1,X2)
    | c_Finite__Set_Ocard(tc_sum(X3,X1),c_Sum__Type_OPlus(X3,X1,X4,X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_787]),
    [final] ).

cnf(i_0_1507,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_792]),
    [final] ).

cnf(i_0_1508,plain,
    ( X2 = X3
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_810]),
    [final] ).

cnf(i_0_1509,plain,
    ( X2 = X3
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_811]),
    [final] ).

cnf(i_0_1510,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_812]),
    [final] ).

cnf(i_0_1511,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_813]),
    [final] ).

cnf(i_0_1512,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_814]),
    [final] ).

cnf(i_0_1513,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_815]),
    [final] ).

cnf(i_0_1514,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X3,X5)),hAPP(X4,X5)))
    | ~ class_Orderings_Oord(X1)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_816]),
    [final] ).

cnf(i_0_1515,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X3,X5)),hAPP(X4,X5)))
    | ~ class_Orderings_Oord(X1)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_817]),
    [final] ).

cnf(i_0_1516,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,hAPP(X3,X5)),hAPP(X4,X5)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2),X3),X4))
    | ~ class_Orderings_Oord(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_623]),
    [final] ).

cnf(i_0_1517,plain,
    ( c_Finite__Set_Ofinite(X3,c_Set_Oimage(X1,X3,X4,X2))
    | ~ c_Finite__Set_Ofinite(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_818]),
    [final] ).

cnf(i_0_1518,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X1,X3)),c_Finite__Set_Ocard(X1,X2)))
    | ~ c_Finite__Set_Ofinite(X1,X2)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_819]),
    [final] ).

cnf(i_0_1519,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),X3)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_820]),
    [final] ).

cnf(i_0_1520,plain,
    ( X2 = X3
    | hAPP(X1,X2) != hAPP(X1,X3)
    | ~ c_Fun_Oinj__on(X4,X5,X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_821]),
    [final] ).

cnf(i_0_1521,plain,
    ( X4 = X5
    | ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
    | hAPP(X3,X4) != hAPP(X3,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_822]),
    [final] ).

cnf(i_0_1522,plain,
    ( X1 = X2
    | c_SetInterval_Oord__class_OatLeastLessThan(X3,X1,X4) != c_SetInterval_Oord__class_OatLeastLessThan(X3,X2,X5)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),X5))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),X4))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_823]),
    [final] ).

cnf(i_0_1523,plain,
    ( X1 = X2
    | c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1) != c_SetInterval_Oord__class_OatLeastLessThan(X3,X5,X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X5),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X4),X1))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_823]),
    [final] ).

cnf(i_0_1524,plain,
    ( X2 = X4
    | ~ class_Orderings_Olinorder(X1)
    | c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X3) != c_SetInterval_Oord__class_OatLeastLessThan(X1,X4,X5)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_824]),
    [final] ).

cnf(i_0_1525,plain,
    ( X3 = X5
    | ~ class_Orderings_Olinorder(X1)
    | c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X3) != c_SetInterval_Oord__class_OatLeastLessThan(X1,X4,X5)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_825]),
    [final] ).

cnf(i_0_1526,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk33_2(X2,X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_826]),
    [final] ).

cnf(i_0_1527,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))),
    inference(split_conjunct,[status(thm)],[i_0_827]),
    [final] ).

cnf(i_0_1528,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)))),
    inference(split_conjunct,[status(thm)],[i_0_828]),
    [final] ).

cnf(i_0_1529,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X4,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_802]),
    [final] ).

cnf(i_0_1530,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X4,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_829]),
    [final] ).

cnf(i_0_1531,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X4,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_830]),
    [final] ).

cnf(i_0_1532,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_804]),
    [final] ).

cnf(i_0_1533,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_831]),
    [final] ).

cnf(i_0_1534,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Finite__Set_Ocard(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))))
    | ~ c_Finite__Set_Ofinite(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_832]),
    [final] ).

cnf(i_0_1535,plain,
    c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,esk39_0,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[i_0_833]),
    [final] ).

cnf(i_0_1536,plain,
    c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,v_h____,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[fact_surjh]),
    [final] ).

cnf(i_0_1537,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool)),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_801]),
    [final] ).

cnf(i_0_1538,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_834]),
    [final] ).

cnf(i_0_1539,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_835]),
    [final] ).

cnf(i_0_1540,plain,
    ( c_Finite__Set_Ocard(X2,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | c_Finite__Set_Ofinite(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
    | ~ c_Finite__Set_Ofinite(tc_fun(X1,X2),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X1,X2),tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_836]),
    [final] ).

cnf(i_0_1541,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_793]),
    [final] ).

cnf(i_0_1542,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_793]),
    [final] ).

cnf(i_0_1543,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))
    | ~ class_Orderings_Opreorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_837]),
    [final] ).

cnf(i_0_1544,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X3))
    | ~ class_Orderings_Oorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_838]),
    [final] ).

cnf(i_0_1545,plain,
    c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1,X2)) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X2)),
    inference(split_conjunct,[status(thm)],[i_0_839]),
    [final] ).

cnf(i_0_1546,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X3) != c_Groups_Ozero__class_Ozero(X2)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2)),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2)),X1))
    | ~ class_Groups_Oordered__comm__monoid__add(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_840]),
    [final] ).

cnf(i_0_1547,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X3),X1) != c_Groups_Ozero__class_Ozero(X2)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2)),X1))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2)),X3))
    | ~ class_Groups_Oordered__comm__monoid__add(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_840]),
    [final] ).

cnf(i_0_1548,plain,
    c_Sum__Type_OPlus(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X1,X2),tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_841]),
    [final] ).

cnf(i_0_1549,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_842]),
    [final] ).

cnf(i_0_1550,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_843]),
    [final] ).

cnf(i_0_1551,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_844]),
    [final] ).

cnf(i_0_1552,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_845]),
    [final] ).

cnf(i_0_1553,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk31_2(X1,X2)),X1))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_846]),
    [final] ).

cnf(i_0_1554,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_847]),
    [final] ).

cnf(i_0_1555,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))
    | ~ class_Groups_Oab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_848]),
    [final] ).

cnf(i_0_1556,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_849]),
    [final] ).

cnf(i_0_1557,plain,
    ( X2 = X4
    | hBOOL(hAPP(X3,X4))
    | ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_850]),
    [final] ).

cnf(i_0_1558,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X3) = c_Groups_Ozero__class_Ozero(X2)
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | X3 != c_Groups_Ozero__class_Ozero(X2)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2)),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2)),X1))
    | ~ class_Groups_Oordered__comm__monoid__add(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_840]),
    [final] ).

cnf(i_0_1559,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_851]),
    [final] ).

cnf(i_0_1560,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_852]),
    [final] ).

cnf(i_0_1561,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))
    | ~ class_Orderings_Opreorder(X1)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_853]),
    [final] ).

cnf(i_0_1562,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))
    | ~ class_Orderings_Opreorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_854]),
    [final] ).

cnf(i_0_1563,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X3))
    | ~ class_Orderings_Oorder(X1)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_855]),
    [final] ).

cnf(i_0_1564,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X3))
    | ~ class_Orderings_Oorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_856]),
    [final] ).

cnf(i_0_1565,plain,
    ( c_Finite__Set_Ofinite(tc_sum(X1,X2),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X1,X2),tc_HOL_Obool)))
    | ~ c_Finite__Set_Ofinite(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
    | ~ c_Finite__Set_Ofinite(X2,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_857]),
    [final] ).

cnf(i_0_1566,plain,
    ( c_Finite__Set_Ofinite(tc_prod(X1,X2),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)))
    | ~ c_Finite__Set_Ofinite(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
    | ~ c_Finite__Set_Ofinite(X2,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_858]),
    [final] ).

cnf(i_0_1567,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_859]),
    [final] ).

cnf(i_0_1568,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Set_Oinsert(X1,X3,X2))),
    inference(split_conjunct,[status(thm)],[i_0_860]),
    [final] ).

cnf(i_0_1569,plain,
    ( X3 = X4
    | hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
    | hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | c_Set_Oinsert(X1,X2,X3) != c_Set_Oinsert(X1,X2,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_861]),
    [final] ).

cnf(i_0_1570,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_862]),
    [final] ).

cnf(i_0_1571,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_863]),
    [final] ).

cnf(i_0_1572,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_834]),
    [final] ).

cnf(i_0_1573,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_864]),
    [final] ).

cnf(i_0_1574,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_865]),
    [final] ).

cnf(i_0_1575,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_866]),
    [final] ).

cnf(i_0_1576,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_867]),
    [final] ).

cnf(i_0_1577,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_868]),
    [final] ).

cnf(i_0_1578,plain,
    ( c_Finite__Set_Ofinite(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
    | ~ c_Finite__Set_Ofinite(tc_sum(X1,X2),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X1,X2),tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_857]),
    [final] ).

cnf(i_0_1579,plain,
    ( c_Finite__Set_Ofinite(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
    | ~ c_Finite__Set_Ofinite(tc_sum(X2,X1),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X2,X1),tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_857]),
    [final] ).

cnf(i_0_1580,plain,
    ( c_Finite__Set_Ofinite(X2,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))
    | ~ c_Finite__Set_Ofinite(tc_fun(X1,X2),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X1,X2),tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_869]),
    [final] ).

cnf(i_0_1581,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_870]),
    [final] ).

cnf(i_0_1582,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),
    inference(split_conjunct,[status(thm)],[i_0_871]),
    [final] ).

cnf(i_0_1583,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_872]),
    [final] ).

cnf(i_0_1584,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_873]),
    [final] ).

cnf(i_0_1585,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_874]),
    [final] ).

cnf(i_0_1586,plain,
    ( hBOOL(hAPP(X3,X4))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
    | ~ hBOOL(hAPP(X2,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_875]),
    [final] ).

cnf(i_0_1587,plain,
    ( hBOOL(hAPP(X4,X2))
    | ~ hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_876]),
    [final] ).

cnf(i_0_1588,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
    | ~ class_Orderings_Opreorder(X1)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_877]),
    [final] ).

cnf(i_0_1589,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
    | ~ class_Orderings_Oorder(X1)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_878]),
    [final] ).

cnf(i_0_1590,plain,
    ( hAPP(c_Nat_OSuc,X1) = X2
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_879]),
    [final] ).

cnf(i_0_1591,plain,
    ( ~ class_Orderings_Oorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_880]),
    [final] ).

cnf(i_0_1592,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_881]),
    [final] ).

cnf(i_0_1593,plain,
    ( ~ class_Orderings_Opreorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_882]),
    [final] ).

cnf(i_0_1594,plain,
    ( ~ class_Orderings_Opreorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_883]),
    [final] ).

cnf(i_0_1595,plain,
    ( ~ class_Orderings_Opreorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_884]),
    [final] ).

cnf(i_0_1596,plain,
    ( ~ class_Orderings_Opreorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_885]),
    [final] ).

cnf(i_0_1597,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Oone__class_Oone(X1))))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_886]),
    [final] ).

cnf(i_0_1598,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_887]),
    [final] ).

cnf(i_0_1599,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_888]),
    [final] ).

cnf(i_0_1600,plain,
    ( hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),esk33_2(X2,X3)))
    | ~ hBOOL(hAPP(X3,X1))
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_826]),
    [final] ).

cnf(i_0_1601,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_852]),
    [final] ).

cnf(i_0_1602,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
    | c_Finite__Set_Ocard(X1,c_Set_Oinsert(X1,X3,X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Finite__Set_Ocard(X1,X2))
    | ~ c_Finite__Set_Ofinite(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_889]),
    [final] ).

cnf(i_0_1603,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | ~ class_Orderings_Opreorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_890]),
    [final] ).

cnf(i_0_1604,plain,
    ( c_Finite__Set_Ocard(X1,c_Set_Oinsert(X1,X2,X3)) = c_Finite__Set_Ocard(X1,X3)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ c_Finite__Set_Ofinite(X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_891]),
    [final] ).

cnf(i_0_1605,plain,
    ( c_Finite__Set_Ofinite(tc_Nat_Onat,X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk42_2(X1,X2)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_892]),
    [final] ).

cnf(i_0_1606,plain,
    ( hBOOL(hAPP(hAPP(c_member(X3),X1),c_Set_Oinsert(X3,X2,X4)))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_802]),
    [final] ).

cnf(i_0_1607,plain,
    ( hBOOL(hAPP(hAPP(c_member(X3),X1),c_Set_Oinsert(X3,X2,X4)))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_830]),
    [final] ).

cnf(i_0_1608,plain,
    c_Set_Oinsert(X1,X2,c_Set_Oinsert(X1,X3,X4)) = c_Set_Oinsert(X1,X3,c_Set_Oinsert(X1,X2,X4)),
    inference(split_conjunct,[status(thm)],[i_0_893]),
    [final] ).

cnf(i_0_1609,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X2,X3))),
    inference(split_conjunct,[status(thm)],[i_0_894]),
    [final] ).

cnf(i_0_1610,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X1 = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_895]),
    [final] ).

cnf(i_0_1611,plain,
    ( X1 = X2
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_896]),
    [final] ).

cnf(i_0_1612,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X2 = X1
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_897]),
    [final] ).

cnf(i_0_1613,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X1 = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_898]),
    [final] ).

cnf(i_0_1614,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk8_0),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))))),
    inference(split_conjunct,[status(thm)],[i_0_604]),
    [final] ).

cnf(i_0_1615,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk7_0),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))))),
    inference(split_conjunct,[status(thm)],[i_0_605]),
    [final] ).

cnf(i_0_1616,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),v_n____),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))))),
    inference(split_conjunct,[status(thm)],[fact_n_I1_J]),
    [final] ).

cnf(i_0_1617,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_899]),
    [final] ).

cnf(i_0_1618,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_873]),
    [final] ).

cnf(i_0_1619,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_874]),
    [final] ).

cnf(i_0_1620,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_900]),
    [final] ).

cnf(i_0_1621,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_901]),
    [final] ).

cnf(i_0_1622,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X3)))
    | X1 != hAPP(c_Nat_OSuc,X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_846]),
    [final] ).

cnf(i_0_1623,plain,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
    | ~ c_Finite__Set_Ofinite(X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_902]),
    [final] ).

cnf(i_0_1624,plain,
    ( c_Finite__Set_Ofinite(X1,X3)
    | ~ c_Finite__Set_Ofinite(X1,X2)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_903]),
    [final] ).

cnf(i_0_1625,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),X2))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3,X1),X2))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_904]),
    [final] ).

cnf(i_0_1626,plain,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_905]),
    [final] ).

cnf(i_0_1627,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_906]),
    [final] ).

cnf(i_0_1628,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_907]),
    [final] ).

cnf(i_0_1629,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
    | ~ class_Orderings_Opreorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_890]),
    [final] ).

cnf(i_0_1630,plain,
    ( X2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk32_2(X2,X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_908]),
    [final] ).

cnf(i_0_1631,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_909]),
    [final] ).

cnf(i_0_1632,plain,
    ( c_Finite__Set_Ofinite(tc_Nat_Onat,X1)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk44_2(X1,X2)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_910]),
    [final] ).

cnf(i_0_1633,plain,
    ( hBOOL(hAPP(c_Set_Oinsert(X3,X4,X1),X2))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_850]),
    [final] ).

cnf(i_0_1634,plain,
    c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,esk39_0,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
    inference(split_conjunct,[status(thm)],[i_0_833]),
    [final] ).

cnf(i_0_1635,plain,
    c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,v_h____,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
    inference(split_conjunct,[status(thm)],[fact_injh]),
    [final] ).

cnf(i_0_1636,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | c_Finite__Set_Ocard(X1,c_Set_Oinsert(X1,X2,X3)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X1,X3))
    | ~ c_Finite__Set_Ofinite(X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_891]),
    [final] ).

cnf(i_0_1637,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
    | c_Finite__Set_Ocard(X1,c_Set_Oinsert(X1,X3,X2)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X1,X2))
    | ~ c_Finite__Set_Ofinite(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_911]),
    [final] ).

cnf(i_0_1638,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_895]),
    [final] ).

cnf(i_0_1639,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_912]),
    [final] ).

cnf(i_0_1640,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2) != c_Groups_Ozero__class_Ozero(X1)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1)))
    | ~ class_Int_Oring__char__0(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_913]),
    [final] ).

cnf(i_0_1641,plain,
    c_Nat_Onat_Onat__case(X1,X2,X3,hAPP(c_Nat_OSuc,X4)) = hAPP(X3,X4),
    inference(split_conjunct,[status(thm)],[i_0_914]),
    [final] ).

cnf(i_0_1642,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk33_2(X1,X2)),X1))
    | hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(X2,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_826]),
    [final] ).

cnf(i_0_1643,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
    | X1 = hAPP(c_Nat_OSuc,X2)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_915]),
    [final] ).

cnf(i_0_1644,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
    | X1 = hAPP(c_Nat_OSuc,X2)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_916]),
    [final] ).

cnf(i_0_1645,plain,
    ( hBOOL(hAPP(X1,esk45_2(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2))
    | ~ hBOOL(hAPP(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_776]),
    [final] ).

cnf(i_0_1646,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[i_0_917]),
    [final] ).

cnf(i_0_1647,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),esk41_1(X1)))
    | ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X1)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_892]),
    [final] ).

cnf(i_0_1648,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | hBOOL(hAPP(hAPP(X3,X1),X2))
    | X2 = X1
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_918]),
    [final] ).

cnf(i_0_1649,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),
    inference(split_conjunct,[status(thm)],[i_0_919]),
    [final] ).

cnf(i_0_1650,plain,
    ( X2 = X3
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_920]),
    [final] ).

cnf(i_0_1651,plain,
    ( X2 = X3
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_921]),
    [final] ).

cnf(i_0_1652,plain,
    ( X2 = X3
    | ~ class_Orderings_Oorder(X1)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_922]),
    [final] ).

cnf(i_0_1653,plain,
    ( X3 = X2
    | ~ class_Orderings_Oorder(X1)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_923]),
    [final] ).

cnf(i_0_1654,plain,
    ( X1 = hAPP(c_Nat_OSuc,esk31_2(X2,X1))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_846]),
    [final] ).

cnf(i_0_1655,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
    | X1 != X2
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_887]),
    [final] ).

cnf(i_0_1656,plain,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Finite__Set_Ocard(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_924]),
    [final] ).

cnf(i_0_1657,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
    inference(split_conjunct,[status(thm)],[i_0_925]),
    [final] ).

cnf(i_0_1658,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_926]),
    [final] ).

cnf(i_0_1659,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_909]),
    [final] ).

cnf(i_0_1660,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X1) = c_Groups_Ozero__class_Ozero(X2)
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X1),c_Int_Oring__1__class_OInts(X2)))
    | ~ class_Int_Oring__char__0(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_913]),
    [final] ).

cnf(i_0_1661,plain,
    ( X2 = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))
    | ~ c_Finite__Set_Ofinite(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
    | c_Finite__Set_Ocard(X1,X2) != c_Finite__Set_Ocard(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_927]),
    [final] ).

cnf(i_0_1662,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))
    | X1 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_908]),
    [final] ).

cnf(i_0_1663,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),esk43_1(X1)))
    | ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X1)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_910]),
    [final] ).

cnf(i_0_1664,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_928]),
    [final] ).

cnf(i_0_1665,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_929]),
    [final] ).

cnf(i_0_1666,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | ~ class_Orderings_Opreorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_930]),
    [final] ).

cnf(i_0_1667,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ class_Orderings_Opreorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_890]),
    [final] ).

cnf(i_0_1668,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))),
    inference(split_conjunct,[status(thm)],[i_0_931]),
    [final] ).

cnf(i_0_1669,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1))),
    inference(split_conjunct,[status(thm)],[i_0_932]),
    [final] ).

cnf(i_0_1670,plain,
    c_Set_Oimage(X1,X1,c_COMBI(X1),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_933]),
    [final] ).

cnf(i_0_1671,plain,
    c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
    inference(split_conjunct,[status(thm)],[i_0_934]),
    [final] ).

cnf(i_0_1672,plain,
    c_Nat_Onat_Onat__case(X1,X2,X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_935]),
    [final] ).

cnf(i_0_1673,plain,
    ( hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_850]),
    [final] ).

cnf(i_0_1674,plain,
    ( X3 = X2
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ class_Orderings_Oorder(X1)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_936]),
    [final] ).

cnf(i_0_1675,plain,
    ( X2 = X3
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ class_Orderings_Oorder(X1)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_937]),
    [final] ).

cnf(i_0_1676,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | X2 = X3
    | ~ class_Orderings_Oorder(X1)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_938]),
    [final] ).

cnf(i_0_1677,plain,
    ( X2 = X3
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ class_Orderings_Oorder(X1)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_939]),
    [final] ).

cnf(i_0_1678,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | X2 = X3
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_928]),
    [final] ).

cnf(i_0_1679,plain,
    ( X2 = X3
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_929]),
    [final] ).

cnf(i_0_1680,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | X2 = X3
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_904]),
    [final] ).

cnf(i_0_1681,plain,
    ( X2 = X3
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_940]),
    [final] ).

cnf(i_0_1682,plain,
    ( X2 = X3
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
    | ~ class_Orderings_Oorder(X1)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_941]),
    [final] ).

cnf(i_0_1683,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_863]),
    [final] ).

cnf(i_0_1684,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
    inference(split_conjunct,[status(thm)],[i_0_942]),
    [final] ).

cnf(i_0_1685,plain,
    c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1),
    inference(split_conjunct,[status(thm)],[i_0_943]),
    [final] ).

cnf(i_0_1686,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_944]),
    [final] ).

cnf(i_0_1687,plain,
    ( X2 = X3
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_945]),
    [final] ).

cnf(i_0_1688,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X2)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_946]),
    [final] ).

cnf(i_0_1689,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X2)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_916]),
    [final] ).

cnf(i_0_1690,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_896]),
    [final] ).

cnf(i_0_1691,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_870]),
    [final] ).

cnf(i_0_1692,plain,
    ( ~ class_Rings_Olinordered__semidom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Ozero__class_Ozero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_947]),
    [final] ).

cnf(i_0_1693,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_948]),
    [final] ).

cnf(i_0_1694,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_949]),
    [final] ).

cnf(i_0_1695,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_950]),
    [final] ).

cnf(i_0_1696,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_951]),
    [final] ).

cnf(i_0_1697,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_952]),
    [final] ).

cnf(i_0_1698,plain,
    ( c_Set_Oinsert(X1,X2,X3) = X3
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_953]),
    [final] ).

cnf(i_0_1699,plain,
    ( X1 = X2
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),X1))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_954]),
    [final] ).

cnf(i_0_1700,plain,
    ( X2 = X3
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_955]),
    [final] ).

cnf(i_0_1701,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | X2 = X3
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_956]),
    [final] ).

cnf(i_0_1702,plain,
    ( X2 = X3
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_957]),
    [final] ).

cnf(i_0_1703,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | X2 = X3
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_958]),
    [final] ).

cnf(i_0_1704,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | X2 = X3
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_959]),
    [final] ).

cnf(i_0_1705,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
    | X2 = X3
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_881]),
    [final] ).

cnf(i_0_1706,plain,
    ( c_Finite__Set_Ofinite(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
    | ~ c_Finite__Set_Ofinite(tc_Option_Ooption(X1),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X1),tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_960]),
    [final] ).

cnf(i_0_1707,plain,
    ( X1 = X2
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_948]),
    [final] ).

cnf(i_0_1708,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X1 = X2
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_949]),
    [final] ).

cnf(i_0_1709,plain,
    ( X1 = X2
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_961]),
    [final] ).

cnf(i_0_1710,plain,
    c_Set_Oinsert(X1,X2,c_Set_Oinsert(X1,X2,X3)) = c_Set_Oinsert(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[i_0_962]),
    [final] ).

cnf(i_0_1711,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk44_2(X1,X2)),X1))
    | c_Finite__Set_Ofinite(tc_Nat_Onat,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_910]),
    [final] ).

cnf(i_0_1712,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk42_2(X1,X2)),X1))
    | c_Finite__Set_Ofinite(tc_Nat_Onat,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_892]),
    [final] ).

cnf(i_0_1713,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[i_0_963]),
    [final] ).

cnf(i_0_1714,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[i_0_964]),
    [final] ).

cnf(i_0_1715,plain,
    ( c_Finite__Set_Ofinite(X1,X3)
    | ~ c_Finite__Set_Ofinite(X1,c_Set_Oinsert(X1,X2,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_965]),
    [final] ).

cnf(i_0_1716,plain,
    ( c_Finite__Set_Ofinite(tc_Option_Ooption(X1),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X1),tc_HOL_Obool)))
    | ~ c_Finite__Set_Ofinite(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_960]),
    [final] ).

cnf(i_0_1717,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3,X1),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),X2))
    | X1 != X2
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_940]),
    [final] ).

cnf(i_0_1718,plain,
    ( hBOOL(hAPP(X3,X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_966]),
    [final] ).

cnf(i_0_1719,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_967]),
    [final] ).

cnf(i_0_1720,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_968]),
    [final] ).

cnf(i_0_1721,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_907]),
    [final] ).

cnf(i_0_1722,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_969]),
    [final] ).

cnf(i_0_1723,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_906]),
    [final] ).

cnf(i_0_1724,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_970]),
    [final] ).

cnf(i_0_1725,plain,
    ( ~ class_Rings_Olinordered__semidom(X1)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1)),c_Groups_Ozero__class_Ozero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_971]),
    [final] ).

cnf(i_0_1726,plain,
    ( X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk18_2(X2,X1))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_972]),
    [final] ).

cnf(i_0_1727,plain,
    ( X1 = X2
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_973]),
    [final] ).

cnf(i_0_1728,plain,
    ( X1 = X2
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_974]),
    [final] ).

cnf(i_0_1729,plain,
    ( X1 = hAPP(c_Nat_OSuc,esk30_1(X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_975]),
    [final] ).

cnf(i_0_1730,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),X2))
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_929]),
    [final] ).

cnf(i_0_1731,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),X2))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_881]),
    [final] ).

cnf(i_0_1732,plain,
    ( ~ class_Orderings_Oorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | X3 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_976]),
    [final] ).

cnf(i_0_1733,plain,
    ( ~ class_Orderings_Oorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | X2 != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_977]),
    [final] ).

cnf(i_0_1734,plain,
    ( ~ class_Orderings_Oorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | X2 != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_978]),
    [final] ).

cnf(i_0_1735,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | X2 != X3
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_954]),
    [final] ).

cnf(i_0_1736,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | X3 != X2
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_954]),
    [final] ).

cnf(i_0_1737,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
    | X2 != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_979]),
    [final] ).

cnf(i_0_1738,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
    | X3 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_979]),
    [final] ).

cnf(i_0_1739,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
    | X2 != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_810]),
    [final] ).

cnf(i_0_1740,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
    | X3 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_810]),
    [final] ).

cnf(i_0_1741,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_980]),
    [final] ).

cnf(i_0_1742,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_800]),
    [final] ).

cnf(i_0_1743,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2),X1))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_981]),
    [final] ).

cnf(i_0_1744,plain,
    ( ~ class_Orderings_Opreorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_982]),
    [final] ).

cnf(i_0_1745,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
    inference(split_conjunct,[status(thm)],[i_0_983]),
    [final] ).

cnf(i_0_1746,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_984]),
    [final] ).

cnf(i_0_1747,plain,
    ( X2 = X4
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)
    | ~ class_Groups_Ocancel__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_985]),
    [final] ).

cnf(i_0_1748,plain,
    ( X2 = X4
    | ~ class_Groups_Ocancel__semigroup__add(X1)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_986]),
    [final] ).

cnf(i_0_1749,plain,
    ( X3 = X4
    | ~ class_Groups_Ocancel__ab__semigroup__add(X1)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_987]),
    [final] ).

cnf(i_0_1750,plain,
    ( X3 = X4
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)
    | ~ class_Groups_Ocancel__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_988]),
    [final] ).

cnf(i_0_1751,plain,
    ( X3 = X4
    | ~ class_Groups_Ocancel__semigroup__add(X1)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_989]),
    [final] ).

cnf(i_0_1752,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_990]),
    [final] ).

cnf(i_0_1753,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_991]),
    [final] ).

cnf(i_0_1754,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_992]),
    [final] ).

cnf(i_0_1755,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)),
    inference(split_conjunct,[status(thm)],[i_0_993]),
    [final] ).

cnf(i_0_1756,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_942]),
    [final] ).

cnf(i_0_1757,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(split_conjunct,[status(thm)],[i_0_994]),
    [final] ).

cnf(i_0_1758,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(split_conjunct,[status(thm)],[i_0_995]),
    [final] ).

cnf(i_0_1759,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(split_conjunct,[status(thm)],[i_0_996]),
    [final] ).

cnf(i_0_1760,plain,
    c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_Nat_Onat,X1)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(split_conjunct,[status(thm)],[i_0_997]),
    [final] ).

cnf(i_0_1761,plain,
    ( hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(c_fequal,X2)))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_945]),
    [final] ).

cnf(i_0_1762,plain,
    ( hBOOL(hAPP(hAPP(c_member(X3),X2),X1))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_966]),
    [final] ).

cnf(i_0_1763,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_998]),
    [final] ).

cnf(i_0_1764,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_999]),
    [final] ).

cnf(i_0_1765,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X1))),
    inference(split_conjunct,[status(thm)],[i_0_1000]),
    [final] ).

cnf(i_0_1766,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_948]),
    [final] ).

cnf(i_0_1767,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_973]),
    [final] ).

cnf(i_0_1768,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X2 != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_973]),
    [final] ).

cnf(i_0_1769,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X2 != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_1001]),
    [final] ).

cnf(i_0_1770,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_1002]),
    [final] ).

cnf(i_0_1771,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1))
    | X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_972]),
    [final] ).

cnf(i_0_1772,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Oone__class_Oone(X1)))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1003]),
    [final] ).

cnf(i_0_1773,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),c_Groups_Ozero__class_Ozero(X1)),c_Int_Oring__1__class_OInts(X1)))
    | ~ class_Rings_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1004]),
    [final] ).

cnf(i_0_1774,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),c_Groups_Oone__class_Oone(X1)),c_Int_Oring__1__class_OInts(X1)))
    | ~ class_Rings_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1005]),
    [final] ).

cnf(i_0_1775,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_1006]),
    [final] ).

cnf(i_0_1776,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_1007]),
    [final] ).

cnf(i_0_1777,plain,
    ( X1 = X3
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1008]),
    [final] ).

cnf(i_0_1778,plain,
    ( X2 = X3
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_1009]),
    [final] ).

cnf(i_0_1779,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_846]),
    [final] ).

cnf(i_0_1780,plain,
    ( c_Finite__Set_Ofinite(X1,c_Set_Oinsert(X1,X3,X2))
    | ~ c_Finite__Set_Ofinite(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_965]),
    [final] ).

cnf(i_0_1781,plain,
    ( c_Finite__Set_Ofinite(X1,c_Set_Oinsert(X1,X3,X2))
    | ~ c_Finite__Set_Ofinite(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1010]),
    [final] ).

cnf(i_0_1782,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_895]),
    [final] ).

cnf(i_0_1783,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X2)))
    | X1 != hAPP(c_Nat_OSuc,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_916]),
    [final] ).

cnf(i_0_1784,plain,
    ( c_Arrow__Order__Mirabelle_Odictator(X1,X2)
    | hAPP(X1,esk17_2(X2,X1)) != hAPP(esk17_2(X2,X1),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_681]),
    [final] ).

cnf(i_0_1785,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
    inference(split_conjunct,[status(thm)],[i_0_1011]),
    [final] ).

cnf(i_0_1786,plain,
    hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2)),
    inference(split_conjunct,[status(thm)],[i_0_1012]),
    [final] ).

cnf(i_0_1787,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(split_conjunct,[status(thm)],[i_0_1013]),
    [final] ).

cnf(i_0_1788,plain,
    ( X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(split_conjunct,[status(thm)],[i_0_1014]),
    [final] ).

cnf(i_0_1789,plain,
    ( X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1015]),
    [final] ).

cnf(i_0_1790,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
    | X1 != hAPP(c_Nat_OSuc,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_975]),
    [final] ).

cnf(i_0_1791,plain,
    ( X1 = X2
    | hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1016]),
    [final] ).

cnf(i_0_1792,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),c_Groups_Oone__class_Oone(X1)))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1017]),
    [final] ).

cnf(i_0_1793,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP(hAPP(c_fequal,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1018]),
    [final] ).

cnf(i_0_1794,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(split_conjunct,[status(thm)],[i_0_1014]),
    [final] ).

cnf(i_0_1795,plain,
    ( X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(split_conjunct,[status(thm)],[i_0_1014]),
    [final] ).

cnf(i_0_1796,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1015]),
    [final] ).

cnf(i_0_1797,plain,
    ( X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1015]),
    [final] ).

cnf(i_0_1798,plain,
    c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_1019]),
    [final] ).

cnf(i_0_1799,plain,
    c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(X1)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(split_conjunct,[status(thm)],[i_0_1020]),
    [final] ).

cnf(i_0_1800,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X2)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1021]),
    [final] ).

cnf(i_0_1801,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_984]),
    [final] ).

cnf(i_0_1802,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1022]),
    [final] ).

cnf(i_0_1803,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(split_conjunct,[status(thm)],[i_0_1014]),
    [final] ).

cnf(i_0_1804,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1015]),
    [final] ).

cnf(i_0_1805,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Orderings_Otop__class_Otop(X1)))
    | ~ class_Orderings_Otop(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1023]),
    [final] ).

cnf(i_0_1806,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1024]),
    [final] ).

cnf(i_0_1807,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Groups_Ozero__class_Ozero(X1) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)
    | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1025]),
    [final] ).

cnf(i_0_1808,plain,
    ( X3 = c_Groups_Ozero__class_Ozero(X2)
    | X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X3)
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1026]),
    [final] ).

cnf(i_0_1809,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(split_conjunct,[status(thm)],[i_0_1014]),
    [final] ).

cnf(i_0_1810,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_1014]),
    [final] ).

cnf(i_0_1811,plain,
    ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(split_conjunct,[status(thm)],[i_0_1015]),
    [final] ).

cnf(i_0_1812,plain,
    ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)
    | X1 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_1015]),
    [final] ).

cnf(i_0_1813,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | X2 != X3
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_920]),
    [final] ).

cnf(i_0_1814,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | X3 != X2
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_920]),
    [final] ).

cnf(i_0_1815,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | ~ class_Orderings_Opreorder(X1)
    | X2 != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_1027]),
    [final] ).

cnf(i_0_1816,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3,X1),X2))
    | X1 != X2
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_928]),
    [final] ).

cnf(i_0_1817,plain,
    hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
    inference(split_conjunct,[status(thm)],[i_0_1028]),
    [final] ).

cnf(i_0_1818,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1),
    inference(split_conjunct,[status(thm)],[i_0_1029]),
    [final] ).

cnf(i_0_1819,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X2))
    | ~ class_Orderings_Opreorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1030]),
    [final] ).

cnf(i_0_1820,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)),
    inference(split_conjunct,[status(thm)],[i_0_1031]),
    [final] ).

cnf(i_0_1821,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)),
    inference(split_conjunct,[status(thm)],[i_0_1032]),
    [final] ).

cnf(i_0_1822,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_1013]),
    [final] ).

cnf(i_0_1823,plain,
    ( hAPP(c_Orderings_Otop__class_Otop(tc_fun(X2,X1)),X3) = c_Orderings_Otop__class_Otop(X1)
    | ~ class_Orderings_Otop(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1033]),
    [final] ).

cnf(i_0_1824,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_1034]),
    [final] ).

cnf(i_0_1825,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_1034]),
    [final] ).

cnf(i_0_1826,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_949]),
    [final] ).

cnf(i_0_1827,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_951]),
    [final] ).

cnf(i_0_1828,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_1035]),
    [final] ).

cnf(i_0_1829,plain,
    ( hBOOL(hAPP(hAPP(c_fequal,X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_1036]),
    [final] ).

cnf(i_0_1830,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_1037]),
    [final] ).

cnf(i_0_1831,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_1038]),
    [final] ).

cnf(i_0_1832,plain,
    ( c_Finite__Set_Ofinite(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
    | ~ class_Finite__Set_Ofinite(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1039]),
    [final] ).

cnf(i_0_1833,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = X2
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1040]),
    [final] ).

cnf(i_0_1834,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = X2
    | ~ class_Groups_Ocomm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1041]),
    [final] ).

cnf(i_0_1835,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = X2
    | ~ class_Groups_Omonoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1042]),
    [final] ).

cnf(i_0_1836,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X1) = c_Groups_Ozero__class_Ozero(X2)
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Groups_Olinordered__ab__group__add(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1024]),
    [final] ).

cnf(i_0_1837,plain,
    ( c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X1)
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Groups_Olinordered__ab__group__add(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1025]),
    [final] ).

cnf(i_0_1838,plain,
    ( X3 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X3),X1)
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1026]),
    [final] ).

cnf(i_0_1839,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = X2
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1043]),
    [final] ).

cnf(i_0_1840,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = X2
    | ~ class_Groups_Ocomm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1044]),
    [final] ).

cnf(i_0_1841,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = X2
    | ~ class_Groups_Omonoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1045]),
    [final] ).

cnf(i_0_1842,plain,
    hAPP(c_Nat_OSuc,X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1),
    inference(split_conjunct,[status(thm)],[i_0_1046]),
    [final] ).

cnf(i_0_1843,plain,
    hAPP(c_Nat_OSuc,X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(split_conjunct,[status(thm)],[i_0_1047]),
    [final] ).

cnf(i_0_1844,plain,
    c_Finite__Set_Ocard(tc_Product__Type_Ounit,c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[fact_card__UNIV__unit]),
    [final] ).

cnf(i_0_1845,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_1034]),
    [final] ).

cnf(i_0_1846,plain,
    c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
    inference(split_conjunct,[status(thm)],[fact_finite__indi]),
    [final] ).

cnf(i_0_1847,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) = X1,
    inference(split_conjunct,[status(thm)],[i_0_1048]),
    [final] ).

cnf(i_0_1848,plain,
    hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),
    inference(split_conjunct,[status(thm)],[i_0_1049]),
    [final] ).

cnf(i_0_1849,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
    inference(split_conjunct,[status(thm)],[i_0_1050]),
    [final] ).

cnf(i_0_1850,plain,
    ( class_Finite__Set_Ofinite(tc_sum(X1,X2))
    | ~ class_Finite__Set_Ofinite(X1)
    | ~ class_Finite__Set_Ofinite(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1051]),
    [final] ).

cnf(i_0_1851,plain,
    ( class_Finite__Set_Ofinite(tc_fun(X1,X2))
    | ~ class_Finite__Set_Ofinite(X1)
    | ~ class_Finite__Set_Ofinite(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1052]),
    [final] ).

cnf(i_0_1852,plain,
    ( class_Finite__Set_Ofinite(tc_prod(X1,X2))
    | ~ class_Finite__Set_Ofinite(X1)
    | ~ class_Finite__Set_Ofinite(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1053]),
    [final] ).

cnf(i_0_1853,plain,
    ( X1 = X2
    | hAPP(c_Nat_OSuc,X1) != hAPP(c_Nat_OSuc,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1054]),
    [final] ).

cnf(i_0_1854,plain,
    ( X1 = X2
    | hAPP(c_Nat_OSuc,X1) != hAPP(c_Nat_OSuc,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1055]),
    [final] ).

cnf(i_0_1855,plain,
    ( class_Orderings_Otop(tc_fun(X2,X1))
    | ~ class_Orderings_Otop(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1056]),
    [final] ).

cnf(i_0_1856,plain,
    ( class_Orderings_Oorder(tc_fun(X2,X1))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1057]),
    [final] ).

cnf(i_0_1857,plain,
    ( class_Orderings_Oord(tc_fun(X2,X1))
    | ~ class_Orderings_Oord(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1058]),
    [final] ).

cnf(i_0_1858,plain,
    ( class_Orderings_Opreorder(tc_fun(X2,X1))
    | ~ class_Orderings_Opreorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1059]),
    [final] ).

cnf(i_0_1859,plain,
    ( c_Finite__Set_Ofinite(X1,X2)
    | c_Finite__Set_Ocard(X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_636]),
    [final] ).

cnf(i_0_1860,plain,
    ( c_Finite__Set_Ofinite(X1,X2)
    | c_Finite__Set_Ocard(X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_1060]),
    [final] ).

cnf(i_0_1861,plain,
    hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_1061]),
    [final] ).

cnf(i_0_1862,plain,
    hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_1062]),
    [final] ).

cnf(i_0_1863,plain,
    hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_1063]),
    [final] ).

cnf(i_0_1864,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
    inference(split_conjunct,[status(thm)],[i_0_1064]),
    [final] ).

cnf(i_0_1865,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
    inference(split_conjunct,[status(thm)],[i_0_1065]),
    [final] ).

cnf(i_0_1866,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
    inference(split_conjunct,[status(thm)],[i_0_1066]),
    [final] ).

cnf(i_0_1867,plain,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ class_Finite__Set_Ofinite(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1067]),
    [final] ).

cnf(i_0_1868,plain,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ class_Finite__Set_Ofinite(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1068]),
    [final] ).

cnf(i_0_1869,plain,
    hAPP(c_Nat_OSuc,X1) != X1,
    inference(split_conjunct,[status(thm)],[i_0_1069]),
    [final] ).

cnf(i_0_1870,plain,
    X1 != hAPP(c_Nat_OSuc,X1),
    inference(split_conjunct,[status(thm)],[i_0_1070]),
    [final] ).

cnf(i_0_1871,plain,
    hAPP(c_COMBI(X1),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_1071]),
    [final] ).

cnf(i_0_1872,plain,
    ( ~ class_Rings_Ozero__neq__one(X1)
    | c_Groups_Ozero__class_Ozero(X1) != c_Groups_Oone__class_Oone(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1072]),
    [final] ).

cnf(i_0_1873,plain,
    ( ~ class_Rings_Ozero__neq__one(X1)
    | c_Groups_Oone__class_Oone(X1) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1073]),
    [final] ).

cnf(i_0_1874,plain,
    c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[fact_nat_Osize_I3_J]),
    [final] ).

cnf(i_0_1875,plain,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(split_conjunct,[status(thm)],[fact_One__nat__def]),
    [final] ).

cnf(i_0_1876,plain,
    ( class_Finite__Set_Ofinite(tc_Option_Ooption(X1))
    | ~ class_Finite__Set_Ofinite(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1074]),
    [final] ).

cnf(i_0_1877,plain,
    c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
    inference(split_conjunct,[status(thm)],[i_0_1075]),
    [final] ).

cnf(i_0_1878,plain,
    c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[fact_nat_Osize_I1_J]),
    [final] ).

cnf(i_0_1879,plain,
    ~ hBOOL(c_fFalse),
    inference(split_conjunct,[status(thm)],[i_0_1076]),
    [final] ).

cnf(i_0_1880,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]),
    [final] ).

cnf(i_0_1881,plain,
    class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring__1]),
    [final] ).

cnf(i_0_1882,plain,
    class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oordered__comm__monoid__add]),
    [final] ).

cnf(i_0_1883,plain,
    class_Groups_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ozero]),
    [final] ).

cnf(i_0_1884,plain,
    class_Rings_Ozero__neq__one(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ozero__neq__one]),
    [final] ).

cnf(i_0_1885,plain,
    class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ocomm__monoid__add]),
    [final] ).

cnf(i_0_1886,plain,
    class_Groups_Omonoid__add(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__add]),
    [final] ).

cnf(i_0_1887,plain,
    class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
    inference(split_conjunct,[status(thm)],[arity_Product____Type__Ounit__Finite__Set_Ofinite]),
    [final] ).

cnf(i_0_1888,plain,
    class_Finite__Set_Ofinite(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Finite__Set_Ofinite]),
    [final] ).

cnf(i_0_1889,plain,
    class_Orderings_Otop(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Otop]),
    [final] ).

cnf(i_0_1890,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oordered__ab__semigroup__add]),
    [final] ).

cnf(i_0_1891,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le]),
    [final] ).

cnf(i_0_1892,plain,
    class_Groups_Oone(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oone]),
    [final] ).

cnf(i_0_1893,plain,
    class_Groups_Oab__semigroup__add(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oab__semigroup__add]),
    [final] ).

cnf(i_0_1894,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add]),
    [final] ).

cnf(i_0_1895,plain,
    class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__semigroup__add]),
    [final] ).

cnf(i_0_1896,plain,
    class_Orderings_Oorder(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]),
    [final] ).

cnf(i_0_1897,plain,
    class_Orderings_Oorder(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]),
    [final] ).

cnf(i_0_1898,plain,
    class_Orderings_Oord(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oord]),
    [final] ).

cnf(i_0_1899,plain,
    class_Orderings_Oord(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oord]),
    [final] ).

cnf(i_0_1900,plain,
    class_Orderings_Olinorder(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]),
    [final] ).

cnf(i_0_1901,plain,
    class_Orderings_Opreorder(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]),
    [final] ).

cnf(i_0_1902,plain,
    class_Orderings_Opreorder(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]),
    [final] ).

cnf(i_0_1903,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add]),
    [final] ).

cnf(i_0_1904,plain,
    class_Rings_Olinordered__semidom(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semidom]),
    [final] ).

cnf(i_0_1905,plain,
    c_Arrow__Order__Mirabelle_Ounanimity(v_F),
    inference(split_conjunct,[status(thm)],[fact_u]),
    [final] ).

cnf(i_0_1906,plain,
    c_Arrow__Order__Mirabelle_OIIA(v_F),
    inference(split_conjunct,[status(thm)],[fact_assms_I3_J]),
    [final] ).

cnf(i_0_1907,plain,
    v_c____ != v_d____,
    inference(split_conjunct,[status(thm)],[fact__096c_A_126_061_Ad_096]),
    [final] ).

cnf(i_0_1908,plain,
    v_a____ != v_b____,
    inference(split_conjunct,[status(thm)],[fact__096a_A_126_061_Ab_096]),
    [final] ).

cnf(i_0_1909,axiom,
    X1 = X1 ).

cnf(i_0_1910,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_1911,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_1912,axiom,
    ( X1 != X2
    | hAPP(X1,X3) = hAPP(X2,X3) ) ).

cnf(i_0_1913,axiom,
    ( X1 != X2
    | hAPP(X3,X1) = hAPP(X3,X2) ) ).

cnf(i_0_1914,axiom,
    ( X1 != X2
    | c_Groups_Oone__class_Oone(X1) = c_Groups_Oone__class_Oone(X2) ) ).

cnf(i_0_1915,axiom,
    ( X1 != X2
    | c_Orderings_Oord__class_Oless__eq(X1,X3) = c_Orderings_Oord__class_Oless__eq(X2,X3) ) ).

cnf(i_0_1916,axiom,
    ( X1 != X2
    | c_Orderings_Oord__class_Oless__eq(X3,X1) = c_Orderings_Oord__class_Oless__eq(X3,X2) ) ).

cnf(i_0_1917,axiom,
    ( X1 != X2
    | c_FuncSet_OPi(X1,X3,X4,X5) = c_FuncSet_OPi(X2,X3,X4,X5) ) ).

cnf(i_0_1918,axiom,
    ( X1 != X2
    | c_FuncSet_OPi(X3,X1,X4,X5) = c_FuncSet_OPi(X3,X2,X4,X5) ) ).

cnf(i_0_1919,axiom,
    ( X1 != X2
    | c_FuncSet_OPi(X3,X4,X1,X5) = c_FuncSet_OPi(X3,X4,X2,X5) ) ).

cnf(i_0_1920,axiom,
    ( X1 != X2
    | c_FuncSet_OPi(X3,X4,X5,X1) = c_FuncSet_OPi(X3,X4,X5,X2) ) ).

cnf(i_0_1921,axiom,
    ( X1 != X2
    | esk15_2(X1,X3) = esk15_2(X2,X3) ) ).

cnf(i_0_1922,axiom,
    ( X1 != X2
    | esk15_2(X3,X1) = esk15_2(X3,X2) ) ).

cnf(i_0_1923,axiom,
    ( X1 != X2
    | esk16_2(X1,X3) = esk16_2(X2,X3) ) ).

cnf(i_0_1924,axiom,
    ( X1 != X2
    | esk16_2(X3,X1) = esk16_2(X3,X2) ) ).

cnf(i_0_1925,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold__image(X1,X3,X4,X5,X6,X7) = c_Finite__Set_Ofold__image(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_1926,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold__image(X3,X1,X4,X5,X6,X7) = c_Finite__Set_Ofold__image(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_1927,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold__image(X3,X4,X1,X5,X6,X7) = c_Finite__Set_Ofold__image(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_1928,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold__image(X3,X4,X5,X1,X6,X7) = c_Finite__Set_Ofold__image(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_1929,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold__image(X3,X4,X5,X6,X1,X7) = c_Finite__Set_Ofold__image(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_1930,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold__image(X3,X4,X5,X6,X7,X1) = c_Finite__Set_Ofold__image(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_1931,axiom,
    ( X1 != X2
    | c_Set_Oimage(X1,X3,X4,X5) = c_Set_Oimage(X2,X3,X4,X5) ) ).

cnf(i_0_1932,axiom,
    ( X1 != X2
    | c_Set_Oimage(X3,X1,X4,X5) = c_Set_Oimage(X3,X2,X4,X5) ) ).

cnf(i_0_1933,axiom,
    ( X1 != X2
    | c_Set_Oimage(X3,X4,X1,X5) = c_Set_Oimage(X3,X4,X2,X5) ) ).

cnf(i_0_1934,axiom,
    ( X1 != X2
    | c_Set_Oimage(X3,X4,X5,X1) = c_Set_Oimage(X3,X4,X5,X2) ) ).

cnf(i_0_1935,axiom,
    ( X1 != X2
    | c_Set_Oinsert(X1,X3,X4) = c_Set_Oinsert(X2,X3,X4) ) ).

cnf(i_0_1936,axiom,
    ( X1 != X2
    | c_Set_Oinsert(X3,X1,X4) = c_Set_Oinsert(X3,X2,X4) ) ).

cnf(i_0_1937,axiom,
    ( X1 != X2
    | c_Set_Oinsert(X3,X4,X1) = c_Set_Oinsert(X3,X4,X2) ) ).

cnf(i_0_1938,axiom,
    ( X1 != X2
    | c_Finite__Set_Ocard(X1,X3) = c_Finite__Set_Ocard(X2,X3) ) ).

cnf(i_0_1939,axiom,
    ( X1 != X2
    | c_Finite__Set_Ocard(X3,X1) = c_Finite__Set_Ocard(X3,X2) ) ).

cnf(i_0_1940,axiom,
    ( X1 != X2
    | c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).

cnf(i_0_1941,axiom,
    ( X1 != X2
    | c_Orderings_Otop__class_Otop(X1) = c_Orderings_Otop__class_Otop(X2) ) ).

cnf(i_0_1942,axiom,
    ( X1 != X2
    | esk35_5(X1,X3,X4,X5,X6) = esk35_5(X2,X3,X4,X5,X6) ) ).

cnf(i_0_1943,axiom,
    ( X1 != X2
    | esk35_5(X3,X1,X4,X5,X6) = esk35_5(X3,X2,X4,X5,X6) ) ).

cnf(i_0_1944,axiom,
    ( X1 != X2
    | esk35_5(X3,X4,X1,X5,X6) = esk35_5(X3,X4,X2,X5,X6) ) ).

cnf(i_0_1945,axiom,
    ( X1 != X2
    | esk35_5(X3,X4,X5,X1,X6) = esk35_5(X3,X4,X5,X2,X6) ) ).

cnf(i_0_1946,axiom,
    ( X1 != X2
    | esk35_5(X3,X4,X5,X6,X1) = esk35_5(X3,X4,X5,X6,X2) ) ).

cnf(i_0_1947,axiom,
    ( X1 != X2
    | esk34_4(X1,X3,X4,X5) = esk34_4(X2,X3,X4,X5) ) ).

cnf(i_0_1948,axiom,
    ( X1 != X2
    | esk34_4(X3,X1,X4,X5) = esk34_4(X3,X2,X4,X5) ) ).

cnf(i_0_1949,axiom,
    ( X1 != X2
    | esk34_4(X3,X4,X1,X5) = esk34_4(X3,X4,X2,X5) ) ).

cnf(i_0_1950,axiom,
    ( X1 != X2
    | esk34_4(X3,X4,X5,X1) = esk34_4(X3,X4,X5,X2) ) ).

cnf(i_0_1951,axiom,
    ( X1 != X2
    | esk38_3(X1,X3,X4) = esk38_3(X2,X3,X4) ) ).

cnf(i_0_1952,axiom,
    ( X1 != X2
    | esk38_3(X3,X1,X4) = esk38_3(X3,X2,X4) ) ).

cnf(i_0_1953,axiom,
    ( X1 != X2
    | esk38_3(X3,X4,X1) = esk38_3(X3,X4,X2) ) ).

cnf(i_0_1954,axiom,
    ( X1 != X2
    | esk13_4(X1,X3,X4,X5) = esk13_4(X2,X3,X4,X5) ) ).

cnf(i_0_1955,axiom,
    ( X1 != X2
    | esk13_4(X3,X1,X4,X5) = esk13_4(X3,X2,X4,X5) ) ).

cnf(i_0_1956,axiom,
    ( X1 != X2
    | esk13_4(X3,X4,X1,X5) = esk13_4(X3,X4,X2,X5) ) ).

cnf(i_0_1957,axiom,
    ( X1 != X2
    | esk13_4(X3,X4,X5,X1) = esk13_4(X3,X4,X5,X2) ) ).

cnf(i_0_1958,axiom,
    ( X1 != X2
    | esk12_4(X1,X3,X4,X5) = esk12_4(X2,X3,X4,X5) ) ).

cnf(i_0_1959,axiom,
    ( X1 != X2
    | esk12_4(X3,X1,X4,X5) = esk12_4(X3,X2,X4,X5) ) ).

cnf(i_0_1960,axiom,
    ( X1 != X2
    | esk12_4(X3,X4,X1,X5) = esk12_4(X3,X4,X2,X5) ) ).

cnf(i_0_1961,axiom,
    ( X1 != X2
    | esk12_4(X3,X4,X5,X1) = esk12_4(X3,X4,X5,X2) ) ).

cnf(i_0_1962,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastLessThan(X1,X3,X4) = c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X4) ) ).

cnf(i_0_1963,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastLessThan(X3,X1,X4) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X2,X4) ) ).

cnf(i_0_1964,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X2) ) ).

cnf(i_0_1965,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__case(X1,X3,X4,X5) = c_Nat_Onat_Onat__case(X2,X3,X4,X5) ) ).

cnf(i_0_1966,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__case(X3,X1,X4,X5) = c_Nat_Onat_Onat__case(X3,X2,X4,X5) ) ).

cnf(i_0_1967,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__case(X3,X4,X1,X5) = c_Nat_Onat_Onat__case(X3,X4,X2,X5) ) ).

cnf(i_0_1968,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__case(X3,X4,X5,X1) = c_Nat_Onat_Onat__case(X3,X4,X5,X2) ) ).

cnf(i_0_1969,axiom,
    ( X1 != X2
    | c_Sum__Type_OPlus(X1,X3,X4,X5) = c_Sum__Type_OPlus(X2,X3,X4,X5) ) ).

cnf(i_0_1970,axiom,
    ( X1 != X2
    | c_Sum__Type_OPlus(X3,X1,X4,X5) = c_Sum__Type_OPlus(X3,X2,X4,X5) ) ).

cnf(i_0_1971,axiom,
    ( X1 != X2
    | c_Sum__Type_OPlus(X3,X4,X1,X5) = c_Sum__Type_OPlus(X3,X4,X2,X5) ) ).

cnf(i_0_1972,axiom,
    ( X1 != X2
    | c_Sum__Type_OPlus(X3,X4,X5,X1) = c_Sum__Type_OPlus(X3,X4,X5,X2) ) ).

cnf(i_0_1973,axiom,
    ( X1 != X2
    | c_Nat_Osize__class_Osize(X1,X3) = c_Nat_Osize__class_Osize(X2,X3) ) ).

cnf(i_0_1974,axiom,
    ( X1 != X2
    | c_Nat_Osize__class_Osize(X3,X1) = c_Nat_Osize__class_Osize(X3,X2) ) ).

cnf(i_0_1975,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__size(X1) = c_Nat_Onat_Onat__size(X2) ) ).

cnf(i_0_1976,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__idom(X1)
    | class_Rings_Olinordered__idom(X2) ) ).

cnf(i_0_1977,axiom,
    ( X1 != X2
    | ~ c_FunDef_Oin__rel(X1,X3,X4,X5,X6)
    | c_FunDef_Oin__rel(X2,X3,X4,X5,X6) ) ).

cnf(i_0_1978,axiom,
    ( X1 != X2
    | ~ c_FunDef_Oin__rel(X3,X1,X4,X5,X6)
    | c_FunDef_Oin__rel(X3,X2,X4,X5,X6) ) ).

cnf(i_0_1979,axiom,
    ( X1 != X2
    | ~ c_FunDef_Oin__rel(X3,X4,X1,X5,X6)
    | c_FunDef_Oin__rel(X3,X4,X2,X5,X6) ) ).

cnf(i_0_1980,axiom,
    ( X1 != X2
    | ~ c_FunDef_Oin__rel(X3,X4,X5,X1,X6)
    | c_FunDef_Oin__rel(X3,X4,X5,X2,X6) ) ).

cnf(i_0_1981,axiom,
    ( X1 != X2
    | ~ c_FunDef_Oin__rel(X3,X4,X5,X6,X1)
    | c_FunDef_Oin__rel(X3,X4,X5,X6,X2) ) ).

cnf(i_0_1982,axiom,
    ( X1 != X2
    | ~ class_Orderings_Olinorder(X1)
    | class_Orderings_Olinorder(X2) ) ).

cnf(i_0_1983,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | class_Groups_Oordered__ab__semigroup__add__imp__le(X2) ) ).

cnf(i_0_1984,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
    | class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).

cnf(i_0_1985,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__semigroup__add(X1)
    | class_Groups_Oordered__ab__semigroup__add(X2) ) ).

cnf(i_0_1986,axiom,
    ( X1 != X2
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | class_Groups_Olinordered__ab__group__add(X2) ) ).

cnf(i_0_1987,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | class_Groups_Oordered__comm__monoid__add(X2) ) ).

cnf(i_0_1988,axiom,
    ( X1 != X2
    | ~ class_Rings_Oring__1(X1)
    | class_Rings_Oring__1(X2) ) ).

cnf(i_0_1989,axiom,
    ( X1 != X2
    | ~ class_Rings_Ocomm__semiring__1(X1)
    | class_Rings_Ocomm__semiring__1(X2) ) ).

cnf(i_0_1990,axiom,
    ( X1 != X2
    | ~ hBOOL(X1)
    | hBOOL(X2) ) ).

cnf(i_0_1991,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semidom(X1)
    | class_Rings_Olinordered__semidom(X2) ) ).

cnf(i_0_1992,axiom,
    ( X1 != X2
    | ~ class_Int_Oring__char__0(X1)
    | class_Int_Oring__char__0(X2) ) ).

cnf(i_0_1993,axiom,
    ( X1 != X2
    | ~ class_Orderings_Opreorder(X1)
    | class_Orderings_Opreorder(X2) ) ).

cnf(i_0_1994,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oorder(X1)
    | class_Orderings_Oorder(X2) ) ).

cnf(i_0_1995,axiom,
    ( X1 != X2
    | ~ class_Groups_Oab__semigroup__add(X1)
    | class_Groups_Oab__semigroup__add(X2) ) ).

cnf(i_0_1996,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocancel__semigroup__add(X1)
    | class_Groups_Ocancel__semigroup__add(X2) ) ).

cnf(i_0_1997,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocancel__ab__semigroup__add(X1)
    | class_Groups_Ocancel__ab__semigroup__add(X2) ) ).

cnf(i_0_1998,axiom,
    ( X1 != X2
    | ~ class_Orderings_Otop(X1)
    | class_Orderings_Otop(X2) ) ).

cnf(i_0_1999,axiom,
    ( X1 != X2
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ).

cnf(i_0_2000,axiom,
    ( X1 != X2
    | ~ class_Finite__Set_Ofinite(X1)
    | class_Finite__Set_Ofinite(X2) ) ).

cnf(i_0_2001,axiom,
    ( X1 != X2
    | ~ c_Arrow__Order__Mirabelle_OIIA(X1)
    | c_Arrow__Order__Mirabelle_OIIA(X2) ) ).

cnf(i_0_2002,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | class_Groups_Ocomm__monoid__add(X2) ) ).

cnf(i_0_2003,axiom,
    ( X1 != X2
    | ~ class_Groups_Omonoid__add(X1)
    | class_Groups_Omonoid__add(X2) ) ).

cnf(i_0_2004,axiom,
    ( X1 != X2
    | ~ class_Rings_Ozero__neq__one(X1)
    | class_Rings_Ozero__neq__one(X2) ) ).

cnf(i_0_2005,axiom,
    ( X1 != X2
    | ~ class_Groups_Ozero(X1)
    | class_Groups_Ozero(X2) ) ).

cnf(i_0_2006,axiom,
    ( X1 != X2
    | ~ class_Groups_Oone(X1)
    | class_Groups_Oone(X2) ) ).

cnf(i_0_2007,axiom,
    ( X1 != X2
    | ~ c_Arrow__Order__Mirabelle_Odictator(X1,X3)
    | c_Arrow__Order__Mirabelle_Odictator(X2,X3) ) ).

cnf(i_0_2008,axiom,
    ( X1 != X2
    | ~ c_Arrow__Order__Mirabelle_Odictator(X3,X1)
    | c_Arrow__Order__Mirabelle_Odictator(X3,X2) ) ).

cnf(i_0_2009,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image__simple(X1,X3,X4,X5,X6,X7)
    | c_Finite__Set_Ofolding__image__simple(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_2010,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image__simple(X3,X1,X4,X5,X6,X7)
    | c_Finite__Set_Ofolding__image__simple(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_2011,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image__simple(X3,X4,X1,X5,X6,X7)
    | c_Finite__Set_Ofolding__image__simple(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_2012,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image__simple(X3,X4,X5,X1,X6,X7)
    | c_Finite__Set_Ofolding__image__simple(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_2013,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image__simple(X3,X4,X5,X6,X1,X7)
    | c_Finite__Set_Ofolding__image__simple(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_2014,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image__simple(X3,X4,X5,X6,X7,X1)
    | c_Finite__Set_Ofolding__image__simple(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_2015,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofinite(X1,X3)
    | c_Finite__Set_Ofinite(X2,X3) ) ).

cnf(i_0_2016,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofinite(X3,X1)
    | c_Finite__Set_Ofinite(X3,X2) ) ).

cnf(i_0_2017,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oord(X1)
    | class_Orderings_Oord(X2) ) ).

cnf(i_0_2018,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X1,X3,X4,X5)
    | c_Fun_Oinj__on(X2,X3,X4,X5) ) ).

cnf(i_0_2019,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X1,X4,X5)
    | c_Fun_Oinj__on(X3,X2,X4,X5) ) ).

cnf(i_0_2020,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X4,X1,X5)
    | c_Fun_Oinj__on(X3,X4,X2,X5) ) ).

cnf(i_0_2021,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X4,X5,X1)
    | c_Fun_Oinj__on(X3,X4,X5,X2) ) ).

cnf(i_0_2022,axiom,
    ( X1 != X2
    | ~ c_Arrow__Order__Mirabelle_Ounanimity(X1)
    | c_Arrow__Order__Mirabelle_Ounanimity(X2) ) ).

cnf(i_0_1909_001,axiom,
    X1 = X1 ).

cnf(i_0_1910_002,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_1911_003,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_1912_004,axiom,
    ( X1 != X2
    | hAPP(X1,X3) = hAPP(X2,X3) ) ).

cnf(i_0_1913_005,axiom,
    ( X1 != X2
    | hAPP(X3,X1) = hAPP(X3,X2) ) ).

cnf(i_0_1914_006,axiom,
    ( X1 != X2
    | c_Groups_Oone__class_Oone(X1) = c_Groups_Oone__class_Oone(X2) ) ).

cnf(i_0_1915_007,axiom,
    ( X1 != X2
    | c_Orderings_Oord__class_Oless__eq(X1,X3) = c_Orderings_Oord__class_Oless__eq(X2,X3) ) ).

cnf(i_0_1916_008,axiom,
    ( X1 != X2
    | c_Orderings_Oord__class_Oless__eq(X3,X1) = c_Orderings_Oord__class_Oless__eq(X3,X2) ) ).

cnf(i_0_1917_009,axiom,
    ( X1 != X2
    | c_FuncSet_OPi(X1,X3,X4,X5) = c_FuncSet_OPi(X2,X3,X4,X5) ) ).

cnf(i_0_1918_010,axiom,
    ( X1 != X2
    | c_FuncSet_OPi(X3,X1,X4,X5) = c_FuncSet_OPi(X3,X2,X4,X5) ) ).

cnf(i_0_1919_011,axiom,
    ( X1 != X2
    | c_FuncSet_OPi(X3,X4,X1,X5) = c_FuncSet_OPi(X3,X4,X2,X5) ) ).

cnf(i_0_1920_012,axiom,
    ( X1 != X2
    | c_FuncSet_OPi(X3,X4,X5,X1) = c_FuncSet_OPi(X3,X4,X5,X2) ) ).

cnf(i_0_1921_013,axiom,
    ( X1 != X2
    | esk15_2(X1,X3) = esk15_2(X2,X3) ) ).

cnf(i_0_1922_014,axiom,
    ( X1 != X2
    | esk15_2(X3,X1) = esk15_2(X3,X2) ) ).

cnf(i_0_1923_015,axiom,
    ( X1 != X2
    | esk16_2(X1,X3) = esk16_2(X2,X3) ) ).

cnf(i_0_1924_016,axiom,
    ( X1 != X2
    | esk16_2(X3,X1) = esk16_2(X3,X2) ) ).

cnf(i_0_1925_017,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold__image(X1,X3,X4,X5,X6,X7) = c_Finite__Set_Ofold__image(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_1926_018,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold__image(X3,X1,X4,X5,X6,X7) = c_Finite__Set_Ofold__image(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_1927_019,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold__image(X3,X4,X1,X5,X6,X7) = c_Finite__Set_Ofold__image(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_1928_020,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold__image(X3,X4,X5,X1,X6,X7) = c_Finite__Set_Ofold__image(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_1929_021,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold__image(X3,X4,X5,X6,X1,X7) = c_Finite__Set_Ofold__image(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_1930_022,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold__image(X3,X4,X5,X6,X7,X1) = c_Finite__Set_Ofold__image(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_1931_023,axiom,
    ( X1 != X2
    | c_Set_Oimage(X1,X3,X4,X5) = c_Set_Oimage(X2,X3,X4,X5) ) ).

cnf(i_0_1932_024,axiom,
    ( X1 != X2
    | c_Set_Oimage(X3,X1,X4,X5) = c_Set_Oimage(X3,X2,X4,X5) ) ).

cnf(i_0_1933_025,axiom,
    ( X1 != X2
    | c_Set_Oimage(X3,X4,X1,X5) = c_Set_Oimage(X3,X4,X2,X5) ) ).

cnf(i_0_1934_026,axiom,
    ( X1 != X2
    | c_Set_Oimage(X3,X4,X5,X1) = c_Set_Oimage(X3,X4,X5,X2) ) ).

cnf(i_0_1935_027,axiom,
    ( X1 != X2
    | c_Set_Oinsert(X1,X3,X4) = c_Set_Oinsert(X2,X3,X4) ) ).

cnf(i_0_1936_028,axiom,
    ( X1 != X2
    | c_Set_Oinsert(X3,X1,X4) = c_Set_Oinsert(X3,X2,X4) ) ).

cnf(i_0_1937_029,axiom,
    ( X1 != X2
    | c_Set_Oinsert(X3,X4,X1) = c_Set_Oinsert(X3,X4,X2) ) ).

cnf(i_0_1938_030,axiom,
    ( X1 != X2
    | c_Finite__Set_Ocard(X1,X3) = c_Finite__Set_Ocard(X2,X3) ) ).

cnf(i_0_1939_031,axiom,
    ( X1 != X2
    | c_Finite__Set_Ocard(X3,X1) = c_Finite__Set_Ocard(X3,X2) ) ).

cnf(i_0_1940_032,axiom,
    ( X1 != X2
    | c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).

cnf(i_0_1941_033,axiom,
    ( X1 != X2
    | c_Orderings_Otop__class_Otop(X1) = c_Orderings_Otop__class_Otop(X2) ) ).

cnf(i_0_1942_034,axiom,
    ( X1 != X2
    | esk35_5(X1,X3,X4,X5,X6) = esk35_5(X2,X3,X4,X5,X6) ) ).

cnf(i_0_1943_035,axiom,
    ( X1 != X2
    | esk35_5(X3,X1,X4,X5,X6) = esk35_5(X3,X2,X4,X5,X6) ) ).

cnf(i_0_1944_036,axiom,
    ( X1 != X2
    | esk35_5(X3,X4,X1,X5,X6) = esk35_5(X3,X4,X2,X5,X6) ) ).

cnf(i_0_1945_037,axiom,
    ( X1 != X2
    | esk35_5(X3,X4,X5,X1,X6) = esk35_5(X3,X4,X5,X2,X6) ) ).

cnf(i_0_1946_038,axiom,
    ( X1 != X2
    | esk35_5(X3,X4,X5,X6,X1) = esk35_5(X3,X4,X5,X6,X2) ) ).

cnf(i_0_1947_039,axiom,
    ( X1 != X2
    | esk34_4(X1,X3,X4,X5) = esk34_4(X2,X3,X4,X5) ) ).

cnf(i_0_1948_040,axiom,
    ( X1 != X2
    | esk34_4(X3,X1,X4,X5) = esk34_4(X3,X2,X4,X5) ) ).

cnf(i_0_1949_041,axiom,
    ( X1 != X2
    | esk34_4(X3,X4,X1,X5) = esk34_4(X3,X4,X2,X5) ) ).

cnf(i_0_1950_042,axiom,
    ( X1 != X2
    | esk34_4(X3,X4,X5,X1) = esk34_4(X3,X4,X5,X2) ) ).

cnf(i_0_1951_043,axiom,
    ( X1 != X2
    | esk38_3(X1,X3,X4) = esk38_3(X2,X3,X4) ) ).

cnf(i_0_1952_044,axiom,
    ( X1 != X2
    | esk38_3(X3,X1,X4) = esk38_3(X3,X2,X4) ) ).

cnf(i_0_1953_045,axiom,
    ( X1 != X2
    | esk38_3(X3,X4,X1) = esk38_3(X3,X4,X2) ) ).

cnf(i_0_1954_046,axiom,
    ( X1 != X2
    | esk13_4(X1,X3,X4,X5) = esk13_4(X2,X3,X4,X5) ) ).

cnf(i_0_1955_047,axiom,
    ( X1 != X2
    | esk13_4(X3,X1,X4,X5) = esk13_4(X3,X2,X4,X5) ) ).

cnf(i_0_1956_048,axiom,
    ( X1 != X2
    | esk13_4(X3,X4,X1,X5) = esk13_4(X3,X4,X2,X5) ) ).

cnf(i_0_1957_049,axiom,
    ( X1 != X2
    | esk13_4(X3,X4,X5,X1) = esk13_4(X3,X4,X5,X2) ) ).

cnf(i_0_1958_050,axiom,
    ( X1 != X2
    | esk12_4(X1,X3,X4,X5) = esk12_4(X2,X3,X4,X5) ) ).

cnf(i_0_1959_051,axiom,
    ( X1 != X2
    | esk12_4(X3,X1,X4,X5) = esk12_4(X3,X2,X4,X5) ) ).

cnf(i_0_1960_052,axiom,
    ( X1 != X2
    | esk12_4(X3,X4,X1,X5) = esk12_4(X3,X4,X2,X5) ) ).

cnf(i_0_1961_053,axiom,
    ( X1 != X2
    | esk12_4(X3,X4,X5,X1) = esk12_4(X3,X4,X5,X2) ) ).

cnf(i_0_1962_054,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastLessThan(X1,X3,X4) = c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X4) ) ).

cnf(i_0_1963_055,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastLessThan(X3,X1,X4) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X2,X4) ) ).

cnf(i_0_1964_056,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X2) ) ).

cnf(i_0_1965_057,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__case(X1,X3,X4,X5) = c_Nat_Onat_Onat__case(X2,X3,X4,X5) ) ).

cnf(i_0_1966_058,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__case(X3,X1,X4,X5) = c_Nat_Onat_Onat__case(X3,X2,X4,X5) ) ).

cnf(i_0_1967_059,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__case(X3,X4,X1,X5) = c_Nat_Onat_Onat__case(X3,X4,X2,X5) ) ).

cnf(i_0_1968_060,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__case(X3,X4,X5,X1) = c_Nat_Onat_Onat__case(X3,X4,X5,X2) ) ).

cnf(i_0_1969_061,axiom,
    ( X1 != X2
    | c_Sum__Type_OPlus(X1,X3,X4,X5) = c_Sum__Type_OPlus(X2,X3,X4,X5) ) ).

cnf(i_0_1970_062,axiom,
    ( X1 != X2
    | c_Sum__Type_OPlus(X3,X1,X4,X5) = c_Sum__Type_OPlus(X3,X2,X4,X5) ) ).

cnf(i_0_1971_063,axiom,
    ( X1 != X2
    | c_Sum__Type_OPlus(X3,X4,X1,X5) = c_Sum__Type_OPlus(X3,X4,X2,X5) ) ).

cnf(i_0_1972_064,axiom,
    ( X1 != X2
    | c_Sum__Type_OPlus(X3,X4,X5,X1) = c_Sum__Type_OPlus(X3,X4,X5,X2) ) ).

cnf(i_0_1973_065,axiom,
    ( X1 != X2
    | c_Nat_Osize__class_Osize(X1,X3) = c_Nat_Osize__class_Osize(X2,X3) ) ).

cnf(i_0_1974_066,axiom,
    ( X1 != X2
    | c_Nat_Osize__class_Osize(X3,X1) = c_Nat_Osize__class_Osize(X3,X2) ) ).

cnf(i_0_1975_067,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__size(X1) = c_Nat_Onat_Onat__size(X2) ) ).

cnf(i_0_1976_068,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__idom(X1)
    | class_Rings_Olinordered__idom(X2) ) ).

cnf(i_0_1977_069,axiom,
    ( X1 != X2
    | ~ c_FunDef_Oin__rel(X1,X3,X4,X5,X6)
    | c_FunDef_Oin__rel(X2,X3,X4,X5,X6) ) ).

cnf(i_0_1978_070,axiom,
    ( X1 != X2
    | ~ c_FunDef_Oin__rel(X3,X1,X4,X5,X6)
    | c_FunDef_Oin__rel(X3,X2,X4,X5,X6) ) ).

cnf(i_0_1979_071,axiom,
    ( X1 != X2
    | ~ c_FunDef_Oin__rel(X3,X4,X1,X5,X6)
    | c_FunDef_Oin__rel(X3,X4,X2,X5,X6) ) ).

cnf(i_0_1980_072,axiom,
    ( X1 != X2
    | ~ c_FunDef_Oin__rel(X3,X4,X5,X1,X6)
    | c_FunDef_Oin__rel(X3,X4,X5,X2,X6) ) ).

cnf(i_0_1981_073,axiom,
    ( X1 != X2
    | ~ c_FunDef_Oin__rel(X3,X4,X5,X6,X1)
    | c_FunDef_Oin__rel(X3,X4,X5,X6,X2) ) ).

cnf(i_0_1982_074,axiom,
    ( X1 != X2
    | ~ class_Orderings_Olinorder(X1)
    | class_Orderings_Olinorder(X2) ) ).

cnf(i_0_1983_075,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | class_Groups_Oordered__ab__semigroup__add__imp__le(X2) ) ).

cnf(i_0_1984_076,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
    | class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).

cnf(i_0_1985_077,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__semigroup__add(X1)
    | class_Groups_Oordered__ab__semigroup__add(X2) ) ).

cnf(i_0_1986_078,axiom,
    ( X1 != X2
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | class_Groups_Olinordered__ab__group__add(X2) ) ).

cnf(i_0_1987_079,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | class_Groups_Oordered__comm__monoid__add(X2) ) ).

cnf(i_0_1988_080,axiom,
    ( X1 != X2
    | ~ class_Rings_Oring__1(X1)
    | class_Rings_Oring__1(X2) ) ).

cnf(i_0_1989_081,axiom,
    ( X1 != X2
    | ~ class_Rings_Ocomm__semiring__1(X1)
    | class_Rings_Ocomm__semiring__1(X2) ) ).

cnf(i_0_1990_082,axiom,
    ( X1 != X2
    | ~ hBOOL(X1)
    | hBOOL(X2) ) ).

cnf(i_0_1991_083,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semidom(X1)
    | class_Rings_Olinordered__semidom(X2) ) ).

cnf(i_0_1992_084,axiom,
    ( X1 != X2
    | ~ class_Int_Oring__char__0(X1)
    | class_Int_Oring__char__0(X2) ) ).

cnf(i_0_1993_085,axiom,
    ( X1 != X2
    | ~ class_Orderings_Opreorder(X1)
    | class_Orderings_Opreorder(X2) ) ).

cnf(i_0_1994_086,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oorder(X1)
    | class_Orderings_Oorder(X2) ) ).

cnf(i_0_1995_087,axiom,
    ( X1 != X2
    | ~ class_Groups_Oab__semigroup__add(X1)
    | class_Groups_Oab__semigroup__add(X2) ) ).

cnf(i_0_1996_088,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocancel__semigroup__add(X1)
    | class_Groups_Ocancel__semigroup__add(X2) ) ).

cnf(i_0_1997_089,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocancel__ab__semigroup__add(X1)
    | class_Groups_Ocancel__ab__semigroup__add(X2) ) ).

cnf(i_0_1998_090,axiom,
    ( X1 != X2
    | ~ class_Orderings_Otop(X1)
    | class_Orderings_Otop(X2) ) ).

cnf(i_0_1999_091,axiom,
    ( X1 != X2
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ).

cnf(i_0_2000_092,axiom,
    ( X1 != X2
    | ~ class_Finite__Set_Ofinite(X1)
    | class_Finite__Set_Ofinite(X2) ) ).

cnf(i_0_2001_093,axiom,
    ( X1 != X2
    | ~ c_Arrow__Order__Mirabelle_OIIA(X1)
    | c_Arrow__Order__Mirabelle_OIIA(X2) ) ).

cnf(i_0_2002_094,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | class_Groups_Ocomm__monoid__add(X2) ) ).

cnf(i_0_2003_095,axiom,
    ( X1 != X2
    | ~ class_Groups_Omonoid__add(X1)
    | class_Groups_Omonoid__add(X2) ) ).

cnf(i_0_2004_096,axiom,
    ( X1 != X2
    | ~ class_Rings_Ozero__neq__one(X1)
    | class_Rings_Ozero__neq__one(X2) ) ).

cnf(i_0_2005_097,axiom,
    ( X1 != X2
    | ~ class_Groups_Ozero(X1)
    | class_Groups_Ozero(X2) ) ).

cnf(i_0_2006_098,axiom,
    ( X1 != X2
    | ~ class_Groups_Oone(X1)
    | class_Groups_Oone(X2) ) ).

cnf(i_0_2007_099,axiom,
    ( X1 != X2
    | ~ c_Arrow__Order__Mirabelle_Odictator(X1,X3)
    | c_Arrow__Order__Mirabelle_Odictator(X2,X3) ) ).

cnf(i_0_2008_100,axiom,
    ( X1 != X2
    | ~ c_Arrow__Order__Mirabelle_Odictator(X3,X1)
    | c_Arrow__Order__Mirabelle_Odictator(X3,X2) ) ).

cnf(i_0_2009_101,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image__simple(X1,X3,X4,X5,X6,X7)
    | c_Finite__Set_Ofolding__image__simple(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_2010_102,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image__simple(X3,X1,X4,X5,X6,X7)
    | c_Finite__Set_Ofolding__image__simple(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_2011_103,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image__simple(X3,X4,X1,X5,X6,X7)
    | c_Finite__Set_Ofolding__image__simple(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_2012_104,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image__simple(X3,X4,X5,X1,X6,X7)
    | c_Finite__Set_Ofolding__image__simple(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_2013_105,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image__simple(X3,X4,X5,X6,X1,X7)
    | c_Finite__Set_Ofolding__image__simple(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_2014_106,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image__simple(X3,X4,X5,X6,X7,X1)
    | c_Finite__Set_Ofolding__image__simple(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_2015_107,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofinite(X1,X3)
    | c_Finite__Set_Ofinite(X2,X3) ) ).

cnf(i_0_2016_108,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofinite(X3,X1)
    | c_Finite__Set_Ofinite(X3,X2) ) ).

cnf(i_0_2017_109,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oord(X1)
    | class_Orderings_Oord(X2) ) ).

cnf(i_0_2018_110,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X1,X3,X4,X5)
    | c_Fun_Oinj__on(X2,X3,X4,X5) ) ).

cnf(i_0_2019_111,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X1,X4,X5)
    | c_Fun_Oinj__on(X3,X2,X4,X5) ) ).

cnf(i_0_2020_112,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X4,X1,X5)
    | c_Fun_Oinj__on(X3,X4,X2,X5) ) ).

cnf(i_0_2021_113,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X4,X5,X1)
    | c_Fun_Oinj__on(X3,X4,X5,X2) ) ).

cnf(i_0_2022_114,axiom,
    ( X1 != X2
    | ~ c_Arrow__Order__Mirabelle_Ounanimity(X1)
    | c_Arrow__Order__Mirabelle_Ounanimity(X2) ) ).

cnf(i_0_2023,plain,
    X1 = X1,
    inference(equality_inference,[],[1140]) ).

cnf(i_0_2024,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X5))),c_Wellfounded_Olex__prod(X1,X2,X6,X7)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X4),X5)),X7)) ),
    inference(equality_inference,[],[1172]) ).

cnf(i_0_2025,plain,
    ( X1 = X1
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X1),c_Set_Oimage(X3,X2,X4,X5)))
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X1),c_Set_Oimage(X3,X2,X4,X5))) ),
    inference(equality_inference,[],[1207]) ).

cnf(i_0_2026,plain,
    ( X1 = X2
    | X3 = X2
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X4),X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X4),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(equality_inference,[],[1208]) ).

cnf(i_0_2027,plain,
    ( X1 = X2
    | X1 = X3
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X4),X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X4),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(equality_inference,[],[1209]) ).

cnf(i_0_2028,plain,
    ( X1 = X2
    | X1 = X3
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),c_Arrow__Order__Mirabelle_Obelow(X4,X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X4),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(equality_inference,[],[1213]) ).

cnf(i_0_2029,plain,
    ( X1 = X2
    | X3 = X2
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)),c_Arrow__Order__Mirabelle_Obelow(X4,X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X4),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(equality_inference,[],[1214]) ).

cnf(i_0_2030,plain,
    ( X1 = X2
    | X3 = X1
    | X3 = X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X4),X1),X2)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X4),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(equality_inference,[],[1239]) ).

cnf(i_0_2031,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X4),X1),X2)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X4),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(equality_inference,[],[1241]) ).

cnf(i_0_2032,plain,
    ( X1 = X2
    | X3 = X2
    | X3 = X2
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X4),X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X4),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(equality_inference,[],[1250]) ).

cnf(i_0_2033,plain,
    ( X1 = X2
    | X1 = X2
    | X1 = X3
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X4),X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X4),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(equality_inference,[],[1251]) ).

cnf(i_0_2034,plain,
    ( X1 = X2
    | X2 = X3
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X4),X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X4),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(equality_inference,[],[1253]) ).

cnf(i_0_2035,plain,
    ( X1 = X2
    | X3 = X2
    | X3 = X1
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),c_Arrow__Order__Mirabelle_Obelow(X4,X1,X2)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X4),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(equality_inference,[],[1254]) ).

cnf(i_0_2036,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),c_Arrow__Order__Mirabelle_Obelow(X4,X1,X2)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X4),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(equality_inference,[],[1257]) ).

cnf(i_0_2037,plain,
    ( X1 = X2
    | X3 = X1
    | X1 = X3
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),c_Arrow__Order__Mirabelle_Obelow(X4,X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X4),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(equality_inference,[],[1266]) ).

cnf(i_0_2038,plain,
    ( X1 = X2
    | X2 = X1
    | X3 = X2
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)),c_Arrow__Order__Mirabelle_Obelow(X4,X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X4),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(equality_inference,[],[1267]) ).

cnf(i_0_2039,plain,
    ( X1 = X2
    | X3 = X1
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),c_Arrow__Order__Mirabelle_Obelow(X4,X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X4),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(equality_inference,[],[1269]) ).

cnf(i_0_2040,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X3)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X4),X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X4),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(equality_inference,[],[1288]) ).

cnf(i_0_2041,plain,
    ( X1 = esk34_4(hAPP(X2,X1),X2,X3,X4)
    | ~ c_Fun_Oinj__on(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))
    | ~ hBOOL(hAPP(hAPP(c_member(X3),hAPP(X2,X1)),c_Set_Oimage(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))) ),
    inference(equality_inference,[],[1295]) ).

cnf(i_0_2042,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X3)),c_Arrow__Order__Mirabelle_Obelow(X4,X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X4),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(equality_inference,[],[1299]) ).

cnf(i_0_2043,plain,
    ( c_Set_Oimage(X1,X2,X3,c_Set_Oimage(X2,X1,c_Hilbert__Choice_Oinv__into(X1,X2,X4,X3),X5)) = X5
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X5),c_Set_Oimage(X1,X2,X3,X4))) ),
    inference(equality_inference,[],[1313]) ).

cnf(i_0_2044,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X2,X1,X3,X4)),c_Set_Oimage(X2,X1,X3,X5)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X4),X5)) ),
    inference(equality_inference,[],[1334]) ).

cnf(i_0_2045,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X3),X1))),
    inference(equality_inference,[],[1343]) ).

cnf(i_0_2046,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X3),X2))),
    inference(equality_inference,[],[1344]) ).

cnf(i_0_2047,plain,
    hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),c_Set_Oimage(X4,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))),
    inference(equality_inference,[],[1356]) ).

cnf(i_0_2048,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),c_Set_Oimage(X4,X1,X2,X5)))
    | ~ hBOOL(hAPP(hAPP(c_member(X4),X3),X5)) ),
    inference(equality_inference,[],[1362]) ).

cnf(i_0_2049,plain,
    ( X1 = X1
    | ~ c_Fun_Oinj__on(X2,X3,X4,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
    inference(equality_inference,[],[1365]) ).

cnf(i_0_2050,plain,
    ( ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
    | hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(X3,X4)) = X4 ),
    inference(equality_inference,[],[1380]) ).

cnf(i_0_2051,plain,
    X1 = X1,
    inference(equality_inference,[],[1381]) ).

cnf(i_0_2052,plain,
    ( ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X4,X3),hAPP(X3,X5)) = X5
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X4)) ),
    inference(equality_inference,[],[1384]) ).

cnf(i_0_2053,plain,
    ( X1 = X2
    | X2 = X1
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X3),X1))) ),
    inference(equality_inference,[],[1392]) ).

cnf(i_0_2054,plain,
    ( X1 = X2
    | X1 = X2
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X3),X2))) ),
    inference(equality_inference,[],[1393]) ).

cnf(i_0_2055,plain,
    ( X1 = X1
    | ~ c_Fun_Oinj__on(X2,X3,X4,X5)
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X1),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X1),X5)) ),
    inference(equality_inference,[],[1450]) ).

cnf(i_0_2056,plain,
    ( X1 = X1
    | ~ c_Fun_Oinj__on(X2,X3,X4,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
    inference(equality_inference,[],[1521]) ).

cnf(i_0_2057,plain,
    ( X1 = X1
    | ~ class_Orderings_Olinorder(X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X3)) ),
    inference(equality_inference,[],[1524]) ).

cnf(i_0_2058,plain,
    ( X1 = X1
    | ~ class_Orderings_Olinorder(X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X3),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X3),X1)) ),
    inference(equality_inference,[],[1525]) ).

cnf(i_0_2059,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X2)),
    inference(equality_inference,[],[1537]) ).

cnf(i_0_2060,plain,
    ( X1 = X1
    | hBOOL(hAPP(hAPP(c_member(X2),X3),X1))
    | hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) ),
    inference(equality_inference,[],[1569]) ).

cnf(i_0_2061,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X2,X3))),
    inference(equality_inference,[],[1607]) ).

cnf(i_0_2062,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(equality_inference,[],[1622]) ).

cnf(i_0_2063,plain,
    ( ~ class_Int_Oring__char__0(X1)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),c_Groups_Ozero__class_Ozero(X1)),c_Int_Oring__1__class_OInts(X1))) ),
    inference(equality_inference,[],[1660]) ).

cnf(i_0_2064,plain,
    ( c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))
    | ~ c_Finite__Set_Ofinite(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(equality_inference,[],[1661]) ).

cnf(i_0_2065,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))),
    inference(equality_inference,[],[1662]) ).

cnf(i_0_2066,plain,
    hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X2)),
    inference(equality_inference,[],[1673]) ).

cnf(i_0_2067,plain,
    ( ~ class_Orderings_Olinorder(X1)
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
    inference(equality_inference,[],[1717]) ).

cnf(i_0_2068,plain,
    ( ~ class_Orderings_Oorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
    inference(equality_inference,[],[1732]) ).

cnf(i_0_2069,plain,
    ( ~ class_Orderings_Oorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
    inference(equality_inference,[],[1734]) ).

cnf(i_0_2070,plain,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
    inference(equality_inference,[],[1735]) ).

cnf(i_0_2071,plain,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
    inference(equality_inference,[],[1736]) ).

cnf(i_0_2072,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
    inference(equality_inference,[],[1742]) ).

cnf(i_0_2073,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
    inference(equality_inference,[],[1743]) ).

cnf(i_0_2074,plain,
    ( X1 = X1
    | ~ class_Groups_Ocancel__semigroup__add(X2) ),
    inference(equality_inference,[],[1748]) ).

cnf(i_0_2075,plain,
    ( X1 = X1
    | ~ class_Groups_Ocancel__ab__semigroup__add(X2) ),
    inference(equality_inference,[],[1749]) ).

cnf(i_0_2076,plain,
    ( X1 = X1
    | ~ class_Groups_Ocancel__semigroup__add(X2) ),
    inference(equality_inference,[],[1751]) ).

cnf(i_0_2077,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))),
    inference(equality_inference,[],[1761]) ).

cnf(i_0_2078,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(equality_inference,[],[1763]) ).

cnf(i_0_2079,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
    inference(equality_inference,[],[1769]) ).

cnf(i_0_2080,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
    inference(equality_inference,[],[1770]) ).

cnf(i_0_2081,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))),
    inference(equality_inference,[],[1771]) ).

cnf(i_0_2082,plain,
    X1 = X1,
    inference(equality_inference,[],[1777]) ).

cnf(i_0_2083,plain,
    X1 = X1,
    inference(equality_inference,[],[1778]) ).

cnf(i_0_2084,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X1))),
    inference(equality_inference,[],[1779]) ).

cnf(i_0_2085,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
    inference(equality_inference,[],[1782]) ).

cnf(i_0_2086,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X1))),
    inference(equality_inference,[],[1790]) ).

cnf(i_0_2087,plain,
    X1 = X1,
    inference(equality_inference,[],[1791]) ).

cnf(i_0_2088,plain,
    ( ~ class_Orderings_Oorder(X1)
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X2)) ),
    inference(equality_inference,[],[1814]) ).

cnf(i_0_2089,plain,
    ( ~ class_Orderings_Opreorder(X1)
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X2)) ),
    inference(equality_inference,[],[1815]) ).

cnf(i_0_2090,plain,
    ( ~ class_Orderings_Oorder(X1)
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X2)) ),
    inference(equality_inference,[],[1816]) ).

cnf(i_0_2091,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
    inference(equality_inference,[],[1828]) ).

cnf(i_0_2092,plain,
    hBOOL(hAPP(hAPP(c_fequal,X1),X1)),
    inference(equality_inference,[],[1829]) ).

cnf(i_0_2093,plain,
    ( ~ class_Groups_Olinordered__ab__group__add(X1)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(equality_inference,[],[1836]) ).

cnf(i_0_2094,plain,
    ( ~ class_Groups_Olinordered__ab__group__add(X1)
    | c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(equality_inference,[],[1837]) ).

cnf(i_0_2095,plain,
    ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(equality_inference,[],[1838]) ).

cnf(i_0_2096,plain,
    X1 = X1,
    inference(equality_inference,[],[1854]) ).

cnf(i_0_2097,plain,
    ( v_e____ = v_d____
    | v_b____ = v_a____
    | epred1_0 ),
    inference(scs_inference,[],[i_0_1124,i_0_1129,i_0_1077]) ).

cnf(i_0_2098,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ epred1_0
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____)))) ),
    inference(scs_inference,[],[i_0_1427,i_0_1088]) ).

cnf(i_0_2099,plain,
    ( hAPP(v_h____,esk47_0) != v_n____
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | ~ epred1_0
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____)))) ),
    inference(scs_inference,[],[i_0_1427,i_0_1094]) ).

cnf(i_0_2100,plain,
    ( hAPP(v_h____,esk47_0) = v_n____
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ epred1_0
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____)))) ),
    inference(scs_inference,[],[i_0_1427,i_0_1096]) ).

cnf(i_0_2101,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | ~ epred1_0
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____)))) ),
    inference(scs_inference,[],[i_0_1354,i_0_2045,i_0_1098]) ).

cnf(i_0_2102,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ epred1_0
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____)))) ),
    inference(scs_inference,[],[i_0_1427,i_0_1109]) ).

cnf(i_0_2103,plain,
    ( hAPP(v_h____,esk47_0) != v_n____
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | ~ epred1_0
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk47_0)),v_c____),v_e____)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____)))) ),
    inference(scs_inference,[],[i_0_1427,i_0_1115]) ).

cnf(i_0_2104,plain,
    ( hAPP(v_h____,esk47_0) = v_n____
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk47_0)),v_e____)))
    | ~ epred1_0
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____)))) ),
    inference(scs_inference,[],[i_0_1427,i_0_1117]) ).

cnf(i_0_2105,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk47_0)),v_n____))
    | ~ epred1_0
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____)))) ),
    inference(scs_inference,[],[i_0_1354,i_0_2045,i_0_1119]) ).

cnf(i_0_2106,plain,
    ( hAPP(v_h____,X1) != v_n____
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1)),v_e____)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1)),v_c____),v_e____))) ),
    inference(scs_inference,[],[i_0_1355,i_0_1197]) ).

cnf(i_0_2107,plain,
    ( hAPP(v_h____,X1) != v_n____
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1)),v_c____),v_e____))) ),
    inference(scs_inference,[],[i_0_1355,i_0_1237]) ).

cnf(i_0_2108,plain,
    ( hAPP(v_h____,X1) != v_n____
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1)),v_c____),v_e____))) ),
    inference(scs_inference,[],[i_0_1429,i_0_1247]) ).

cnf(i_0_2109,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1)),v_e____))) ),
    inference(scs_inference,[],[i_0_1429,i_0_1272]) ).

cnf(i_0_2110,plain,
    ( hAPP(v_h____,X1) = v_n____
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1)),v_e____))) ),
    inference(scs_inference,[],[i_0_1429,i_0_1274]) ).

cnf(i_0_2111,plain,
    ( hAPP(v_h____,X1) != v_n____
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1)),v_c____),v_e____))) ),
    inference(scs_inference,[],[i_0_1427,i_0_1279]) ).

cnf(i_0_2112,plain,
    ( hAPP(v_h____,X1) = v_n____
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1)),v_e____))) ),
    inference(scs_inference,[],[i_0_1427,i_0_1298]) ).

cnf(i_0_2113,plain,
    ~ c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1),X2),X2,X3),
    inference(scs_inference,[],[i_0_2045,i_0_1286]) ).

cnf(i_0_2114,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5))
    | ~ c_FunDef_Oin__rel(X1,X2,X5,X3,X4) ),
    inference(rename_variables,[],[i_0_1286]) ).

cnf(i_0_2115,plain,
    c_FunDef_Oin__rel(X1,X2,hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X3,X4),
    inference(scs_inference,[],[i_0_2045,i_0_2077,i_0_1286,i_0_1292]) ).

cnf(i_0_2116,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))),
    inference(rename_variables,[],[i_0_2077]) ).

cnf(i_0_2117,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5))
    | c_FunDef_Oin__rel(X1,X2,X5,X3,X4) ),
    inference(rename_variables,[],[i_0_1292]) ).

cnf(i_0_2118,plain,
    hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),c_Set_Oimage(X4,X1,X2,hAPP(c_fequal,X3)))),
    inference(scs_inference,[],[i_0_2045,i_0_2077,i_0_2116,i_0_1286,i_0_1292,i_0_1353]) ).

cnf(i_0_2119,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hBOOL(hAPP(hAPP(c_member(X4),hAPP(X5,X2)),c_Set_Oimage(X1,X4,X5,X3))) ),
    inference(rename_variables,[],[i_0_1353]) ).

cnf(i_0_2120,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X3,c_Set_Oinsert(X1,X2,X4)))),
    inference(scs_inference,[],[i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_1286,i_0_1292,i_0_1353,i_0_1391]) ).

cnf(i_0_2121,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Set_Oinsert(X1,X3,X2))),
    inference(rename_variables,[],[i_0_1568]) ).

cnf(i_0_2122,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1,X2,X3)),X4))
    | hBOOL(hAPP(hAPP(c_member(X1),X2),X4)) ),
    inference(rename_variables,[],[i_0_1391]) ).

cnf(i_0_2123,plain,
    c_Set_Oinsert(X1,hAPP(X2,X3),c_Set_Oimage(X4,X1,X2,hAPP(c_fequal,X3))) = c_Set_Oimage(X4,X1,X2,hAPP(c_fequal,X3)),
    inference(scs_inference,[],[i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403]) ).

cnf(i_0_2124,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | c_Set_Oinsert(X4,hAPP(X5,X2),c_Set_Oimage(X1,X4,X5,X3)) = c_Set_Oimage(X1,X4,X5,X3) ),
    inference(rename_variables,[],[i_0_1403]) ).

cnf(i_0_2125,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X3,hAPP(c_fequal,X2)))),
    inference(scs_inference,[],[i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531]) ).

cnf(i_0_2126,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X4,X3))) ),
    inference(rename_variables,[],[i_0_1531]) ).

cnf(i_0_2127,plain,
    c_Set_Oinsert(X1,X2,hAPP(c_fequal,X2)) = hAPP(c_fequal,X2),
    inference(scs_inference,[],[i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698]) ).

cnf(i_0_2128,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | c_Set_Oinsert(X1,X2,X3) = X3 ),
    inference(rename_variables,[],[i_0_1698]) ).

cnf(i_0_2129,plain,
    hBOOL(hAPP(c_Set_Oimage(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),hAPP(X3,X4))),
    inference(scs_inference,[],[i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_1351,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718]) ).

cnf(i_0_2130,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hBOOL(hAPP(X3,X2)) ),
    inference(rename_variables,[],[i_0_1718]) ).

cnf(i_0_2131,plain,
    ~ hBOOL(hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1),X2),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3))),
    inference(scs_inference,[],[i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_1351,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762]) ).

cnf(i_0_2132,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(rename_variables,[],[i_0_1762]) ).

cnf(i_0_2133,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),X2)),c_Wellfounded_Ofinite__psubset(X1))),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_1351,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199]) ).

cnf(i_0_2134,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),X3)),c_Wellfounded_Ofinite__psubset(X1))) ),
    inference(rename_variables,[],[i_0_1199]) ).

cnf(i_0_2135,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X1,X1,c_COMBI(X1),X2)),X2)),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_1351,i_0_1325,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203]) ).

cnf(i_0_2136,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X1,X2,X4,hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X5))))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),c_Set_Oimage(X1,X2,X3,X4)),X5)) ),
    inference(rename_variables,[],[i_0_1203]) ).

cnf(i_0_2137,plain,
    c_Set_Oimage(X1,X2,X3,X4) = c_Set_Oimage(X1,X2,X3,esk37_5(X4,X3,X1,c_Set_Oimage(X1,X2,X3,X4),X2)),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_1745,i_0_1351,i_0_1325,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221]) ).

cnf(i_0_2138,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
    inference(rename_variables,[],[i_0_1745]) ).

cnf(i_0_2139,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Set_Oimage(X3,X1,X4,X5)))
    | X2 = c_Set_Oimage(X3,X1,X4,esk37_5(X5,X4,X3,X2,X1)) ),
    inference(rename_variables,[],[i_0_1221]) ).

cnf(i_0_2140,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,X2),tc_HOL_Obool),c_FuncSet_OPi(X1,X2,c_Set_Oinsert(X1,X3,X4),X5)),c_FuncSet_OPi(X1,X2,X4,X5))),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_2121,i_0_1745,i_0_1351,i_0_1325,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248]) ).

cnf(i_0_2141,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,X4),tc_HOL_Obool),c_FuncSet_OPi(X1,X4,X3,X5)),c_FuncSet_OPi(X1,X4,X2,X5))) ),
    inference(rename_variables,[],[i_0_1248]) ).

cnf(i_0_2142,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X2,X1,X3,X4)),c_Set_Oimage(X2,X1,X3,c_Set_Oinsert(X2,X5,X4)))),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_2121,i_0_1745,i_0_1351,i_0_1325,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271]) ).

cnf(i_0_2143,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Set_Oimage(X1,X4,X5,X2)),c_Set_Oimage(X1,X4,X5,X3))) ),
    inference(rename_variables,[],[i_0_1271]) ).

cnf(i_0_2144,plain,
    hAPP(X1,hAPP(c_Hilbert__Choice_Oinv__into(X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),X1),hAPP(X1,X4))) = hAPP(X1,X4),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_2121,i_0_1745,i_0_1351,i_0_1325,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296]) ).

cnf(i_0_2145,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oimage(X3,X1,X4,X5)))
    | hAPP(X4,hAPP(c_Hilbert__Choice_Oinv__into(X3,X1,X5,X4),X2)) = X2 ),
    inference(rename_variables,[],[i_0_1296]) ).

cnf(i_0_2146,plain,
    c_Fun_Oinj__on(X1,X2,c_Hilbert__Choice_Oinv__into(X2,X1,X3,X4),c_Set_Oimage(X2,X1,X4,X3)),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_2121,i_0_1745,i_0_2138,i_0_1351,i_0_1325,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301]) ).

cnf(i_0_2147,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
    inference(rename_variables,[],[i_0_1745]) ).

cnf(i_0_2148,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Set_Oimage(X3,X1,X4,X5)))
    | c_Fun_Oinj__on(X1,X3,c_Hilbert__Choice_Oinv__into(X3,X1,X5,X4),X2) ),
    inference(rename_variables,[],[i_0_1301]) ).

cnf(i_0_2149,plain,
    hAPP(X1,X2) = hAPP(X1,esk36_4(c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)),X1,X3,hAPP(X1,X2))),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_2121,i_0_1745,i_0_2138,i_0_1351,i_0_1325,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318]) ).

cnf(i_0_2150,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oimage(X3,X1,X4,X5)))
    | X2 = hAPP(X4,esk36_4(X5,X4,X3,X2)) ),
    inference(rename_variables,[],[i_0_1318]) ).

cnf(i_0_2151,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),c_Wellfounded_Omeasure(X1,X3))),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_2121,i_0_1745,i_0_2138,i_0_1776,i_0_1351,i_0_1325,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328]) ).

cnf(i_0_2152,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
    inference(rename_variables,[],[i_0_1776]) ).

cnf(i_0_2153,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1,X2)),hAPP(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_Wellfounded_Omeasure(X4,X1))) ),
    inference(rename_variables,[],[i_0_1328]) ).

cnf(i_0_2154,plain,
    hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,esk11_0),X1)),c_Arrow__Order__Mirabelle_OLin)),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_2121,i_0_1745,i_0_2138,i_0_1776,i_0_1351,i_0_1325,i_0_1494,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331]) ).

cnf(i_0_2155,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1),X2)),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(rename_variables,[],[i_0_1331]) ).

cnf(i_0_2156,plain,
    hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,esk11_0),X1)),c_Arrow__Order__Mirabelle_OLin)),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_2121,i_0_1745,i_0_2138,i_0_1776,i_0_1351,i_0_1325,i_0_1494,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332]) ).

cnf(i_0_2157,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1),X2)),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(rename_variables,[],[i_0_1332]) ).

cnf(i_0_2158,plain,
    c_Set_Oimage(X1,X2,c_Nat_OSuc,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_2121,i_0_1745,i_0_2138,i_0_1776,i_0_1351,i_0_1325,i_0_1494,i_0_1863,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339]) ).

cnf(i_0_2159,plain,
    hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(rename_variables,[],[i_0_1863]) ).

cnf(i_0_2160,plain,
    ( hAPP(X1,hAPP(c_Hilbert__Choice_Oinv__into(X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),X1),X4)) = X4
    | c_Set_Oimage(X2,X3,X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)) ),
    inference(rename_variables,[],[i_0_1339]) ).

cnf(i_0_2161,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),hAPP(c_Nat_OSuc,X2))),c_Wellfounded_Omlex__prod(X1,c_Nat_OSuc,X3))),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_2121,i_0_1785,i_0_1745,i_0_2138,i_0_1776,i_0_1351,i_0_1325,i_0_1494,i_0_1863,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340]) ).

cnf(i_0_2162,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
    inference(rename_variables,[],[i_0_1785]) ).

cnf(i_0_2163,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1,X2)),hAPP(X1,X3)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_Wellfounded_Omlex__prod(X4,X1,X5))) ),
    inference(rename_variables,[],[i_0_1340]) ).

cnf(i_0_2164,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),hAPP(c_Nat_OSuc,X2))),c_Wellfounded_Omeasure(X1,c_Nat_OSuc))),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_2121,i_0_1785,i_0_2162,i_0_1745,i_0_2138,i_0_1776,i_0_1351,i_0_1325,i_0_1494,i_0_1863,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346]) ).

cnf(i_0_2165,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
    inference(rename_variables,[],[i_0_1785]) ).

cnf(i_0_2166,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1,X2)),hAPP(X1,X3)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_Wellfounded_Omeasure(X4,X1))) ),
    inference(rename_variables,[],[i_0_1346]) ).

cnf(i_0_2167,plain,
    hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),hAPP(c_COMBC(X3,tc_fun(X3,tc_HOL_Obool),tc_HOL_Obool),c_member(X3))),hAPP(hAPP(c_COMBC(X3,tc_fun(X3,tc_HOL_Obool),tc_HOL_Obool),c_member(X3)),X4)) = X4,
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_2121,i_0_1785,i_0_2162,i_0_1745,i_0_2138,i_0_1776,i_0_1351,i_0_1325,i_0_1494,i_0_1863,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381]) ).

cnf(i_0_2168,plain,
    ( hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2) != hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)
    | X2 = X3 ),
    inference(rename_variables,[],[i_0_1381]) ).

cnf(i_0_2169,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1,X2,X3)),c_Set_Oinsert(X1,X2,c_Set_Oinsert(X1,X4,X3)))),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_2121,i_0_1785,i_0_2162,i_0_1745,i_0_2138,i_0_1776,i_0_1351,i_0_1325,i_0_1494,i_0_1863,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387]) ).

cnf(i_0_2170,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1,X4,X2)),c_Set_Oinsert(X1,X4,X3))) ),
    inference(rename_variables,[],[i_0_1387]) ).

cnf(i_0_2171,plain,
    ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_2121,i_0_1785,i_0_2162,i_0_1745,i_0_2138,i_0_1776,i_0_1657,i_0_1351,i_0_1325,i_0_1494,i_0_1863,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402]) ).

cnf(i_0_2172,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2))
    | ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
    inference(rename_variables,[],[i_0_1402]) ).

cnf(i_0_2173,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3))))),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_2121,i_0_1785,i_0_2162,i_0_1745,i_0_2138,i_0_1776,i_0_1657,i_0_1351,i_0_1325,i_0_1528,i_0_1494,i_0_1863,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438]) ).

cnf(i_0_2174,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)))),
    inference(rename_variables,[],[i_0_1528]) ).

cnf(i_0_2175,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X3)) ),
    inference(rename_variables,[],[i_0_1438]) ).

cnf(i_0_2176,plain,
    hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X1))),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_2121,i_0_1831,i_0_1785,i_0_2162,i_0_1745,i_0_2138,i_0_1776,i_0_1657,i_0_1351,i_0_1325,i_0_1528,i_0_1494,i_0_1863,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440]) ).

cnf(i_0_2177,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
    inference(rename_variables,[],[i_0_1831]) ).

cnf(i_0_2178,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2))
    | hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
    inference(rename_variables,[],[i_0_1440]) ).

cnf(i_0_2179,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3))),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_2121,i_0_1831,i_0_1785,i_0_2162,i_0_1745,i_0_2138,i_0_1776,i_0_1657,i_0_1351,i_0_1668,i_0_1325,i_0_1528,i_0_1494,i_0_1863,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454]) ).

cnf(i_0_2180,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))),
    inference(rename_variables,[],[i_0_1668]) ).

cnf(i_0_2181,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3)) ),
    inference(rename_variables,[],[i_0_1454]) ).

cnf(i_0_2182,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)),X3))),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_2121,i_0_1831,i_0_1785,i_0_2162,i_0_1745,i_0_2138,i_0_1776,i_0_1657,i_0_1351,i_0_1668,i_0_2180,i_0_1325,i_0_1528,i_0_1494,i_0_1863,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455]) ).

cnf(i_0_2183,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))),
    inference(rename_variables,[],[i_0_1668]) ).

cnf(i_0_2184,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3)) ),
    inference(rename_variables,[],[i_0_1455]) ).

cnf(i_0_2185,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Set_Oinsert(X1,X3,c_Set_Oinsert(X1,X4,X2)))),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_2121,i_0_1831,i_0_1785,i_0_2162,i_0_1745,i_0_2138,i_0_1776,i_0_1657,i_0_1351,i_0_1668,i_0_2180,i_0_1325,i_0_1528,i_0_1494,i_0_1863,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480]) ).

cnf(i_0_2186,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Set_Oinsert(X1,X4,X3))) ),
    inference(rename_variables,[],[i_0_1480]) ).

cnf(i_0_2187,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_2121,i_0_1831,i_0_1785,i_0_2162,i_0_1759,i_0_1745,i_0_2138,i_0_1776,i_0_1657,i_0_1351,i_0_1668,i_0_2180,i_0_1325,i_0_1528,i_0_1494,i_0_1863,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539]) ).

cnf(i_0_2188,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2))) ),
    inference(rename_variables,[],[i_0_1539]) ).

cnf(i_0_2189,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))),X2)),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_2121,i_0_1831,i_0_1785,i_0_2162,i_0_1759,i_0_1745,i_0_2138,i_0_1776,i_0_1657,i_0_1351,i_0_1668,i_0_2180,i_0_1325,i_0_1470,i_0_1528,i_0_1494,i_0_1863,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550]) ).

cnf(i_0_2190,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X2)),
    inference(rename_variables,[],[i_0_1470]) ).

cnf(i_0_2191,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(rename_variables,[],[i_0_1550]) ).

cnf(i_0_2192,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))),X3)),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_2121,i_0_1831,i_0_1785,i_0_2162,i_0_1759,i_0_1745,i_0_2138,i_0_1776,i_0_1657,i_0_1351,i_0_1668,i_0_2180,i_0_1325,i_0_1470,i_0_2190,i_0_1528,i_0_1494,i_0_1863,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552]) ).

cnf(i_0_2193,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X2)),
    inference(rename_variables,[],[i_0_1470]) ).

cnf(i_0_2194,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X3)) ),
    inference(rename_variables,[],[i_0_1552]) ).

cnf(i_0_2195,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)))),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_2121,i_0_1831,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_1776,i_0_1657,i_0_1351,i_0_1668,i_0_2180,i_0_1325,i_0_1470,i_0_2190,i_0_1528,i_0_1494,i_0_1863,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570]) ).

cnf(i_0_2196,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
    inference(rename_variables,[],[i_0_1785]) ).

cnf(i_0_2197,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(rename_variables,[],[i_0_1570]) ).

cnf(i_0_2198,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)),X1)),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_2121,i_0_1831,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_1776,i_0_1657,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_1325,i_0_1470,i_0_2190,i_0_1528,i_0_1494,i_0_1863,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571]) ).

cnf(i_0_2199,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))),
    inference(rename_variables,[],[i_0_1668]) ).

cnf(i_0_2200,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
    inference(rename_variables,[],[i_0_1571]) ).

cnf(i_0_2201,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)))),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_2121,i_0_1831,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_1776,i_0_1657,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_1325,i_0_1470,i_0_2190,i_0_1528,i_0_1494,i_0_1863,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573]) ).

cnf(i_0_2202,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2))) ),
    inference(rename_variables,[],[i_0_1573]) ).

cnf(i_0_2203,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))),X1)),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_2121,i_0_1831,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_1776,i_0_1657,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_1325,i_0_1470,i_0_2190,i_0_1528,i_0_1494,i_0_1863,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575]) ).

cnf(i_0_2204,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
    inference(rename_variables,[],[i_0_1657]) ).

cnf(i_0_2205,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
    inference(rename_variables,[],[i_0_1575]) ).

cnf(i_0_2206,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))),X2)),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_2121,i_0_1831,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_1776,i_0_1657,i_0_2204,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_1325,i_0_1470,i_0_2190,i_0_1528,i_0_1494,i_0_1863,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577]) ).

cnf(i_0_2207,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
    inference(rename_variables,[],[i_0_1657]) ).

cnf(i_0_2208,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3)) ),
    inference(rename_variables,[],[i_0_1577]) ).

cnf(i_0_2209,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))),hAPP(c_Nat_OSuc,v_n____))),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_2121,i_0_1831,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_1776,i_0_1657,i_0_2204,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_1616,i_0_1325,i_0_1470,i_0_2190,i_0_1528,i_0_1494,i_0_1863,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581]) ).

cnf(i_0_2210,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X1))) ),
    inference(rename_variables,[],[i_0_1581]) ).

cnf(i_0_2211,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_2121,i_0_1831,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_1776,i_0_1657,i_0_2204,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1470,i_0_2190,i_0_1528,i_0_1494,i_0_1863,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585]) ).

cnf(i_0_2212,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))),
    inference(rename_variables,[],[i_0_1668]) ).

cnf(i_0_2213,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(rename_variables,[],[i_0_1585]) ).

cnf(i_0_2214,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X1))),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_2121,i_0_1831,i_0_2177,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_1776,i_0_1657,i_0_2204,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1470,i_0_2190,i_0_1528,i_0_1494,i_0_1863,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599]) ).

cnf(i_0_2215,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
    inference(rename_variables,[],[i_0_1831]) ).

cnf(i_0_2216,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
    inference(rename_variables,[],[i_0_1599]) ).

cnf(i_0_2217,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))),X2)),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_2121,i_0_1831,i_0_2177,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_1776,i_0_1657,i_0_2204,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1470,i_0_2190,i_0_1528,i_0_1494,i_0_1863,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601]) ).

cnf(i_0_2218,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
    inference(rename_variables,[],[i_0_1601]) ).

cnf(i_0_2219,plain,
    hAPP(c_Nat_OSuc,X1) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk32_2(hAPP(c_Nat_OSuc,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_2121,i_0_1831,i_0_2177,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_1776,i_0_1657,i_0_2204,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1470,i_0_2190,i_0_1528,i_0_1494,i_0_1863,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630]) ).

cnf(i_0_2220,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk32_2(X2,X1))) ),
    inference(rename_variables,[],[i_0_1630]) ).

cnf(i_0_2221,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)))),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_2121,i_0_1831,i_0_2177,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_1776,i_0_1657,i_0_2204,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1470,i_0_2190,i_0_1528,i_0_1494,i_0_1863,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631]) ).

cnf(i_0_2222,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
    inference(rename_variables,[],[i_0_1631]) ).

cnf(i_0_2223,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),v_n____),hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))))),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_2121,i_0_1831,i_0_2177,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_1776,i_0_1657,i_0_2204,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1470,i_0_2190,i_0_1528,i_0_1494,i_0_1863,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639]) ).

cnf(i_0_2224,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))) ),
    inference(rename_variables,[],[i_0_1639]) ).

cnf(i_0_2225,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_2121,i_0_1831,i_0_2177,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_1776,i_0_1657,i_0_2204,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1470,i_0_2190,i_0_1528,i_0_1494,i_0_1863,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659]) ).

cnf(i_0_2226,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
    inference(rename_variables,[],[i_0_1659]) ).

cnf(i_0_2227,plain,
    X1 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_2121,i_0_1831,i_0_2177,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_1776,i_0_2152,i_0_1657,i_0_2204,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1470,i_0_2190,i_0_1528,i_0_1494,i_0_1863,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662]) ).

cnf(i_0_2228,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X2 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)) ),
    inference(rename_variables,[],[i_0_1662]) ).

cnf(i_0_2229,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))),X1)),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_2121,i_0_1831,i_0_2177,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_1776,i_0_2152,i_0_1657,i_0_2204,i_0_2207,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1470,i_0_2190,i_0_1528,i_0_1494,i_0_1863,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689]) ).

cnf(i_0_2230,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
    inference(rename_variables,[],[i_0_1657]) ).

cnf(i_0_2231,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X2)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
    inference(rename_variables,[],[i_0_1689]) ).

cnf(i_0_2232,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1))))),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_2121,i_0_1831,i_0_2177,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_1776,i_0_2152,i_0_1657,i_0_2204,i_0_2207,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1470,i_0_2190,i_0_1528,i_0_1494,i_0_1863,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691]) ).

cnf(i_0_2233,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X1))) ),
    inference(rename_variables,[],[i_0_1691]) ).

cnf(i_0_2234,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))))),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_2121,i_0_1831,i_0_2177,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_1776,i_0_2152,i_0_1657,i_0_2204,i_0_2207,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1470,i_0_2190,i_0_1528,i_0_1494,i_0_1863,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697]) ).

cnf(i_0_2235,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
    inference(rename_variables,[],[i_0_1697]) ).

cnf(i_0_2236,plain,
    X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk18_2(X1,X1)),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_2121,i_0_1831,i_0_2177,i_0_2215,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_1776,i_0_2152,i_0_1657,i_0_2204,i_0_2207,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1470,i_0_2190,i_0_1528,i_0_1494,i_0_1863,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726]) ).

cnf(i_0_2237,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
    | X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk18_2(X2,X1)) ),
    inference(rename_variables,[],[i_0_1726]) ).

cnf(i_0_2238,plain,
    hAPP(c_Nat_OSuc,X1) = hAPP(c_Nat_OSuc,esk30_1(hAPP(c_Nat_OSuc,X1))),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_2121,i_0_1831,i_0_2177,i_0_2215,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_1776,i_0_2152,i_0_1657,i_0_2204,i_0_2207,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1470,i_0_2190,i_0_1528,i_0_1494,i_0_1863,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729]) ).

cnf(i_0_2239,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
    | X1 = hAPP(c_Nat_OSuc,esk30_1(X1)) ),
    inference(rename_variables,[],[i_0_1729]) ).

cnf(i_0_2240,plain,
    c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_2121,i_0_1831,i_0_2177,i_0_2215,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_1776,i_0_2152,i_0_1657,i_0_2204,i_0_2207,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1470,i_0_2190,i_0_1528,i_0_1494,i_0_1863,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763]) ).

cnf(i_0_2241,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(rename_variables,[],[i_0_1763]) ).

cnf(i_0_2242,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_2121,i_0_1831,i_0_2177,i_0_2215,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_1776,i_0_2152,i_0_1657,i_0_2204,i_0_2207,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1470,i_0_2190,i_0_1528,i_0_1494,i_0_1863,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764]) ).

cnf(i_0_2243,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
    inference(rename_variables,[],[i_0_1764]) ).

cnf(i_0_2244,plain,
    c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) != v_n____,
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_2121,i_0_1831,i_0_2177,i_0_2215,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_1776,i_0_2152,i_0_1657,i_0_2204,i_0_2207,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1470,i_0_2190,i_0_1528,i_0_1494,i_0_1863,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769]) ).

cnf(i_0_2245,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X2 != X1 ),
    inference(rename_variables,[],[i_0_1769]) ).

cnf(i_0_2246,plain,
    v_n____ != c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_2121,i_0_1831,i_0_2177,i_0_2215,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_1776,i_0_2152,i_0_1657,i_0_2204,i_0_2207,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1470,i_0_2190,i_0_1528,i_0_1494,i_0_1863,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770]) ).

cnf(i_0_2247,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X1 != X2 ),
    inference(rename_variables,[],[i_0_1770]) ).

cnf(i_0_2248,plain,
    X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_2121,i_0_1831,i_0_2177,i_0_2215,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_1776,i_0_2152,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1470,i_0_2190,i_0_1528,i_0_1494,i_0_1863,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771]) ).

cnf(i_0_2249,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
    | X2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3) ),
    inference(rename_variables,[],[i_0_1771]) ).

cnf(i_0_2250,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_2121,i_0_1831,i_0_2177,i_0_2215,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_1776,i_0_2152,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1469,i_0_1470,i_0_2190,i_0_1528,i_0_1494,i_0_1863,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779]) ).

cnf(i_0_2251,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X1)),
    inference(rename_variables,[],[i_0_1469]) ).

cnf(i_0_2252,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(rename_variables,[],[i_0_1779]) ).

cnf(i_0_2253,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2) != X1,
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1568,i_0_2121,i_0_1831,i_0_2177,i_0_2215,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_1776,i_0_2152,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1469,i_0_2251,i_0_1470,i_0_2190,i_0_1528,i_0_1494,i_0_1863,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782]) ).

cnf(i_0_2254,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X1)),
    inference(rename_variables,[],[i_0_1469]) ).

cnf(i_0_2255,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
    | X1 != X2 ),
    inference(rename_variables,[],[i_0_1782]) ).

cnf(i_0_2256,plain,
    c_Nat_OSuc = hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1842,i_0_1568,i_0_2121,i_0_1831,i_0_2177,i_0_2215,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_1776,i_0_2152,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1469,i_0_2251,i_0_1470,i_0_2190,i_0_1528,i_0_1494,i_0_1863,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791]) ).

cnf(i_0_2257,plain,
    hAPP(c_Nat_OSuc,X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1),
    inference(rename_variables,[],[i_0_1842]) ).

cnf(i_0_2258,plain,
    ( hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1))
    | X1 = X2 ),
    inference(rename_variables,[],[i_0_1791]) ).

cnf(i_0_2259,plain,
    ~ class_Orderings_Otop(tc_Nat_Onat),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1842,i_0_1568,i_0_2121,i_0_1831,i_0_2177,i_0_2215,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_1776,i_0_2152,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1469,i_0_2251,i_0_1470,i_0_2190,i_0_1528,i_0_1494,i_0_1863,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805]) ).

cnf(i_0_2260,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
    inference(rename_variables,[],[i_0_1657]) ).

cnf(i_0_2261,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Orderings_Otop__class_Otop(X1)))
    | ~ class_Orderings_Otop(X1) ),
    inference(rename_variables,[],[i_0_1805]) ).

cnf(i_0_2262,plain,
    hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)) != X1,
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1842,i_0_1568,i_0_2121,i_0_1831,i_0_2177,i_0_2215,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_1776,i_0_2152,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1469,i_0_2251,i_0_1470,i_0_2190,i_0_1528,i_0_1494,i_0_1863,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828]) ).

cnf(i_0_2263,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
    | X1 != X2 ),
    inference(rename_variables,[],[i_0_1828]) ).

cnf(i_0_2264,plain,
    X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk32_2(hAPP(c_Nat_OSuc,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1842,i_0_1568,i_0_2121,i_0_1831,i_0_2177,i_0_2215,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_1776,i_0_2152,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1469,i_0_2251,i_0_1470,i_0_2190,i_0_1528,i_0_1494,i_0_1863,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854]) ).

cnf(i_0_2265,plain,
    ( hAPP(c_Nat_OSuc,X1) != hAPP(c_Nat_OSuc,X2)
    | X1 = X2 ),
    inference(rename_variables,[],[i_0_1854]) ).

cnf(i_0_2266,plain,
    c_Set_Oimage(X1,X2,X3,c_Set_Oimage(X2,X1,c_Hilbert__Choice_Oinv__into(X1,X2,X4,X3),c_Set_Oimage(X1,X2,X3,X4))) = c_Set_Oimage(X1,X2,X3,X4),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1842,i_0_1568,i_0_2121,i_0_1831,i_0_2177,i_0_2215,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_1776,i_0_2152,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1469,i_0_2251,i_0_1470,i_0_2190,i_0_1528,i_0_1494,i_0_1863,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043]) ).

cnf(i_0_2267,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
    inference(rename_variables,[],[i_0_1745]) ).

cnf(i_0_2268,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Set_Oimage(X3,X1,X4,X5)))
    | c_Set_Oimage(X3,X1,X4,c_Set_Oimage(X1,X3,c_Hilbert__Choice_Oinv__into(X3,X1,X5,X4),X2)) = X2 ),
    inference(rename_variables,[],[i_0_2043]) ).

cnf(i_0_2269,plain,
    X1 = c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1877,i_0_1842,i_0_1568,i_0_2121,i_0_1831,i_0_2177,i_0_2215,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_1776,i_0_2152,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1469,i_0_2251,i_0_1470,i_0_2190,i_0_1528,i_0_1494,i_0_1863,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910]) ).

cnf(i_0_2270,plain,
    hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(X1,X2))) != X1,
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1877,i_0_1842,i_0_1568,i_0_2121,i_0_1831,i_0_2177,i_0_2215,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_1776,i_0_2152,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1469,i_0_2251,i_0_1470,i_0_2190,i_0_1528,i_0_1494,i_0_1863,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912]) ).

cnf(i_0_2271,plain,
    c_Fun_Oinj__on(X1,X1,c_Hilbert__Choice_Oinv__into(X1,X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_COMBI(X1)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1877,i_0_1670,i_0_1842,i_0_1568,i_0_2121,i_0_1831,i_0_2177,i_0_2215,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_1776,i_0_2152,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1469,i_0_2251,i_0_1470,i_0_2190,i_0_1528,i_0_1494,i_0_1863,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349]) ).

cnf(i_0_2272,plain,
    c_Set_Oimage(X1,X1,c_COMBI(X1),X2) = X2,
    inference(rename_variables,[],[i_0_1670]) ).

cnf(i_0_2273,plain,
    ( c_Set_Oimage(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))
    | c_Fun_Oinj__on(X2,X1,c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
    inference(rename_variables,[],[i_0_1349]) ).

cnf(i_0_2274,plain,
    c_Finite__Set_Ofinite(tc_Product__Type_Ounit,X1),
    inference(scs_inference,[],[i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1877,i_0_1670,i_0_1842,i_0_1568,i_0_2121,i_0_1831,i_0_2177,i_0_2215,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_1776,i_0_2152,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1469,i_0_2251,i_0_1470,i_0_2190,i_0_1528,i_0_1494,i_0_1863,i_0_1887,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868]) ).

cnf(i_0_2275,plain,
    ( ~ class_Finite__Set_Ofinite(X1)
    | c_Finite__Set_Ofinite(X1,X2) ),
    inference(rename_variables,[],[i_0_1868]) ).

cnf(i_0_2276,plain,
    hAPP(c_Set_Oinsert(X1,X2,X3),X2) != hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),X5),X5),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1877,i_0_1670,i_0_1842,i_0_1568,i_0_2121,i_0_1831,i_0_2177,i_0_2215,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_1776,i_0_2152,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1469,i_0_2251,i_0_1470,i_0_2190,i_0_1528,i_0_1494,i_0_1863,i_0_1887,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990]) ).

cnf(i_0_2277,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),esk11_0)),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1877,i_0_1670,i_0_1842,i_0_1568,i_0_2121,i_0_1831,i_0_2177,i_0_2215,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_1776,i_0_2152,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1469,i_0_2251,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1863,i_0_1887,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243]) ).

cnf(i_0_2278,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),X1))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)),X1)) ),
    inference(rename_variables,[],[i_0_1243]) ).

cnf(i_0_2279,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),c_Wellfounded_Omlex__prod(X1,X3,hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2))))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1877,i_0_1670,i_0_1842,i_0_1568,i_0_2121,i_0_1831,i_0_2177,i_0_2215,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_1776,i_0_2152,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1469,i_0_2251,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1863,i_0_1887,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276]) ).

cnf(i_0_2280,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))),
    inference(rename_variables,[],[i_0_2077]) ).

cnf(i_0_2281,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
    inference(rename_variables,[],[i_0_1831]) ).

cnf(i_0_2282,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X5,X2)),hAPP(X5,X3)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Wellfounded_Omlex__prod(X1,X5,X4))) ),
    inference(rename_variables,[],[i_0_1276]) ).

cnf(i_0_2283,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Nat_OSuc,X1)),X2)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X3),hAPP(c_Nat_OSuc,X1))),X1))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2077,i_0_2116,i_0_1877,i_0_1670,i_0_1842,i_0_1568,i_0_2121,i_0_1831,i_0_2177,i_0_2215,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_1776,i_0_2152,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1469,i_0_2251,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1869,i_0_1863,i_0_1887,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302]) ).

cnf(i_0_2284,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X3),X1))),
    inference(rename_variables,[],[i_0_2045]) ).

cnf(i_0_2285,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X3),X4)))
    | X1 = X4 ),
    inference(rename_variables,[],[i_0_1302]) ).

cnf(i_0_2286,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),hAPP(c_Nat_OSuc,X2))),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X3),X1)),X2))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2077,i_0_2116,i_0_1877,i_0_1670,i_0_1842,i_0_1568,i_0_2121,i_0_1831,i_0_2177,i_0_2215,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_1776,i_0_2152,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1469,i_0_2251,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1869,i_0_1863,i_0_1887,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303]) ).

cnf(i_0_2287,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X3),X1))),
    inference(rename_variables,[],[i_0_2045]) ).

cnf(i_0_2288,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X3),X4)))
    | X2 = X4 ),
    inference(rename_variables,[],[i_0_1303]) ).

cnf(i_0_2289,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2)),c_FuncSet_OPi(X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_fequal,X2),hAPP(c_Arrow__Order__Mirabelle_Omktop,X3)))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2077,i_0_2116,i_0_2280,i_0_1877,i_0_1670,i_0_1842,i_0_1568,i_0_2121,i_0_1831,i_0_2177,i_0_2215,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_1776,i_0_2152,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1469,i_0_2251,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1869,i_0_1863,i_0_1887,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306]) ).

cnf(i_0_2290,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))),
    inference(rename_variables,[],[i_0_2077]) ).

cnf(i_0_2291,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X3),X1))),
    inference(rename_variables,[],[i_0_2045]) ).

cnf(i_0_2292,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hBOOL(hAPP(hAPP(c_member(X4),hAPP(X5,X2)),hAPP(X6,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X4)),X5),c_FuncSet_OPi(X1,X4,X3,X6))) ),
    inference(rename_variables,[],[i_0_1306]) ).

cnf(i_0_2293,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(c_COMBI(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2))),c_Set_Oimage(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_COMBI(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X3),X1)))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_1877,i_0_1670,i_0_1842,i_0_1568,i_0_2121,i_0_1831,i_0_2177,i_0_2215,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_1776,i_0_2152,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1469,i_0_2251,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1671,i_0_1869,i_0_1863,i_0_1887,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307]) ).

cnf(i_0_2294,plain,
    c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
    inference(rename_variables,[],[i_0_1671]) ).

cnf(i_0_2295,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X4),hAPP(X5,X2)),c_Set_Oimage(X1,X4,X5,X3)))
    | ~ c_Fun_Oinj__on(X1,X4,X5,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(rename_variables,[],[i_0_1307]) ).

cnf(i_0_2296,plain,
    hBOOL(hAPP(hAPP(c_member(X1),c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(X2,X3))),c_Set_Oimage(X4,X1,X2,hAPP(c_fequal,X3)))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_1877,i_0_1670,i_0_1842,i_0_1568,i_0_2121,i_0_1831,i_0_2177,i_0_2215,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_1776,i_0_2152,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1469,i_0_2251,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1671,i_0_1869,i_0_1863,i_0_1887,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362]) ).

cnf(i_0_2297,plain,
    c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
    inference(rename_variables,[],[i_0_1877]) ).

cnf(i_0_2298,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hBOOL(hAPP(hAPP(c_member(X4),X5),c_Set_Oimage(X1,X4,X6,X3)))
    | X5 != hAPP(X6,X2) ),
    inference(rename_variables,[],[i_0_1362]) ).

cnf(i_0_2299,plain,
    hAPP(c_Hilbert__Choice_Oinv__into(X1,X1,hAPP(c_fequal,X2),c_COMBI(X1)),hAPP(c_COMBI(X1),X2)) = X2,
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_1877,i_0_1670,i_0_1842,i_0_1568,i_0_2121,i_0_1831,i_0_2177,i_0_2215,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_1776,i_0_2152,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1469,i_0_2251,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1671,i_0_2294,i_0_1869,i_0_1863,i_0_1887,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383]) ).

cnf(i_0_2300,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))),
    inference(rename_variables,[],[i_0_2077]) ).

cnf(i_0_2301,plain,
    c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
    inference(rename_variables,[],[i_0_1671]) ).

cnf(i_0_2302,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hAPP(c_Hilbert__Choice_Oinv__into(X1,X4,X3,X5),hAPP(X5,X2)) = X2
    | ~ c_Fun_Oinj__on(X1,X4,X5,X3) ),
    inference(rename_variables,[],[i_0_1383]) ).

cnf(i_0_2303,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(c_COMBI(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2))),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_1877,i_0_1670,i_0_1842,i_0_1568,i_0_2121,i_0_1831,i_0_2177,i_0_2215,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_1776,i_0_2152,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1469,i_0_2251,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1671,i_0_2294,i_0_1869,i_0_1863,i_0_1887,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513]) ).

cnf(i_0_2304,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2))
    | hBOOL(hAPP(hAPP(c_member(X1),X4),X3)) ),
    inference(rename_variables,[],[i_0_1513]) ).

cnf(i_0_2305,plain,
    hBOOL(hAPP(c_Set_Oimage(X1,X2,hAPP(c_COMBC(X3,tc_fun(X3,tc_HOL_Obool),tc_HOL_Obool),c_member(X3)),c_Set_Oinsert(X1,X4,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(X3,tc_fun(X3,tc_HOL_Obool),tc_HOL_Obool),c_member(X3)),X5))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_1877,i_0_1670,i_0_1842,i_0_1568,i_0_2121,i_0_1831,i_0_2177,i_0_2215,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_1776,i_0_2152,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1469,i_0_2251,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1671,i_0_2294,i_0_1869,i_0_1863,i_0_1887,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587]) ).

cnf(i_0_2306,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
    | hBOOL(hAPP(X3,X4))
    | ~ hBOOL(hAPP(X2,X4)) ),
    inference(rename_variables,[],[i_0_1587]) ).

cnf(i_0_2307,plain,
    c_Finite__Set_Ocard(tc_Product__Type_Ounit,c_Set_Oinsert(tc_Product__Type_Ounit,X1,hAPP(c_fequal,X1))) = c_Finite__Set_Ocard(tc_Product__Type_Ounit,hAPP(c_fequal,X1)),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_1670,i_0_1842,i_0_1568,i_0_2121,i_0_1831,i_0_2177,i_0_2215,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_1776,i_0_2152,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1469,i_0_2251,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1671,i_0_2294,i_0_1869,i_0_1863,i_0_1887,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604]) ).

cnf(i_0_2308,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))),
    inference(rename_variables,[],[i_0_2077]) ).

cnf(i_0_2309,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | c_Finite__Set_Ocard(X1,c_Set_Oinsert(X1,X2,X3)) = c_Finite__Set_Ocard(X1,X3)
    | ~ c_Finite__Set_Ofinite(X1,X3) ),
    inference(rename_variables,[],[i_0_1604]) ).

cnf(i_0_2310,plain,
    hBOOL(hAPP(c_Set_Oinsert(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2),esk45_2(c_Set_Oinsert(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X3)))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_1670,i_0_1842,i_0_1568,i_0_2121,i_0_1831,i_0_2177,i_0_2215,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_1776,i_0_2152,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1469,i_0_2251,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1671,i_0_2294,i_0_1869,i_0_1863,i_0_1887,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645]) ).

cnf(i_0_2311,plain,
    hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X2)),
    inference(rename_variables,[],[i_0_2066]) ).

cnf(i_0_2312,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | hBOOL(hAPP(X3,esk45_2(X3,X2)))
    | ~ hBOOL(hAPP(X3,X1)) ),
    inference(rename_variables,[],[i_0_1645]) ).

cnf(i_0_2313,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_Nat_Onat),X2),X2)),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_1670,i_0_1842,i_0_1568,i_0_2121,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_1776,i_0_2152,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1469,i_0_2251,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1671,i_0_2294,i_0_1869,i_0_1863,i_0_1887,i_0_1899,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174]) ).

cnf(i_0_2314,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
    inference(rename_variables,[],[i_0_1831]) ).

cnf(i_0_2315,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk9_4(X3,X2,X4,X1))),hAPP(X3,esk9_4(X3,X2,X4,X1))))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X1),X2),X3))
    | ~ class_Orderings_Oord(X1) ),
    inference(rename_variables,[],[i_0_1174]) ).

cnf(i_0_2316,plain,
    c_Set_Oimage(X1,X1,c_COMBI(X1),c_Set_Oimage(X1,X1,c_Hilbert__Choice_Oinv__into(X1,X1,c_Set_Oinsert(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),c_COMBI(X1)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_1776,i_0_2152,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1469,i_0_2251,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1671,i_0_2294,i_0_1869,i_0_1863,i_0_1887,i_0_1899,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313]) ).

cnf(i_0_2317,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Set_Oinsert(X1,X3,X2))),
    inference(rename_variables,[],[i_0_1568]) ).

cnf(i_0_2318,plain,
    c_Set_Oimage(X1,X1,c_COMBI(X1),X2) = X2,
    inference(rename_variables,[],[i_0_1670]) ).

cnf(i_0_2319,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
    | c_Set_Oimage(X4,X1,X5,c_Set_Oimage(X1,X4,c_Hilbert__Choice_Oinv__into(X4,X1,X6,X5),X2)) = X2
    | c_Set_Oimage(X4,X1,X5,X6) != X3 ),
    inference(rename_variables,[],[i_0_1313]) ).

cnf(i_0_2320,plain,
    ~ c_Arrow__Order__Mirabelle_Odictator(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(v_P____,v_P____))),v_P____),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_1776,i_0_2152,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1469,i_0_2251,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_1869,i_0_1863,i_0_1887,i_0_1899,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322]) ).

cnf(i_0_2321,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1),c_Arrow__Order__Mirabelle_OProf))
    | hAPP(X2,X1) = hAPP(X1,X3)
    | ~ c_Arrow__Order__Mirabelle_Odictator(X2,X3) ),
    inference(rename_variables,[],[i_0_1322]) ).

cnf(i_0_2322,plain,
    hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Obelow(esk11_0,hAPP(c_Nat_OSuc,X1),X1)),c_Arrow__Order__Mirabelle_OLin)),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_1776,i_0_2152,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1469,i_0_2251,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_1869,i_0_1863,i_0_1887,i_0_1899,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327]) ).

cnf(i_0_2323,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Obelow(X1,X2,X3)),c_Arrow__Order__Mirabelle_OLin))
    | X2 = X3 ),
    inference(rename_variables,[],[i_0_1327]) ).

cnf(i_0_2324,plain,
    c_Set_Oimage(X1,X1,c_Hilbert__Choice_Oinv__into(X1,X1,c_Set_Oinsert(X1,X2,X3),c_COMBI(X1)),c_Set_Oimage(X1,X1,c_COMBI(X1),X3)) = X3,
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_1776,i_0_2152,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1469,i_0_2251,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_1869,i_0_1863,i_0_1887,i_0_1899,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329]) ).

cnf(i_0_2325,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Set_Oinsert(X1,X3,X2))),
    inference(rename_variables,[],[i_0_1568]) ).

cnf(i_0_2326,plain,
    c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
    inference(rename_variables,[],[i_0_1671]) ).

cnf(i_0_2327,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
    | c_Set_Oimage(X4,X1,c_Hilbert__Choice_Oinv__into(X1,X4,X3,X5),c_Set_Oimage(X1,X4,X5,X2)) = X2
    | ~ c_Fun_Oinj__on(X1,X4,X5,X3) ),
    inference(rename_variables,[],[i_0_1329]) ).

cnf(i_0_2328,plain,
    c_Finite__Set_Ofinite(X1,c_Set_Oimage(tc_Nat_Onat,X1,X2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3,X4))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1469,i_0_2251,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_1869,i_0_1863,i_0_1887,i_0_1899,i_0_1798,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330]) ).

cnf(i_0_2329,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
    inference(rename_variables,[],[i_0_1745]) ).

cnf(i_0_2330,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Set_Oimage(X3,X1,X4,X5)))
    | c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Finite__Set_Ofinite(X3,X5) ),
    inference(rename_variables,[],[i_0_1330]) ).

cnf(i_0_2331,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Set_Oimage(X2,X1,X3,X4))),c_Set_Oimage(X2,X1,X3,c_Set_Oinsert(X2,X5,X4)))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1469,i_0_2251,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_1869,i_0_1863,i_0_1887,i_0_1899,i_0_1798,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334]) ).

cnf(i_0_2332,plain,
    c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
    inference(rename_variables,[],[i_0_1877]) ).

cnf(i_0_2333,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X5),c_Set_Oimage(X1,X4,X6,X3)))
    | X5 != c_Set_Oimage(X1,X4,X6,X2) ),
    inference(rename_variables,[],[i_0_1334]) ).

cnf(i_0_2334,plain,
    X1 = esk37_5(X1,c_Nat_OSuc,tc_Nat_Onat,c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1),tc_Nat_Onat),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1469,i_0_2251,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_1869,i_0_1685,i_0_1863,i_0_1887,i_0_1899,i_0_1798,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365]) ).

cnf(i_0_2335,plain,
    c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1),
    inference(rename_variables,[],[i_0_1685]) ).

cnf(i_0_2336,plain,
    ( ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
    | c_Set_Oimage(X1,X2,X3,X4) != c_Set_Oimage(X1,X2,X3,X5)
    | X4 = X5 ),
    inference(rename_variables,[],[i_0_1365]) ).

cnf(i_0_2337,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1469,i_0_2251,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_1869,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1899,i_0_1798,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373]) ).

cnf(i_0_2338,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
    inference(rename_variables,[],[i_0_1373]) ).

cnf(i_0_2339,plain,
    hAPP(c_COMBI(X1),hAPP(c_Nat_OSuc,hAPP(c_Hilbert__Choice_Oinv__into(X1,X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_COMBI(X1)),X2))) != X2,
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1469,i_0_2251,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1899,i_0_1798,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380]) ).

cnf(i_0_2340,plain,
    X1 != hAPP(c_Nat_OSuc,X1),
    inference(rename_variables,[],[i_0_1870]) ).

cnf(i_0_2341,plain,
    c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
    inference(rename_variables,[],[i_0_1671]) ).

cnf(i_0_2342,plain,
    ( hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3),X4) = X5
    | ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
    | hAPP(X3,X5) != X4 ),
    inference(rename_variables,[],[i_0_1380]) ).

cnf(i_0_2343,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1,X2,X3)),X3)),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1469,i_0_2251,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1899,i_0_1798,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400]) ).

cnf(i_0_2344,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X2)),
    inference(rename_variables,[],[i_0_2059]) ).

cnf(i_0_2345,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X4))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X4),X3)) ),
    inference(rename_variables,[],[i_0_1400]) ).

cnf(i_0_2346,plain,
    ~ c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oindi,c_Nat_OSuc,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1469,i_0_2251,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1899,i_0_1798,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416]) ).

cnf(i_0_2347,plain,
    ( c_Set_Oimage(X1,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))
    | ~ c_Finite__Set_Ofinite(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(X1,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(rename_variables,[],[i_0_1416]) ).

cnf(i_0_2348,plain,
    c_Set_Oinsert(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_1646,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1469,i_0_2251,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1899,i_0_1798,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503]) ).

cnf(i_0_2349,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
    inference(rename_variables,[],[i_0_1646]) ).

cnf(i_0_2350,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
    | X2 = X3 ),
    inference(rename_variables,[],[i_0_1503]) ).

cnf(i_0_2351,plain,
    c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) = c_Set_Oinsert(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_1646,i_0_2349,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1469,i_0_2251,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1899,i_0_1798,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509]) ).

cnf(i_0_2352,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Set_Oinsert(X1,X3,X2))),
    inference(rename_variables,[],[i_0_1568]) ).

cnf(i_0_2353,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
    inference(rename_variables,[],[i_0_1646]) ).

cnf(i_0_2354,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3),X2))
    | X2 = X3 ),
    inference(rename_variables,[],[i_0_1509]) ).

cnf(i_0_2355,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,hAPP(X1,X2)),hAPP(c_Set_Oinsert(X3,X4,X1),X2))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_1646,i_0_2349,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1469,i_0_2251,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1898,i_0_1899,i_0_1798,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516]) ).

cnf(i_0_2356,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2),X3),X4))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,hAPP(X3,X5)),hAPP(X4,X5)))
    | ~ class_Orderings_Oord(X2) ),
    inference(rename_variables,[],[i_0_1516]) ).

cnf(i_0_2357,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,X1)),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_1646,i_0_2349,i_0_2353,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1469,i_0_2251,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1898,i_0_1899,i_0_1798,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518]) ).

cnf(i_0_2358,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
    inference(rename_variables,[],[i_0_1646]) ).

cnf(i_0_2359,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X1,X2)),c_Finite__Set_Ocard(X1,X3)))
    | ~ c_Finite__Set_Ofinite(X1,X3) ),
    inference(rename_variables,[],[i_0_1518]) ).

cnf(i_0_2360,plain,
    hAPP(hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X1),hAPP(c_Nat_OSuc,X2)) != hAPP(hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X1),X2),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_1646,i_0_2349,i_0_2353,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1469,i_0_2251,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1898,i_0_1899,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521]) ).

cnf(i_0_2361,plain,
    c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X1),X2),
    inference(rename_variables,[],[i_0_1462]) ).

cnf(i_0_2362,plain,
    ( ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
    | hAPP(X3,X4) != hAPP(X3,X5)
    | X4 = X5 ),
    inference(rename_variables,[],[i_0_1521]) ).

cnf(i_0_2363,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_1646,i_0_2349,i_0_2353,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1469,i_0_2251,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1898,i_0_1899,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567]) ).

cnf(i_0_2364,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X4))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X4) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2) ),
    inference(rename_variables,[],[i_0_1567]) ).

cnf(i_0_2365,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X1)),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_1646,i_0_2349,i_0_2353,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1469,i_0_2251,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1897,i_0_1898,i_0_1899,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591]) ).

cnf(i_0_2366,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
    | ~ class_Orderings_Oorder(X1) ),
    inference(rename_variables,[],[i_0_1591]) ).

cnf(i_0_2367,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))),v_n____)),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_1646,i_0_2349,i_0_2353,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1325,i_0_1469,i_0_2251,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592]) ).

cnf(i_0_2368,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(rename_variables,[],[i_0_1592]) ).

cnf(i_0_2369,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))),esk7_0)),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_1646,i_0_2349,i_0_2353,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1325,i_0_1469,i_0_2251,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596]) ).

cnf(i_0_2370,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
    | ~ class_Orderings_Opreorder(X1) ),
    inference(rename_variables,[],[i_0_1596]) ).

cnf(i_0_2371,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))),v_n____)),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_1646,i_0_2349,i_0_2353,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1325,i_0_1469,i_0_2251,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598]) ).

cnf(i_0_2372,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1))
    | X1 = X2 ),
    inference(rename_variables,[],[i_0_1598]) ).

cnf(i_0_2373,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Nat_OSuc,X1))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_1646,i_0_2349,i_0_2353,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613]) ).

cnf(i_0_2374,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X1)),
    inference(rename_variables,[],[i_0_1469]) ).

cnf(i_0_2375,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
    | X1 = X2 ),
    inference(rename_variables,[],[i_0_1613]) ).

cnf(i_0_2376,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))),X2)),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_1646,i_0_2349,i_0_2353,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621]) ).

cnf(i_0_2377,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
    inference(rename_variables,[],[i_0_1657]) ).

cnf(i_0_2378,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X2))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X1)) ),
    inference(rename_variables,[],[i_0_1621]) ).

cnf(i_0_2379,plain,
    hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_1646,i_0_2349,i_0_2353,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622]) ).

cnf(i_0_2380,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
    inference(rename_variables,[],[i_0_1776]) ).

cnf(i_0_2381,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_OSuc,X2)))
    | X3 != hAPP(c_Nat_OSuc,X1) ),
    inference(rename_variables,[],[i_0_1622]) ).

cnf(i_0_2382,plain,
    c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,X1),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624]) ).

cnf(i_0_2383,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
    inference(rename_variables,[],[i_0_1646]) ).

cnf(i_0_2384,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
    | c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Finite__Set_Ofinite(X1,X3) ),
    inference(rename_variables,[],[i_0_1624]) ).

cnf(i_0_2385,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))),esk7_0)),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628]) ).

cnf(i_0_2386,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(rename_variables,[],[i_0_1628]) ).

cnf(i_0_2387,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))),esk8_0)),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629]) ).

cnf(i_0_2388,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
    | ~ class_Orderings_Opreorder(X1) ),
    inference(rename_variables,[],[i_0_1629]) ).

cnf(i_0_2389,plain,
    ~ c_Finite__Set_Ofinite(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1714,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647]) ).

cnf(i_0_2390,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
    inference(rename_variables,[],[i_0_1714]) ).

cnf(i_0_2391,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
    inference(rename_variables,[],[i_0_1776]) ).

cnf(i_0_2392,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),esk41_1(X2)))
    | ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X2) ),
    inference(rename_variables,[],[i_0_1647]) ).

cnf(i_0_2393,plain,
    hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_OSuc,esk31_2(hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1714,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654]) ).

cnf(i_0_2394,plain,
    hAPP(c_Nat_OSuc,X1) != X1,
    inference(rename_variables,[],[i_0_1869]) ).

cnf(i_0_2395,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
    | X1 = hAPP(c_Nat_OSuc,esk31_2(X2,X1))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(rename_variables,[],[i_0_1654]) ).

cnf(i_0_2396,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk7_0),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1714,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665]) ).

cnf(i_0_2397,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | ~ class_Orderings_Oorder(X1) ),
    inference(rename_variables,[],[i_0_1665]) ).

cnf(i_0_2398,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk8_0),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1714,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667]) ).

cnf(i_0_2399,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | ~ class_Orderings_Opreorder(X1) ),
    inference(rename_variables,[],[i_0_1667]) ).

cnf(i_0_2400,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Nat_OSuc,X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1714,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709]) ).

cnf(i_0_2401,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X1)),
    inference(rename_variables,[],[i_0_1469]) ).

cnf(i_0_2402,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
    | X1 = X2 ),
    inference(rename_variables,[],[i_0_1709]) ).

cnf(i_0_2403,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1714,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723]) ).

cnf(i_0_2404,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(rename_variables,[],[i_0_1723]) ).

cnf(i_0_2405,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Nat_OSuc,X1)))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1714,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728]) ).

cnf(i_0_2406,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X1)),
    inference(rename_variables,[],[i_0_1469]) ).

cnf(i_0_2407,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))
    | X1 = X2 ),
    inference(rename_variables,[],[i_0_1728]) ).

cnf(i_0_2408,plain,
    c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) != esk7_0,
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1714,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732]) ).

cnf(i_0_2409,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | X3 != X2
    | ~ class_Orderings_Oorder(X1) ),
    inference(rename_variables,[],[i_0_1732]) ).

cnf(i_0_2410,plain,
    esk7_0 != c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1714,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734]) ).

cnf(i_0_2411,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | X2 != X3
    | ~ class_Orderings_Oorder(X1) ),
    inference(rename_variables,[],[i_0_1734]) ).

cnf(i_0_2412,plain,
    esk8_0 != c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1714,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735]) ).

cnf(i_0_2413,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | X2 != X3
    | ~ class_Orderings_Olinorder(X1) ),
    inference(rename_variables,[],[i_0_1735]) ).

cnf(i_0_2414,plain,
    c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) != esk8_0,
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1714,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736]) ).

cnf(i_0_2415,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | X3 != X2
    | ~ class_Orderings_Olinorder(X1) ),
    inference(rename_variables,[],[i_0_1736]) ).

cnf(i_0_2416,plain,
    X1 = esk32_2(hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1714,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749]) ).

cnf(i_0_2417,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)
    | X3 = X4
    | ~ class_Groups_Ocancel__ab__semigroup__add(X1) ),
    inference(rename_variables,[],[i_0_1749]) ).

cnf(i_0_2418,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X1))))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1714,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753]) ).

cnf(i_0_2419,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(rename_variables,[],[i_0_1753]) ).

cnf(i_0_2420,plain,
    esk18_2(hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1714,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_2394,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804]) ).

cnf(i_0_2421,plain,
    hAPP(c_Nat_OSuc,X1) != X1,
    inference(rename_variables,[],[i_0_1869]) ).

cnf(i_0_2422,plain,
    ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(rename_variables,[],[i_0_1804]) ).

cnf(i_0_2423,plain,
    hAPP(c_Nat_OSuc,X1) != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X1))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1714,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_2394,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814]) ).

cnf(i_0_2424,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | X3 != X2
    | ~ class_Orderings_Oorder(X1) ),
    inference(rename_variables,[],[i_0_1814]) ).

cnf(i_0_2425,plain,
    hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))) != hAPP(c_Nat_OSuc,X2),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1714,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_2394,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815]) ).

cnf(i_0_2426,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | ~ class_Orderings_Opreorder(X1)
    | X2 != X3 ),
    inference(rename_variables,[],[i_0_1815]) ).

cnf(i_0_2427,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)) != X2,
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1714,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_2394,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816]) ).

cnf(i_0_2428,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | X2 != X3
    | ~ class_Orderings_Oorder(X1) ),
    inference(rename_variables,[],[i_0_1816]) ).

cnf(i_0_2429,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X1)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,esk11_0),hAPP(c_Nat_OSuc,X2)),X2))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1714,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_2394,i_0_2421,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040]) ).

cnf(i_0_2430,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X2)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1),X3),X4)))
    | X3 = X4 ),
    inference(rename_variables,[],[i_0_2040]) ).

cnf(i_0_2431,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X1)),c_Arrow__Order__Mirabelle_Obelow(esk11_0,hAPP(c_Nat_OSuc,X2),X2))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1714,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_2394,i_0_2421,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042]) ).

cnf(i_0_2432,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X2)),c_Arrow__Order__Mirabelle_Obelow(X1,X3,X4)))
    | X3 = X4 ),
    inference(rename_variables,[],[i_0_2042]) ).

cnf(i_0_2433,plain,
    hAPP(c_Nat_OSuc,X1) != c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1714,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_2394,i_0_2421,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911]) ).

cnf(i_0_2434,plain,
    c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
    inference(rename_variables,[],[i_0_1877]) ).

cnf(i_0_2435,plain,
    class_Finite__Set_Ofinite(esk37_5(tc_Product__Type_Ounit,c_Nat_OSuc,tc_Nat_Onat,c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,tc_Product__Type_Ounit),tc_Nat_Onat)),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1714,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_2394,i_0_2421,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000]) ).

cnf(i_0_2436,plain,
    c_Arrow__Order__Mirabelle_OIIA(esk32_2(hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),v_F)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1714,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_2394,i_0_2421,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001]) ).

cnf(i_0_2437,plain,
    ~ c_Arrow__Order__Mirabelle_Odictator(c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(v_P____,v_P____)))),v_P____),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1714,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_2394,i_0_2421,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007]) ).

cnf(i_0_2438,plain,
    c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
    inference(rename_variables,[],[i_0_1877]) ).

cnf(i_0_2439,plain,
    ~ c_Arrow__Order__Mirabelle_Odictator(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(v_P____,v_P____))),c_Nat_Osize__class_Osize(tc_Nat_Onat,v_P____)),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1714,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_2394,i_0_2421,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008]) ).

cnf(i_0_2440,plain,
    c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
    inference(rename_variables,[],[i_0_1877]) ).

cnf(i_0_2441,plain,
    ~ c_Finite__Set_Ofinite(c_Nat_Osize__class_Osize(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1714,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_2394,i_0_2421,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015]) ).

cnf(i_0_2442,plain,
    c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
    inference(rename_variables,[],[i_0_1877]) ).

cnf(i_0_2443,plain,
    ~ c_Finite__Set_Ofinite(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1714,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_2394,i_0_2421,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016]) ).

cnf(i_0_2444,plain,
    c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
    inference(rename_variables,[],[i_0_1877]) ).

cnf(i_0_2445,plain,
    ~ c_Fun_Oinj__on(c_Nat_Osize__class_Osize(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,c_Nat_OSuc,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1714,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_2394,i_0_2421,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018]) ).

cnf(i_0_2446,plain,
    c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
    inference(rename_variables,[],[i_0_1877]) ).

cnf(i_0_2447,plain,
    ~ c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,c_Nat_Osize__class_Osize(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oindi),c_Nat_OSuc,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1714,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_2394,i_0_2421,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019]) ).

cnf(i_0_2448,plain,
    c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
    inference(rename_variables,[],[i_0_1877]) ).

cnf(i_0_2449,plain,
    ~ c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oindi,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Nat_OSuc),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1714,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_2394,i_0_2421,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020]) ).

cnf(i_0_2450,plain,
    c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
    inference(rename_variables,[],[i_0_1877]) ).

cnf(i_0_2451,plain,
    ~ c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oindi,c_Nat_OSuc,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1714,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_2394,i_0_2421,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021]) ).

cnf(i_0_2452,plain,
    c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
    inference(rename_variables,[],[i_0_1877]) ).

cnf(i_0_2453,plain,
    c_Arrow__Order__Mirabelle_Ounanimity(esk32_2(hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),v_F)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1714,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_2394,i_0_2421,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1905,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022]) ).

cnf(i_0_2454,plain,
    ~ c_FunDef_Oin__rel(c_Nat_Osize__class_Osize(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1714,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_2394,i_0_2421,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1905,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977]) ).

cnf(i_0_2455,plain,
    c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
    inference(rename_variables,[],[i_0_1877]) ).

cnf(i_0_2456,plain,
    ~ c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,c_Nat_Osize__class_Osize(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1714,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_2394,i_0_2421,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1905,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978]) ).

cnf(i_0_2457,plain,
    c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
    inference(rename_variables,[],[i_0_1877]) ).

cnf(i_0_2458,plain,
    ~ c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1714,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_2394,i_0_2421,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1905,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979]) ).

cnf(i_0_2459,plain,
    c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
    inference(rename_variables,[],[i_0_1877]) ).

cnf(i_0_2460,plain,
    ~ c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1714,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_2394,i_0_2421,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1905,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980]) ).

cnf(i_0_2461,plain,
    c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
    inference(rename_variables,[],[i_0_1877]) ).

cnf(i_0_2462,plain,
    tc_HOL_Obool != tc_Nat_Onat,
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_1670,i_0_2272,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1714,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_2394,i_0_2421,i_0_1870,i_0_1685,i_0_1863,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1905,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998]) ).

cnf(i_0_2463,plain,
    ~ c_Fun_Oinj__on(X1,X2,hAPP(c_COMBK(X3,X4),X5),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_1670,i_0_2272,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1714,i_0_2390,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_2394,i_0_2421,i_0_1870,i_0_2340,i_0_1685,i_0_1863,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1905,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384]) ).

cnf(i_0_2464,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
    inference(rename_variables,[],[i_0_1714]) ).

cnf(i_0_2465,plain,
    X1 != hAPP(c_Nat_OSuc,X1),
    inference(rename_variables,[],[i_0_1870]) ).

cnf(i_0_2466,plain,
    hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
    inference(rename_variables,[],[i_0_1817]) ).

cnf(i_0_2467,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hAPP(c_Hilbert__Choice_Oinv__into(X1,X4,X3,X5),X6) = X2
    | hAPP(X5,X2) != X6
    | ~ c_Fun_Oinj__on(X1,X4,X5,X3) ),
    inference(rename_variables,[],[i_0_1384]) ).

cnf(i_0_2468,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk33_2(hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),v_F)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_1670,i_0_2272,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1714,i_0_2390,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_2394,i_0_2421,i_0_1870,i_0_2340,i_0_1685,i_0_1863,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1905,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600]) ).

cnf(i_0_2469,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
    inference(rename_variables,[],[i_0_1776]) ).

cnf(i_0_2470,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
    inference(rename_variables,[],[i_0_1831]) ).

cnf(i_0_2471,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X1))),
    inference(rename_variables,[],[i_0_1765]) ).

cnf(i_0_2472,plain,
    ( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),esk33_2(X3,X1)))
    | ~ hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,X3)) ),
    inference(rename_variables,[],[i_0_1600]) ).

cnf(i_0_2473,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Nat_OSuc,v_a____)),v_b____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,esk11_0),v_a____),hAPP(c_Nat_OSuc,v_a____)))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_1670,i_0_2272,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1714,i_0_2390,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_2394,i_0_2421,i_0_1870,i_0_2340,i_0_2465,i_0_1685,i_0_1863,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1905,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031]) ).

cnf(i_0_2474,plain,
    X1 != hAPP(c_Nat_OSuc,X1),
    inference(rename_variables,[],[i_0_1870]) ).

cnf(i_0_2475,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1),X4),X2)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X3)),X1))
    | X4 = X2 ),
    inference(rename_variables,[],[i_0_2031]) ).

cnf(i_0_2476,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),hAPP(c_Nat_OSuc,v_b____))),c_Arrow__Order__Mirabelle_Obelow(esk11_0,hAPP(c_Nat_OSuc,v_b____),v_b____))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_1670,i_0_2272,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1714,i_0_2390,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_1869,i_0_2394,i_0_2421,i_0_1870,i_0_2340,i_0_2465,i_0_1685,i_0_1863,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1905,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036]) ).

cnf(i_0_2477,plain,
    hAPP(c_Nat_OSuc,X1) != X1,
    inference(rename_variables,[],[i_0_1869]) ).

cnf(i_0_2478,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),c_Arrow__Order__Mirabelle_Obelow(X1,X3,X4)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X4)),X1))
    | X3 = X4 ),
    inference(rename_variables,[],[i_0_2036]) ).

cnf(i_0_2479,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,X1)),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Set_Oinsert(tc_Arrow__Order__Mirabelle_Oindi,X2,c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oindi,c_COMBI(tc_Arrow__Order__Mirabelle_Oindi),X1))))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_1670,i_0_2272,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1714,i_0_2390,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_1870,i_0_2340,i_0_2465,i_0_1685,i_0_1863,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1905,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235]) ).

cnf(i_0_2480,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Set_Oinsert(X1,X3,X2))),
    inference(rename_variables,[],[i_0_1568]) ).

cnf(i_0_2481,plain,
    c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
    inference(rename_variables,[],[i_0_1671]) ).

cnf(i_0_2482,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X2,X1,X3,X4)),X5))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2,X4)),c_Finite__Set_Ocard(X1,X5)))
    | ~ c_Finite__Set_Ofinite(X1,X5)
    | ~ c_Fun_Oinj__on(X2,X1,X3,X4) ),
    inference(rename_variables,[],[i_0_1235]) ).

cnf(i_0_2483,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Nat_Osize__class_Osize(tc_Nat_Onat,X1)),X1)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,esk11_0),hAPP(c_Nat_OSuc,X2)),X2))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_1670,i_0_2272,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1714,i_0_2390,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_1870,i_0_2340,i_0_2465,i_0_1685,i_0_1863,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1905,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288]) ).

cnf(i_0_2484,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1),X4),X5)))
    | X4 = X5
    | X2 != X3 ),
    inference(rename_variables,[],[i_0_1288]) ).

cnf(i_0_2485,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Nat_Osize__class_Osize(tc_Nat_Onat,X1)),X1)),c_Arrow__Order__Mirabelle_Obelow(esk11_0,hAPP(c_Nat_OSuc,X2),X2))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_1670,i_0_2272,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1714,i_0_2390,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_1870,i_0_2340,i_0_2465,i_0_1685,i_0_1863,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1905,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299]) ).

cnf(i_0_2486,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),c_Arrow__Order__Mirabelle_Obelow(X1,X4,X5)))
    | X4 = X5
    | X2 != X3 ),
    inference(rename_variables,[],[i_0_1299]) ).

cnf(i_0_2487,plain,
    c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,esk40_4(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1,X2),tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1,X2),tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1,X2)),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_1670,i_0_2272,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_1765,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1714,i_0_2390,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_1870,i_0_2340,i_0_2465,i_0_1685,i_0_1863,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1905,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376]) ).

cnf(i_0_2488,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
    inference(rename_variables,[],[i_0_1831]) ).

cnf(i_0_2489,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X1,X2)),c_Finite__Set_Ocard(X3,X4)))
    | c_Fun_Oinj__on(X1,X3,esk40_4(X4,X3,X2,X1),X2)
    | ~ c_Finite__Set_Ofinite(X3,X4)
    | ~ c_Finite__Set_Ofinite(X1,X2) ),
    inference(rename_variables,[],[i_0_1376]) ).

cnf(i_0_2490,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))),X1)),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_1670,i_0_2272,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1714,i_0_2390,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_1470,i_0_2190,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_1870,i_0_2340,i_0_2465,i_0_1685,i_0_1863,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1905,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397]) ).

cnf(i_0_2491,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X1)),
    inference(rename_variables,[],[i_0_1469]) ).

cnf(i_0_2492,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X5))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(rename_variables,[],[i_0_1397]) ).

cnf(i_0_2493,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)),X2)),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_1670,i_0_2272,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_1714,i_0_2390,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_1470,i_0_2190,i_0_2193,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_1870,i_0_2340,i_0_2465,i_0_1685,i_0_1863,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1905,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398]) ).

cnf(i_0_2494,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X2)),
    inference(rename_variables,[],[i_0_1470]) ).

cnf(i_0_2495,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X5))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(rename_variables,[],[i_0_1398]) ).

cnf(i_0_2496,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Set_Oinsert(tc_Arrow__Order__Mirabelle_Oindi,X1,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))))),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_1670,i_0_2272,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_1714,i_0_2390,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_1470,i_0_2190,i_0_2193,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_1870,i_0_2340,i_0_2465,i_0_1685,i_0_1863,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1905,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404]) ).

cnf(i_0_2497,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
    inference(rename_variables,[],[i_0_1646]) ).

cnf(i_0_2498,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X1,X2)),c_Finite__Set_Ocard(X1,X3)))
    | ~ c_Finite__Set_Ofinite(X1,X3) ),
    inference(rename_variables,[],[i_0_1404]) ).

cnf(i_0_2499,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_1670,i_0_2272,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_2488,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_1714,i_0_2390,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_1470,i_0_2190,i_0_2193,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_1870,i_0_2340,i_0_2465,i_0_1685,i_0_1863,i_0_1882,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1905,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404,i_0_1439]) ).

cnf(i_0_2500,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
    inference(rename_variables,[],[i_0_1831]) ).

cnf(i_0_2501,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(rename_variables,[],[i_0_1439]) ).

cnf(i_0_2502,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))),X2)),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_1670,i_0_2272,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_2488,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_1714,i_0_2390,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_1470,i_0_2190,i_0_2193,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_1870,i_0_2340,i_0_2465,i_0_1685,i_0_1863,i_0_1882,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1904,i_0_1905,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404,i_0_1439,i_0_1473]) ).

cnf(i_0_2503,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(rename_variables,[],[i_0_1473]) ).

cnf(i_0_2504,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),X3))),X3)),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_1670,i_0_2272,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_2488,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_1714,i_0_2390,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_1470,i_0_2190,i_0_2193,i_0_2494,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_1870,i_0_2340,i_0_2465,i_0_1685,i_0_1863,i_0_1882,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1904,i_0_1905,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404,i_0_1439,i_0_1473,i_0_1483]) ).

cnf(i_0_2505,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X2)),
    inference(rename_variables,[],[i_0_1470]) ).

cnf(i_0_2506,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(rename_variables,[],[i_0_1483]) ).

cnf(i_0_2507,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))),X1)),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_1670,i_0_2272,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_2488,i_0_2500,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_1714,i_0_2390,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_1470,i_0_2190,i_0_2193,i_0_2494,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_1870,i_0_2340,i_0_2465,i_0_1685,i_0_1863,i_0_1882,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1904,i_0_1905,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404,i_0_1439,i_0_1473,i_0_1483,i_0_1498]) ).

cnf(i_0_2508,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
    inference(rename_variables,[],[i_0_1831]) ).

cnf(i_0_2509,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(rename_variables,[],[i_0_1498]) ).

cnf(i_0_2510,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),X2)),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_1670,i_0_2272,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_2488,i_0_2500,i_0_2508,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_1714,i_0_2390,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_1470,i_0_2190,i_0_2193,i_0_2494,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_1870,i_0_2340,i_0_2465,i_0_1685,i_0_1863,i_0_1882,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1904,i_0_1905,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404,i_0_1439,i_0_1473,i_0_1483,i_0_1498,i_0_1499]) ).

cnf(i_0_2511,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
    inference(rename_variables,[],[i_0_1831]) ).

cnf(i_0_2512,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(rename_variables,[],[i_0_1499]) ).

cnf(i_0_2513,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))),esk8_0)),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_1670,i_0_2272,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_2488,i_0_2500,i_0_2508,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_2469,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_1714,i_0_2390,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_1470,i_0_2190,i_0_2193,i_0_2494,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_1870,i_0_2340,i_0_2465,i_0_1685,i_0_1863,i_0_1882,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1904,i_0_1905,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404,i_0_1439,i_0_1473,i_0_1483,i_0_1498,i_0_1499,i_0_1543]) ).

cnf(i_0_2514,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
    inference(rename_variables,[],[i_0_1776]) ).

cnf(i_0_2515,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X2))
    | ~ class_Orderings_Opreorder(X1) ),
    inference(rename_variables,[],[i_0_1543]) ).

cnf(i_0_2516,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))))),v_n____)),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_1670,i_0_2272,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_2488,i_0_2500,i_0_2508,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_2469,i_0_2514,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_1714,i_0_2390,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_1470,i_0_2190,i_0_2193,i_0_2494,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_1870,i_0_2340,i_0_2465,i_0_1685,i_0_1863,i_0_1882,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1904,i_0_1905,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404,i_0_1439,i_0_1473,i_0_1483,i_0_1498,i_0_1499,i_0_1543,i_0_1544]) ).

cnf(i_0_2517,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
    inference(rename_variables,[],[i_0_1776]) ).

cnf(i_0_2518,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))
    | ~ class_Orderings_Oorder(X1) ),
    inference(rename_variables,[],[i_0_1544]) ).

cnf(i_0_2519,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),v_F)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_1670,i_0_2272,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_2488,i_0_2500,i_0_2508,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_2469,i_0_2514,i_0_2517,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_1714,i_0_2390,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_1470,i_0_2190,i_0_2193,i_0_2494,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_1870,i_0_2340,i_0_2465,i_0_1685,i_0_1863,i_0_1882,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1904,i_0_1905,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404,i_0_1439,i_0_1473,i_0_1483,i_0_1498,i_0_1499,i_0_1543,i_0_1544,i_0_1561]) ).

cnf(i_0_2520,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
    inference(rename_variables,[],[i_0_1776]) ).

cnf(i_0_2521,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X2))
    | ~ class_Orderings_Opreorder(X1) ),
    inference(rename_variables,[],[i_0_1561]) ).

cnf(i_0_2522,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))),X3)),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_1670,i_0_2272,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_2488,i_0_2500,i_0_2508,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_2469,i_0_2514,i_0_2517,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_1714,i_0_2390,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_1470,i_0_2190,i_0_2193,i_0_2494,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_1870,i_0_2340,i_0_2465,i_0_1685,i_0_1863,i_0_1882,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1904,i_0_1905,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404,i_0_1439,i_0_1473,i_0_1483,i_0_1498,i_0_1499,i_0_1543,i_0_1544,i_0_1561,i_0_1562]) ).

cnf(i_0_2523,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
    inference(rename_variables,[],[i_0_1785]) ).

cnf(i_0_2524,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
    | ~ class_Orderings_Opreorder(X1) ),
    inference(rename_variables,[],[i_0_1562]) ).

cnf(i_0_2525,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))))),v_n____)),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_1670,i_0_2272,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_2488,i_0_2500,i_0_2508,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_2469,i_0_2514,i_0_2517,i_0_2520,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_1714,i_0_2390,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_1470,i_0_2190,i_0_2193,i_0_2494,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_1870,i_0_2340,i_0_2465,i_0_1685,i_0_1863,i_0_1882,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1904,i_0_1905,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404,i_0_1439,i_0_1473,i_0_1483,i_0_1498,i_0_1499,i_0_1543,i_0_1544,i_0_1561,i_0_1562,i_0_1563]) ).

cnf(i_0_2526,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
    inference(rename_variables,[],[i_0_1776]) ).

cnf(i_0_2527,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4))
    | ~ class_Orderings_Oorder(X1) ),
    inference(rename_variables,[],[i_0_1563]) ).

cnf(i_0_2528,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_1670,i_0_2272,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_2488,i_0_2500,i_0_2508,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_2469,i_0_2514,i_0_2517,i_0_2520,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_1714,i_0_2390,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_2491,i_0_1470,i_0_2190,i_0_2193,i_0_2494,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_1870,i_0_2340,i_0_2465,i_0_1685,i_0_1863,i_0_1882,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1904,i_0_1905,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404,i_0_1439,i_0_1473,i_0_1483,i_0_1498,i_0_1499,i_0_1543,i_0_1544,i_0_1561,i_0_1562,i_0_1563,i_0_1564]) ).

cnf(i_0_2529,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X1)),
    inference(rename_variables,[],[i_0_1469]) ).

cnf(i_0_2530,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
    | ~ class_Orderings_Oorder(X1) ),
    inference(rename_variables,[],[i_0_1564]) ).

cnf(i_0_2531,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))),X1)),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_1670,i_0_2272,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_2488,i_0_2500,i_0_2508,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_2469,i_0_2514,i_0_2517,i_0_2520,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_1714,i_0_2390,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_2377,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_2491,i_0_1470,i_0_2190,i_0_2193,i_0_2494,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_1870,i_0_2340,i_0_2465,i_0_1685,i_0_1863,i_0_1882,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1904,i_0_1905,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404,i_0_1439,i_0_1473,i_0_1483,i_0_1498,i_0_1499,i_0_1543,i_0_1544,i_0_1561,i_0_1562,i_0_1563,i_0_1564,i_0_1588]) ).

cnf(i_0_2532,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
    inference(rename_variables,[],[i_0_1657]) ).

cnf(i_0_2533,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X2))
    | ~ class_Orderings_Opreorder(X1) ),
    inference(rename_variables,[],[i_0_1588]) ).

cnf(i_0_2534,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))),X3)),X2)),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_1670,i_0_2272,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_2488,i_0_2500,i_0_2508,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_2469,i_0_2514,i_0_2517,i_0_2520,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_1714,i_0_2390,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_2377,i_0_2532,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_2491,i_0_1470,i_0_2190,i_0_2193,i_0_2494,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_1870,i_0_2340,i_0_2465,i_0_1685,i_0_1863,i_0_1882,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1904,i_0_1905,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404,i_0_1439,i_0_1473,i_0_1483,i_0_1498,i_0_1499,i_0_1543,i_0_1544,i_0_1561,i_0_1562,i_0_1563,i_0_1564,i_0_1588,i_0_1589]) ).

cnf(i_0_2535,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4))
    | ~ class_Orderings_Oorder(X1) ),
    inference(rename_variables,[],[i_0_1589]) ).

cnf(i_0_2536,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk33_2(hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),v_F)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_1670,i_0_2272,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_2488,i_0_2500,i_0_2508,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_2469,i_0_2514,i_0_2517,i_0_2520,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_1714,i_0_2390,i_0_1821,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_2377,i_0_2532,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_2491,i_0_1470,i_0_2190,i_0_2193,i_0_2494,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_1870,i_0_2340,i_0_2465,i_0_1685,i_0_1863,i_0_1882,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1904,i_0_1905,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404,i_0_1439,i_0_1473,i_0_1483,i_0_1498,i_0_1499,i_0_1543,i_0_1544,i_0_1561,i_0_1562,i_0_1563,i_0_1564,i_0_1588,i_0_1589,i_0_1603]) ).

cnf(i_0_2537,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)),
    inference(rename_variables,[],[i_0_1821]) ).

cnf(i_0_2538,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
    | ~ class_Orderings_Opreorder(X1) ),
    inference(rename_variables,[],[i_0_1603]) ).

cnf(i_0_2539,plain,
    c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Set_Oinsert(tc_Arrow__Order__Mirabelle_Oindi,X1,c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oindi,c_COMBI(tc_Arrow__Order__Mirabelle_Oindi),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))))) = c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_1670,i_0_2272,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_2488,i_0_2500,i_0_2508,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_2469,i_0_2514,i_0_2517,i_0_2520,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_1714,i_0_2390,i_0_1821,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_2377,i_0_2532,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_2491,i_0_1470,i_0_2190,i_0_2193,i_0_2494,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_1870,i_0_2340,i_0_2465,i_0_1685,i_0_1863,i_0_1882,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1904,i_0_1905,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404,i_0_1439,i_0_1473,i_0_1483,i_0_1498,i_0_1499,i_0_1543,i_0_1544,i_0_1561,i_0_1562,i_0_1563,i_0_1564,i_0_1588,i_0_1589,i_0_1603,i_0_1653]) ).

cnf(i_0_2540,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
    | X3 = X2
    | ~ class_Orderings_Oorder(X1) ),
    inference(rename_variables,[],[i_0_1653]) ).

cnf(i_0_2541,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = esk33_2(hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),v_F)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_1670,i_0_2272,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_2488,i_0_2500,i_0_2508,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_2469,i_0_2514,i_0_2517,i_0_2520,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_1714,i_0_2390,i_0_1821,i_0_2537,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_2377,i_0_2532,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_2491,i_0_1470,i_0_2190,i_0_2193,i_0_2494,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_1870,i_0_2340,i_0_2465,i_0_1685,i_0_1863,i_0_1882,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1904,i_0_1905,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404,i_0_1439,i_0_1473,i_0_1483,i_0_1498,i_0_1499,i_0_1543,i_0_1544,i_0_1561,i_0_1562,i_0_1563,i_0_1564,i_0_1588,i_0_1589,i_0_1603,i_0_1653,i_0_1679]) ).

cnf(i_0_2542,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)),
    inference(rename_variables,[],[i_0_1821]) ).

cnf(i_0_2543,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | ~ class_Orderings_Oorder(X1)
    | X2 = X3 ),
    inference(rename_variables,[],[i_0_1679]) ).

cnf(i_0_2544,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_1670,i_0_2272,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_2488,i_0_2500,i_0_2508,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_2469,i_0_2514,i_0_2517,i_0_2520,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_1714,i_0_2390,i_0_1821,i_0_2537,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_2377,i_0_2532,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_2491,i_0_1470,i_0_2190,i_0_2193,i_0_2494,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_1870,i_0_2340,i_0_2465,i_0_1685,i_0_1863,i_0_1882,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1904,i_0_1905,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404,i_0_1439,i_0_1473,i_0_1483,i_0_1498,i_0_1499,i_0_1543,i_0_1544,i_0_1561,i_0_1562,i_0_1563,i_0_1564,i_0_1588,i_0_1589,i_0_1603,i_0_1653,i_0_1679,i_0_1682]) ).

cnf(i_0_2545,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(rename_variables,[],[i_0_1759]) ).

cnf(i_0_2546,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | ~ class_Orderings_Oorder(X1)
    | X3 = X2 ),
    inference(rename_variables,[],[i_0_1682]) ).

cnf(i_0_2547,plain,
    esk33_2(hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),v_F)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_1670,i_0_2272,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_2488,i_0_2500,i_0_2508,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_2545,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_2469,i_0_2514,i_0_2517,i_0_2520,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_1714,i_0_2390,i_0_1821,i_0_2537,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_2377,i_0_2532,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_2491,i_0_1470,i_0_2190,i_0_2193,i_0_2494,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_1870,i_0_2340,i_0_2465,i_0_1685,i_0_1863,i_0_1882,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1904,i_0_1905,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404,i_0_1439,i_0_1473,i_0_1483,i_0_1498,i_0_1499,i_0_1543,i_0_1544,i_0_1561,i_0_1562,i_0_1563,i_0_1564,i_0_1588,i_0_1589,i_0_1603,i_0_1653,i_0_1679,i_0_1682,i_0_1705]) ).

cnf(i_0_2548,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(rename_variables,[],[i_0_1759]) ).

cnf(i_0_2549,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
    | X3 = X2
    | ~ class_Orderings_Olinorder(X1) ),
    inference(rename_variables,[],[i_0_1705]) ).

cnf(i_0_2550,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X1)) != hAPP(c_Nat_OSuc,X1),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_1670,i_0_2272,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_2488,i_0_2500,i_0_2508,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_2545,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_2469,i_0_2514,i_0_2517,i_0_2520,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_1714,i_0_2390,i_0_1821,i_0_2537,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_2377,i_0_2532,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_2491,i_0_1470,i_0_2190,i_0_2193,i_0_2494,i_0_2505,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_1870,i_0_2340,i_0_2465,i_0_1685,i_0_1863,i_0_1882,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1904,i_0_1905,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404,i_0_1439,i_0_1473,i_0_1483,i_0_1498,i_0_1499,i_0_1543,i_0_1544,i_0_1561,i_0_1562,i_0_1563,i_0_1564,i_0_1588,i_0_1589,i_0_1603,i_0_1653,i_0_1679,i_0_1682,i_0_1705,i_0_1717]) ).

cnf(i_0_2551,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X2)),
    inference(rename_variables,[],[i_0_1470]) ).

cnf(i_0_2552,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | X2 != X3
    | ~ class_Orderings_Olinorder(X1) ),
    inference(rename_variables,[],[i_0_1717]) ).

cnf(i_0_2553,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,v_a____))),v_b____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,esk11_0),v_a____),hAPP(c_Nat_OSuc,v_a____)))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_1670,i_0_2272,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_2488,i_0_2500,i_0_2508,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_2545,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_2469,i_0_2514,i_0_2517,i_0_2520,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_1714,i_0_2390,i_0_1821,i_0_2537,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_2377,i_0_2532,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_2491,i_0_1470,i_0_2190,i_0_2193,i_0_2494,i_0_2505,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_1870,i_0_2340,i_0_2465,i_0_2474,i_0_1685,i_0_1863,i_0_1882,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1904,i_0_1905,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404,i_0_1439,i_0_1473,i_0_1483,i_0_1498,i_0_1499,i_0_1543,i_0_1544,i_0_1561,i_0_1562,i_0_1563,i_0_1564,i_0_1588,i_0_1589,i_0_1603,i_0_1653,i_0_1679,i_0_1682,i_0_1705,i_0_1717,i_0_1241]) ).

cnf(i_0_2554,plain,
    X1 != hAPP(c_Nat_OSuc,X1),
    inference(rename_variables,[],[i_0_1870]) ).

cnf(i_0_2555,plain,
    c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
    inference(rename_variables,[],[i_0_1877]) ).

cnf(i_0_2556,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),X1))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X3)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1),X2),X5)))
    | X2 = X5
    | X4 != X5 ),
    inference(rename_variables,[],[i_0_1241]) ).

cnf(i_0_2557,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,v_b____)))),c_Arrow__Order__Mirabelle_Obelow(esk11_0,hAPP(c_Nat_OSuc,v_b____),v_b____))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_2555,i_0_1670,i_0_2272,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_2488,i_0_2500,i_0_2508,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_1759,i_0_2545,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_2469,i_0_2514,i_0_2517,i_0_2520,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_1714,i_0_2390,i_0_1821,i_0_2537,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_2377,i_0_2532,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_2491,i_0_1470,i_0_2190,i_0_2193,i_0_2494,i_0_2505,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_1870,i_0_2340,i_0_2465,i_0_2474,i_0_1685,i_0_1863,i_0_1882,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1904,i_0_1905,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404,i_0_1439,i_0_1473,i_0_1483,i_0_1498,i_0_1499,i_0_1543,i_0_1544,i_0_1561,i_0_1562,i_0_1563,i_0_1564,i_0_1588,i_0_1589,i_0_1603,i_0_1653,i_0_1679,i_0_1682,i_0_1705,i_0_1717,i_0_1241,i_0_1257]) ).

cnf(i_0_2558,plain,
    hAPP(c_Nat_OSuc,X1) != X1,
    inference(rename_variables,[],[i_0_1869]) ).

cnf(i_0_2559,plain,
    c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
    inference(rename_variables,[],[i_0_1877]) ).

cnf(i_0_2560,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),X1))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X4)),c_Arrow__Order__Mirabelle_Obelow(X1,X5,X3)))
    | X5 = X3
    | X4 != X5 ),
    inference(rename_variables,[],[i_0_1257]) ).

cnf(i_0_2561,plain,
    c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_2555,i_0_1670,i_0_2272,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_2488,i_0_2500,i_0_2508,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_2523,i_0_1759,i_0_2545,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_2469,i_0_2514,i_0_2517,i_0_2520,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_1714,i_0_2390,i_0_1821,i_0_2537,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_2377,i_0_2532,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_2491,i_0_1470,i_0_2190,i_0_2193,i_0_2494,i_0_2505,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_2558,i_0_1870,i_0_2340,i_0_2465,i_0_2474,i_0_1685,i_0_1863,i_0_1882,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1904,i_0_1905,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404,i_0_1439,i_0_1473,i_0_1483,i_0_1498,i_0_1499,i_0_1543,i_0_1544,i_0_1561,i_0_1562,i_0_1563,i_0_1564,i_0_1588,i_0_1589,i_0_1603,i_0_1653,i_0_1679,i_0_1682,i_0_1705,i_0_1717,i_0_1241,i_0_1257,i_0_1524]) ).

cnf(i_0_2562,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
    inference(rename_variables,[],[i_0_1785]) ).

cnf(i_0_2563,plain,
    hAPP(c_Nat_OSuc,X1) != X1,
    inference(rename_variables,[],[i_0_1869]) ).

cnf(i_0_2564,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5))
    | c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X3) != c_SetInterval_Oord__class_OatLeastLessThan(X1,X4,X5)
    | X2 = X4
    | ~ class_Orderings_Olinorder(X1) ),
    inference(rename_variables,[],[i_0_1524]) ).

cnf(i_0_2565,plain,
    c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))) != c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_2555,i_0_1670,i_0_2272,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_2488,i_0_2500,i_0_2508,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_2523,i_0_2562,i_0_1759,i_0_2545,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_2469,i_0_2514,i_0_2517,i_0_2520,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_1714,i_0_2390,i_0_1821,i_0_2537,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_2377,i_0_2532,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_2491,i_0_1470,i_0_2190,i_0_2193,i_0_2494,i_0_2505,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_2558,i_0_2563,i_0_1870,i_0_2340,i_0_2465,i_0_2474,i_0_1685,i_0_1863,i_0_1882,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1904,i_0_1905,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404,i_0_1439,i_0_1473,i_0_1483,i_0_1498,i_0_1499,i_0_1543,i_0_1544,i_0_1561,i_0_1562,i_0_1563,i_0_1564,i_0_1588,i_0_1589,i_0_1603,i_0_1653,i_0_1679,i_0_1682,i_0_1705,i_0_1717,i_0_1241,i_0_1257,i_0_1524,i_0_1525]) ).

cnf(i_0_2566,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
    inference(rename_variables,[],[i_0_1785]) ).

cnf(i_0_2567,plain,
    hAPP(c_Nat_OSuc,X1) != X1,
    inference(rename_variables,[],[i_0_1869]) ).

cnf(i_0_2568,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5))
    | c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X3) != c_SetInterval_Oord__class_OatLeastLessThan(X1,X4,X5)
    | X3 = X5
    | ~ class_Orderings_Olinorder(X1) ),
    inference(rename_variables,[],[i_0_1525]) ).

cnf(i_0_2569,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_2555,i_0_1670,i_0_2272,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_2488,i_0_2500,i_0_2508,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_2523,i_0_2562,i_0_1759,i_0_2545,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_2469,i_0_2514,i_0_2517,i_0_2520,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_1714,i_0_2390,i_0_1821,i_0_2537,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_2377,i_0_2532,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1669,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_2491,i_0_1470,i_0_2190,i_0_2193,i_0_2494,i_0_2505,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_2558,i_0_2563,i_0_1870,i_0_2340,i_0_2465,i_0_2474,i_0_1685,i_0_1863,i_0_1882,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1904,i_0_1905,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404,i_0_1439,i_0_1473,i_0_1483,i_0_1498,i_0_1499,i_0_1543,i_0_1544,i_0_1561,i_0_1562,i_0_1563,i_0_1564,i_0_1588,i_0_1589,i_0_1603,i_0_1653,i_0_1679,i_0_1682,i_0_1705,i_0_1717,i_0_1241,i_0_1257,i_0_1524,i_0_1525,i_0_1546]) ).

cnf(i_0_2570,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1))),
    inference(rename_variables,[],[i_0_1669]) ).

cnf(i_0_2571,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X2) != c_Groups_Ozero__class_Ozero(X1)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(rename_variables,[],[i_0_1546]) ).

cnf(i_0_2572,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X1))),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,esk11_0),hAPP(c_Nat_OSuc,X1))),hAPP(c_Nat_OSuc,X1)),X1))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2046,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_2555,i_0_1670,i_0_2272,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_2488,i_0_2500,i_0_2508,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_2523,i_0_2562,i_0_1759,i_0_2545,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_2469,i_0_2514,i_0_2517,i_0_2520,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_1714,i_0_2390,i_0_1821,i_0_2537,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_2377,i_0_2532,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1669,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_2491,i_0_1470,i_0_2190,i_0_2193,i_0_2494,i_0_2505,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_2558,i_0_2563,i_0_2567,i_0_1870,i_0_2340,i_0_2465,i_0_2474,i_0_1685,i_0_1863,i_0_1882,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1904,i_0_1905,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404,i_0_1439,i_0_1473,i_0_1483,i_0_1498,i_0_1499,i_0_1543,i_0_1544,i_0_1561,i_0_1562,i_0_1563,i_0_1564,i_0_1588,i_0_1589,i_0_1603,i_0_1653,i_0_1679,i_0_1682,i_0_1705,i_0_1717,i_0_1241,i_0_1257,i_0_1524,i_0_1525,i_0_1546,i_0_1240]) ).

cnf(i_0_2573,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X3),X2))),
    inference(rename_variables,[],[i_0_2046]) ).

cnf(i_0_2574,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),X1))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1),X4),X5)))
    | X2 = X5
    | X3 = X5
    | X4 = X5 ),
    inference(rename_variables,[],[i_0_1240]) ).

cnf(i_0_2575,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X1))),c_Arrow__Order__Mirabelle_Obelow(hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,esk11_0),hAPP(c_Nat_OSuc,X1)),X1,hAPP(c_Nat_OSuc,X1)))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2046,i_0_2573,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_2555,i_0_1670,i_0_2272,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_2488,i_0_2500,i_0_2508,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_2523,i_0_2562,i_0_1759,i_0_2545,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_2469,i_0_2514,i_0_2517,i_0_2520,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_1714,i_0_2390,i_0_1821,i_0_2537,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_2377,i_0_2532,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1669,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_2491,i_0_1470,i_0_2190,i_0_2193,i_0_2494,i_0_2505,i_0_1528,i_0_1426,i_0_1494,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_2558,i_0_2563,i_0_2567,i_0_1870,i_0_2340,i_0_2465,i_0_2474,i_0_2554,i_0_1685,i_0_1863,i_0_1882,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1904,i_0_1905,i_0_1906,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404,i_0_1439,i_0_1473,i_0_1483,i_0_1498,i_0_1499,i_0_1543,i_0_1544,i_0_1561,i_0_1562,i_0_1563,i_0_1564,i_0_1588,i_0_1589,i_0_1603,i_0_1653,i_0_1679,i_0_1682,i_0_1705,i_0_1717,i_0_1241,i_0_1257,i_0_1524,i_0_1525,i_0_1546,i_0_1240,i_0_1256]) ).

cnf(i_0_2576,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X3),X2))),
    inference(rename_variables,[],[i_0_2046]) ).

cnf(i_0_2577,plain,
    hAPP(c_Nat_OSuc,X1) != X1,
    inference(rename_variables,[],[i_0_1869]) ).

cnf(i_0_2578,plain,
    hAPP(c_Nat_OSuc,X1) != X1,
    inference(rename_variables,[],[i_0_1869]) ).

cnf(i_0_2579,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),X1))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),c_Arrow__Order__Mirabelle_Obelow(X1,X4,X5)))
    | X3 = X4
    | X2 = X4
    | X4 = X5 ),
    inference(rename_variables,[],[i_0_1256]) ).

cnf(i_0_2580,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,esk10_0),v_a____),hAPP(c_Nat_OSuc,v_a____)))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2046,i_0_2573,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_2555,i_0_1670,i_0_2272,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_2488,i_0_2500,i_0_2508,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_2523,i_0_2562,i_0_1759,i_0_2545,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_2469,i_0_2514,i_0_2517,i_0_2520,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_1714,i_0_2390,i_0_1821,i_0_2537,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_2377,i_0_2532,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1669,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_2491,i_0_1470,i_0_2190,i_0_2193,i_0_2494,i_0_2505,i_0_1528,i_0_1426,i_0_1428,i_0_1494,i_0_1495,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_2558,i_0_2563,i_0_2567,i_0_1870,i_0_2340,i_0_2465,i_0_2474,i_0_2554,i_0_1685,i_0_1863,i_0_1882,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1904,i_0_1905,i_0_1906,i_0_1908,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404,i_0_1439,i_0_1473,i_0_1483,i_0_1498,i_0_1499,i_0_1543,i_0_1544,i_0_1561,i_0_1562,i_0_1563,i_0_1564,i_0_1588,i_0_1589,i_0_1603,i_0_1653,i_0_1679,i_0_1682,i_0_1705,i_0_1717,i_0_1241,i_0_1257,i_0_1524,i_0_1525,i_0_1546,i_0_1240,i_0_1256,i_0_2027]) ).

cnf(i_0_2581,plain,
    X1 != hAPP(c_Nat_OSuc,X1),
    inference(rename_variables,[],[i_0_1870]) ).

cnf(i_0_2582,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1),X2),X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),X1))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),X1))
    | X2 = X4
    | X2 = X3 ),
    inference(rename_variables,[],[i_0_2027]) ).

cnf(i_0_2583,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),c_Arrow__Order__Mirabelle_Obelow(esk10_0,hAPP(c_Nat_OSuc,v_b____),v_b____))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2046,i_0_2573,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_2555,i_0_1670,i_0_2272,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_2488,i_0_2500,i_0_2508,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_2523,i_0_2562,i_0_1759,i_0_2545,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_2469,i_0_2514,i_0_2517,i_0_2520,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_1714,i_0_2390,i_0_1821,i_0_2537,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_2377,i_0_2532,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1669,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_2491,i_0_1470,i_0_2190,i_0_2193,i_0_2494,i_0_2505,i_0_1528,i_0_1426,i_0_1428,i_0_1494,i_0_1495,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_2558,i_0_2563,i_0_2567,i_0_2578,i_0_1870,i_0_2340,i_0_2465,i_0_2474,i_0_2554,i_0_1685,i_0_1863,i_0_1882,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1904,i_0_1905,i_0_1906,i_0_1908,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404,i_0_1439,i_0_1473,i_0_1483,i_0_1498,i_0_1499,i_0_1543,i_0_1544,i_0_1561,i_0_1562,i_0_1563,i_0_1564,i_0_1588,i_0_1589,i_0_1603,i_0_1653,i_0_1679,i_0_1682,i_0_1705,i_0_1717,i_0_1241,i_0_1257,i_0_1524,i_0_1525,i_0_1546,i_0_1240,i_0_1256,i_0_2027,i_0_2029]) ).

cnf(i_0_2584,plain,
    hAPP(c_Nat_OSuc,X1) != X1,
    inference(rename_variables,[],[i_0_1869]) ).

cnf(i_0_2585,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),c_Arrow__Order__Mirabelle_Obelow(X1,X4,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),X1))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),X1))
    | X4 = X3
    | X2 = X3 ),
    inference(rename_variables,[],[i_0_2029]) ).

cnf(i_0_2586,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),c_Arrow__Order__Mirabelle_Obelow(hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,esk11_0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2046,i_0_2573,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_2555,i_0_1670,i_0_2272,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_2488,i_0_2500,i_0_2508,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_2523,i_0_2562,i_0_1759,i_0_2545,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_2469,i_0_2514,i_0_2517,i_0_2520,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_1714,i_0_2390,i_0_1821,i_0_2537,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_2377,i_0_2532,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_1669,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_2491,i_0_1470,i_0_2190,i_0_2193,i_0_2494,i_0_2505,i_0_1528,i_0_1426,i_0_1428,i_0_1494,i_0_1495,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_2558,i_0_2563,i_0_2567,i_0_2578,i_0_2584,i_0_2577,i_0_1870,i_0_2340,i_0_2465,i_0_2474,i_0_2554,i_0_1685,i_0_1863,i_0_2159,i_0_1882,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1904,i_0_1905,i_0_1906,i_0_1908,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404,i_0_1439,i_0_1473,i_0_1483,i_0_1498,i_0_1499,i_0_1543,i_0_1544,i_0_1561,i_0_1562,i_0_1563,i_0_1564,i_0_1588,i_0_1589,i_0_1603,i_0_1653,i_0_1679,i_0_1682,i_0_1705,i_0_1717,i_0_1241,i_0_1257,i_0_1524,i_0_1525,i_0_1546,i_0_1240,i_0_1256,i_0_2027,i_0_2029,i_0_2035]) ).

cnf(i_0_2587,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X3),X1))),
    inference(rename_variables,[],[i_0_2045]) ).

cnf(i_0_2588,plain,
    hAPP(c_Nat_OSuc,X1) != X1,
    inference(rename_variables,[],[i_0_1869]) ).

cnf(i_0_2589,plain,
    hAPP(c_Nat_OSuc,X1) != X1,
    inference(rename_variables,[],[i_0_1869]) ).

cnf(i_0_2590,plain,
    hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(rename_variables,[],[i_0_1863]) ).

cnf(i_0_2591,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),X1))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X3)),c_Arrow__Order__Mirabelle_Obelow(X1,X4,X2)))
    | X3 = X4
    | X4 = X2
    | X3 = X2 ),
    inference(rename_variables,[],[i_0_2035]) ).

cnf(i_0_2592,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2046,i_0_2573,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_2555,i_0_1670,i_0_2272,i_0_1849,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_2488,i_0_2500,i_0_2508,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_2523,i_0_2562,i_0_1759,i_0_2545,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_2469,i_0_2514,i_0_2517,i_0_2520,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_1714,i_0_2390,i_0_1821,i_0_2537,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_2377,i_0_2532,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_2212,i_0_1669,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_2491,i_0_1470,i_0_2190,i_0_2193,i_0_2494,i_0_2505,i_0_1528,i_0_1426,i_0_1428,i_0_1494,i_0_1495,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_2558,i_0_2563,i_0_2567,i_0_2578,i_0_2584,i_0_2577,i_0_1870,i_0_2340,i_0_2465,i_0_2474,i_0_2554,i_0_1685,i_0_1863,i_0_2159,i_0_1882,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1904,i_0_1905,i_0_1906,i_0_1908,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404,i_0_1439,i_0_1473,i_0_1483,i_0_1498,i_0_1499,i_0_1543,i_0_1544,i_0_1561,i_0_1562,i_0_1563,i_0_1564,i_0_1588,i_0_1589,i_0_1603,i_0_1653,i_0_1679,i_0_1682,i_0_1705,i_0_1717,i_0_1241,i_0_1257,i_0_1524,i_0_1525,i_0_1546,i_0_1240,i_0_1256,i_0_2027,i_0_2029,i_0_2035,i_0_1558]) ).

cnf(i_0_2593,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))),
    inference(rename_variables,[],[i_0_1668]) ).

cnf(i_0_2594,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
    inference(rename_variables,[],[i_0_1849]) ).

cnf(i_0_2595,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X2) = c_Groups_Ozero__class_Ozero(X1)
    | X3 != c_Groups_Ozero__class_Ozero(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(rename_variables,[],[i_0_1558]) ).

cnf(i_0_2596,plain,
    hAPP(c_Nat_OSuc,hAPP(c_Hilbert__Choice_Oinv__into(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)),c_Nat_OSuc),esk38_3(c_Nat_OSuc,tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oindi))) != esk38_3(c_Nat_OSuc,tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oindi),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2046,i_0_2573,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_2555,i_0_1670,i_0_2272,i_0_1849,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_2488,i_0_2500,i_0_2508,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_2523,i_0_2562,i_0_1759,i_0_2545,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_2469,i_0_2514,i_0_2517,i_0_2520,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_1714,i_0_2390,i_0_1821,i_0_2537,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_2377,i_0_2532,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_2212,i_0_1669,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_2491,i_0_1470,i_0_2190,i_0_2193,i_0_2494,i_0_2505,i_0_1528,i_0_1426,i_0_1428,i_0_1494,i_0_1495,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_2558,i_0_2563,i_0_2567,i_0_2578,i_0_2584,i_0_2577,i_0_1870,i_0_2340,i_0_2465,i_0_2474,i_0_2554,i_0_1685,i_0_1863,i_0_2159,i_0_1882,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1904,i_0_1905,i_0_1906,i_0_1908,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404,i_0_1439,i_0_1473,i_0_1483,i_0_1498,i_0_1499,i_0_1543,i_0_1544,i_0_1561,i_0_1562,i_0_1563,i_0_1564,i_0_1588,i_0_1589,i_0_1603,i_0_1653,i_0_1679,i_0_1682,i_0_1705,i_0_1717,i_0_1241,i_0_1257,i_0_1524,i_0_1525,i_0_1546,i_0_1240,i_0_1256,i_0_2027,i_0_2029,i_0_2035,i_0_1558,i_0_1300]) ).

cnf(i_0_2597,plain,
    ( c_Set_Oimage(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))
    | hAPP(X3,hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3),esk38_3(X3,X2,X1))) != esk38_3(X3,X2,X1) ),
    inference(rename_variables,[],[i_0_1300]) ).

cnf(i_0_2598,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))),X2)),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2046,i_0_2573,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_2555,i_0_1670,i_0_2272,i_0_1849,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_2488,i_0_2500,i_0_2508,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_2523,i_0_2562,i_0_1759,i_0_2545,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_2469,i_0_2514,i_0_2517,i_0_2520,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_1714,i_0_2390,i_0_1821,i_0_2537,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_2377,i_0_2532,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_2212,i_0_1669,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_2491,i_0_1470,i_0_2190,i_0_2193,i_0_2494,i_0_2505,i_0_1528,i_0_1426,i_0_1428,i_0_1494,i_0_1495,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_2558,i_0_2563,i_0_2567,i_0_2578,i_0_2584,i_0_2577,i_0_1870,i_0_2340,i_0_2465,i_0_2474,i_0_2554,i_0_1685,i_0_1863,i_0_2159,i_0_1882,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1904,i_0_1905,i_0_1906,i_0_1908,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404,i_0_1439,i_0_1473,i_0_1483,i_0_1498,i_0_1499,i_0_1543,i_0_1544,i_0_1561,i_0_1562,i_0_1563,i_0_1564,i_0_1588,i_0_1589,i_0_1603,i_0_1653,i_0_1679,i_0_1682,i_0_1705,i_0_1717,i_0_1241,i_0_1257,i_0_1524,i_0_1525,i_0_1546,i_0_1240,i_0_1256,i_0_2027,i_0_2029,i_0_2035,i_0_1558,i_0_1300,i_0_1458]) ).

cnf(i_0_2599,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3)) ),
    inference(rename_variables,[],[i_0_1458]) ).

cnf(i_0_2600,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))),X3)),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2046,i_0_2573,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_2555,i_0_1670,i_0_2272,i_0_1849,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_2488,i_0_2500,i_0_2508,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_2523,i_0_2562,i_0_1759,i_0_2545,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_2469,i_0_2514,i_0_2517,i_0_2520,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_1714,i_0_2390,i_0_1821,i_0_2537,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_2377,i_0_2532,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_2212,i_0_1669,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_2491,i_0_1470,i_0_2190,i_0_2193,i_0_2494,i_0_2505,i_0_1528,i_0_1426,i_0_1428,i_0_1494,i_0_1495,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_2558,i_0_2563,i_0_2567,i_0_2578,i_0_2584,i_0_2577,i_0_1870,i_0_2340,i_0_2465,i_0_2474,i_0_2554,i_0_1685,i_0_1863,i_0_2159,i_0_1882,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1904,i_0_1905,i_0_1906,i_0_1908,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404,i_0_1439,i_0_1473,i_0_1483,i_0_1498,i_0_1499,i_0_1543,i_0_1544,i_0_1561,i_0_1562,i_0_1563,i_0_1564,i_0_1588,i_0_1589,i_0_1603,i_0_1653,i_0_1679,i_0_1682,i_0_1705,i_0_1717,i_0_1241,i_0_1257,i_0_1524,i_0_1525,i_0_1546,i_0_1240,i_0_1256,i_0_2027,i_0_2029,i_0_2035,i_0_1558,i_0_1300,i_0_1458,i_0_1459]) ).

cnf(i_0_2601,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3)) ),
    inference(rename_variables,[],[i_0_1459]) ).

cnf(i_0_2602,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2046,i_0_2573,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_2555,i_0_1670,i_0_2272,i_0_1849,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_2488,i_0_2500,i_0_2508,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_2523,i_0_2562,i_0_1759,i_0_2545,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_2469,i_0_2514,i_0_2517,i_0_2520,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_1714,i_0_2390,i_0_1821,i_0_2537,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_2377,i_0_2532,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_2212,i_0_1669,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_2491,i_0_1470,i_0_2190,i_0_2193,i_0_2494,i_0_2505,i_0_1528,i_0_1426,i_0_1428,i_0_1494,i_0_1495,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_2558,i_0_2563,i_0_2567,i_0_2578,i_0_2584,i_0_2577,i_0_1870,i_0_2340,i_0_2465,i_0_2474,i_0_2554,i_0_1685,i_0_1863,i_0_2159,i_0_1882,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1904,i_0_1905,i_0_1906,i_0_1908,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404,i_0_1439,i_0_1473,i_0_1483,i_0_1498,i_0_1499,i_0_1543,i_0_1544,i_0_1561,i_0_1562,i_0_1563,i_0_1564,i_0_1588,i_0_1589,i_0_1603,i_0_1653,i_0_1679,i_0_1682,i_0_1705,i_0_1717,i_0_1241,i_0_1257,i_0_1524,i_0_1525,i_0_1546,i_0_1240,i_0_1256,i_0_2027,i_0_2029,i_0_2035,i_0_1558,i_0_1300,i_0_1458,i_0_1459,i_0_1560]) ).

cnf(i_0_2603,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2)))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
    inference(rename_variables,[],[i_0_1560]) ).

cnf(i_0_2604,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))),X1)),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2046,i_0_2573,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_2555,i_0_1670,i_0_2272,i_0_1849,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_2488,i_0_2500,i_0_2508,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_2523,i_0_2562,i_0_1759,i_0_2545,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_2469,i_0_2514,i_0_2517,i_0_2520,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_1714,i_0_2390,i_0_1821,i_0_2537,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_2377,i_0_2532,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_2212,i_0_1669,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_2491,i_0_1470,i_0_2190,i_0_2193,i_0_2494,i_0_2505,i_0_1528,i_0_1426,i_0_1428,i_0_1494,i_0_1495,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_2558,i_0_2563,i_0_2567,i_0_2578,i_0_2584,i_0_2577,i_0_1870,i_0_2340,i_0_2465,i_0_2474,i_0_2554,i_0_1685,i_0_1863,i_0_2159,i_0_1882,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1904,i_0_1905,i_0_1906,i_0_1908,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404,i_0_1439,i_0_1473,i_0_1483,i_0_1498,i_0_1499,i_0_1543,i_0_1544,i_0_1561,i_0_1562,i_0_1563,i_0_1564,i_0_1588,i_0_1589,i_0_1603,i_0_1653,i_0_1679,i_0_1682,i_0_1705,i_0_1717,i_0_1241,i_0_1257,i_0_1524,i_0_1525,i_0_1546,i_0_1240,i_0_1256,i_0_2027,i_0_2029,i_0_2035,i_0_1558,i_0_1300,i_0_1458,i_0_1459,i_0_1560,i_0_1619]) ).

cnf(i_0_2605,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(rename_variables,[],[i_0_1619]) ).

cnf(i_0_2606,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2046,i_0_2573,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_2555,i_0_1670,i_0_2272,i_0_1849,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_2488,i_0_2500,i_0_2508,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_2523,i_0_2562,i_0_1759,i_0_2545,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_2469,i_0_2514,i_0_2517,i_0_2520,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_1714,i_0_2390,i_0_1821,i_0_2537,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_2377,i_0_2532,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_2212,i_0_1669,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_2491,i_0_1470,i_0_2190,i_0_2193,i_0_2494,i_0_2505,i_0_1528,i_0_1426,i_0_1428,i_0_1494,i_0_1495,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_2558,i_0_2563,i_0_2567,i_0_2578,i_0_2584,i_0_2577,i_0_1870,i_0_2340,i_0_2465,i_0_2474,i_0_2554,i_0_1685,i_0_1863,i_0_2159,i_0_1882,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1904,i_0_1905,i_0_1906,i_0_1908,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404,i_0_1439,i_0_1473,i_0_1483,i_0_1498,i_0_1499,i_0_1543,i_0_1544,i_0_1561,i_0_1562,i_0_1563,i_0_1564,i_0_1588,i_0_1589,i_0_1603,i_0_1653,i_0_1679,i_0_1682,i_0_1705,i_0_1717,i_0_1241,i_0_1257,i_0_1524,i_0_1525,i_0_1546,i_0_1240,i_0_1256,i_0_2027,i_0_2029,i_0_2035,i_0_1558,i_0_1300,i_0_1458,i_0_1459,i_0_1560,i_0_1619,i_0_1683]) ).

cnf(i_0_2607,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
    inference(rename_variables,[],[i_0_1683]) ).

cnf(i_0_2608,plain,
    esk33_2(hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),v_F)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) != hAPP(c_Nat_OSuc,X1),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2046,i_0_2573,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_2555,i_0_1670,i_0_2272,i_0_1849,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_2488,i_0_2500,i_0_2508,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_2523,i_0_2562,i_0_1759,i_0_2545,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_2469,i_0_2514,i_0_2517,i_0_2520,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_1714,i_0_2390,i_0_1821,i_0_2537,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_2377,i_0_2532,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_2212,i_0_1669,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_2491,i_0_1470,i_0_2190,i_0_2193,i_0_2494,i_0_2505,i_0_1528,i_0_1426,i_0_1428,i_0_1494,i_0_1495,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_2558,i_0_2563,i_0_2567,i_0_2578,i_0_2584,i_0_2577,i_0_1870,i_0_2340,i_0_2465,i_0_2474,i_0_2554,i_0_1685,i_0_1863,i_0_2159,i_0_1882,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1904,i_0_1905,i_0_1906,i_0_1908,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404,i_0_1439,i_0_1473,i_0_1483,i_0_1498,i_0_1499,i_0_1543,i_0_1544,i_0_1561,i_0_1562,i_0_1563,i_0_1564,i_0_1588,i_0_1589,i_0_1603,i_0_1653,i_0_1679,i_0_1682,i_0_1705,i_0_1717,i_0_1241,i_0_1257,i_0_1524,i_0_1525,i_0_1546,i_0_1240,i_0_1256,i_0_2027,i_0_2029,i_0_2035,i_0_1558,i_0_1300,i_0_1458,i_0_1459,i_0_1560,i_0_1619,i_0_1683,i_0_1790]) ).

cnf(i_0_2609,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
    | X1 != hAPP(c_Nat_OSuc,X2) ),
    inference(rename_variables,[],[i_0_1790]) ).

cnf(i_0_2610,plain,
    hAPP(c_Nat_OSuc,hAPP(c_Hilbert__Choice_Oinv__into(X1,X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_COMBI(X1)),hAPP(c_COMBI(X1),X2))) != X2,
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2046,i_0_2573,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_2555,i_0_1670,i_0_2272,i_0_1849,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_2488,i_0_2500,i_0_2508,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_2523,i_0_2562,i_0_1759,i_0_2545,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_2469,i_0_2514,i_0_2517,i_0_2520,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_1714,i_0_2390,i_0_1821,i_0_2537,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_2377,i_0_2532,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_2212,i_0_1669,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_2491,i_0_1470,i_0_2190,i_0_2193,i_0_2494,i_0_2505,i_0_1528,i_0_1426,i_0_1428,i_0_1494,i_0_1495,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_2558,i_0_2563,i_0_2567,i_0_2578,i_0_2584,i_0_2577,i_0_1870,i_0_2340,i_0_2465,i_0_2474,i_0_2554,i_0_1685,i_0_1863,i_0_2159,i_0_1882,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1904,i_0_1905,i_0_1906,i_0_1908,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404,i_0_1439,i_0_1473,i_0_1483,i_0_1498,i_0_1499,i_0_1543,i_0_1544,i_0_1561,i_0_1562,i_0_1563,i_0_1564,i_0_1588,i_0_1589,i_0_1603,i_0_1653,i_0_1679,i_0_1682,i_0_1705,i_0_1717,i_0_1241,i_0_1257,i_0_1524,i_0_1525,i_0_1546,i_0_1240,i_0_1256,i_0_2027,i_0_2029,i_0_2035,i_0_1558,i_0_1300,i_0_1458,i_0_1459,i_0_1560,i_0_1619,i_0_1683,i_0_1790,i_0_1913]) ).

cnf(i_0_2611,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = esk45_2(c_Set_Oinsert(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),v_F)))
    | hBOOL(hAPP(X2,esk45_2(c_Set_Oinsert(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),v_F))))) ),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2046,i_0_2573,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_2555,i_0_1670,i_0_2272,i_0_1849,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_2488,i_0_2500,i_0_2508,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_2523,i_0_2562,i_0_1759,i_0_2545,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_2469,i_0_2514,i_0_2517,i_0_2520,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_1714,i_0_2390,i_0_1821,i_0_2537,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_2377,i_0_2532,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_2212,i_0_1669,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_2491,i_0_1470,i_0_2190,i_0_2193,i_0_2494,i_0_2505,i_0_1528,i_0_1426,i_0_1428,i_0_1494,i_0_1495,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_2558,i_0_2563,i_0_2567,i_0_2578,i_0_2584,i_0_2577,i_0_1870,i_0_2340,i_0_2465,i_0_2474,i_0_2554,i_0_1685,i_0_1863,i_0_2159,i_0_1882,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1904,i_0_1905,i_0_1906,i_0_1908,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404,i_0_1439,i_0_1473,i_0_1483,i_0_1498,i_0_1499,i_0_1543,i_0_1544,i_0_1561,i_0_1562,i_0_1563,i_0_1564,i_0_1588,i_0_1589,i_0_1603,i_0_1653,i_0_1679,i_0_1682,i_0_1705,i_0_1717,i_0_1241,i_0_1257,i_0_1524,i_0_1525,i_0_1546,i_0_1240,i_0_1256,i_0_2027,i_0_2029,i_0_2035,i_0_1558,i_0_1300,i_0_1458,i_0_1459,i_0_1560,i_0_1619,i_0_1683,i_0_1790,i_0_1913,i_0_1557]) ).

cnf(i_0_2612,plain,
    ( ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4))
    | hBOOL(hAPP(X3,X4))
    | X2 = X4 ),
    inference(rename_variables,[],[i_0_1557]) ).

cnf(i_0_2613,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X2)),
    inference(rename_variables,[],[i_0_2059]) ).

cnf(i_0_2614,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
    inference(rename_variables,[],[i_0_1646]) ).

cnf(i_0_2615,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = esk45_2(c_Set_Oinsert(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),v_F)))
    | ~ c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oindi,c_Nat_OSuc,c_Set_Oinsert(tc_Arrow__Order__Mirabelle_Oindi,X3,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))) ),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2344,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2046,i_0_2573,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_2555,i_0_1670,i_0_2272,i_0_1849,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_2480,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_2488,i_0_2500,i_0_2508,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_2523,i_0_2562,i_0_1759,i_0_2545,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_2469,i_0_2514,i_0_2517,i_0_2520,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_2497,i_0_1714,i_0_2390,i_0_1821,i_0_2537,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_2377,i_0_2532,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_2212,i_0_1669,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_2491,i_0_1470,i_0_2190,i_0_2193,i_0_2494,i_0_2505,i_0_1528,i_0_1426,i_0_1428,i_0_1494,i_0_1495,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_2558,i_0_2563,i_0_2567,i_0_2578,i_0_2584,i_0_2577,i_0_1870,i_0_2340,i_0_2465,i_0_2474,i_0_2554,i_0_1685,i_0_1863,i_0_2159,i_0_1882,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1904,i_0_1905,i_0_1906,i_0_1908,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404,i_0_1439,i_0_1473,i_0_1483,i_0_1498,i_0_1499,i_0_1543,i_0_1544,i_0_1561,i_0_1562,i_0_1563,i_0_1564,i_0_1588,i_0_1589,i_0_1603,i_0_1653,i_0_1679,i_0_1682,i_0_1705,i_0_1717,i_0_1241,i_0_1257,i_0_1524,i_0_1525,i_0_1546,i_0_1240,i_0_1256,i_0_2027,i_0_2029,i_0_2035,i_0_1558,i_0_1300,i_0_1458,i_0_1459,i_0_1560,i_0_1619,i_0_1683,i_0_1790,i_0_1913,i_0_1557,i_0_1399,i_0_1412]) ).

cnf(i_0_2616,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Set_Oinsert(X1,X3,X2))),
    inference(rename_variables,[],[i_0_1568]) ).

cnf(i_0_2617,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
    | c_Fun_Oinj__on(X1,X4,X5,X2)
    | ~ c_Fun_Oinj__on(X1,X4,X5,X3) ),
    inference(rename_variables,[],[i_0_1412]) ).

cnf(i_0_2618,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
    inference(rename_variables,[],[i_0_1646]) ).

cnf(i_0_2619,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = esk45_2(c_Set_Oinsert(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),v_F)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),X5))),X3)) ),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2344,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2046,i_0_2573,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_2555,i_0_1670,i_0_2272,i_0_1849,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_2480,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_2488,i_0_2500,i_0_2508,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_2523,i_0_2562,i_0_1759,i_0_2545,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_2469,i_0_2514,i_0_2517,i_0_2520,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_2497,i_0_2614,i_0_1714,i_0_2390,i_0_1821,i_0_2537,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_2377,i_0_2532,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_2212,i_0_1669,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_2491,i_0_1470,i_0_2190,i_0_2193,i_0_2494,i_0_2505,i_0_1528,i_0_1426,i_0_1428,i_0_1494,i_0_1495,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_2558,i_0_2563,i_0_2567,i_0_2578,i_0_2584,i_0_2577,i_0_1870,i_0_2340,i_0_2465,i_0_2474,i_0_2554,i_0_1685,i_0_1863,i_0_2159,i_0_1882,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1904,i_0_1905,i_0_1906,i_0_1908,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404,i_0_1439,i_0_1473,i_0_1483,i_0_1498,i_0_1499,i_0_1543,i_0_1544,i_0_1561,i_0_1562,i_0_1563,i_0_1564,i_0_1588,i_0_1589,i_0_1603,i_0_1653,i_0_1679,i_0_1682,i_0_1705,i_0_1717,i_0_1241,i_0_1257,i_0_1524,i_0_1525,i_0_1546,i_0_1240,i_0_1256,i_0_2027,i_0_2029,i_0_2035,i_0_1558,i_0_1300,i_0_1458,i_0_1459,i_0_1560,i_0_1619,i_0_1683,i_0_1790,i_0_1913,i_0_1557,i_0_1399,i_0_1412,i_0_1442,i_0_1533]) ).

cnf(i_0_2620,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X3)) ),
    inference(rename_variables,[],[i_0_1533]) ).

cnf(i_0_2621,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = esk45_2(c_Set_Oinsert(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),v_F)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))),hAPP(c_Nat_OSuc,esk7_0))) ),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2344,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2046,i_0_2573,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_2555,i_0_1670,i_0_2272,i_0_1849,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_2480,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_2488,i_0_2500,i_0_2508,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_2523,i_0_2562,i_0_1759,i_0_2545,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_2469,i_0_2514,i_0_2517,i_0_2520,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_2497,i_0_2614,i_0_1714,i_0_2390,i_0_1821,i_0_2537,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_2377,i_0_2532,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_2212,i_0_1669,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_2491,i_0_1470,i_0_2190,i_0_2193,i_0_2494,i_0_2505,i_0_1528,i_0_1426,i_0_1428,i_0_1494,i_0_1495,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_2558,i_0_2563,i_0_2567,i_0_2578,i_0_2584,i_0_2577,i_0_1870,i_0_2340,i_0_2465,i_0_2474,i_0_2554,i_0_1685,i_0_1863,i_0_2159,i_0_1882,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1904,i_0_1905,i_0_1906,i_0_1908,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404,i_0_1439,i_0_1473,i_0_1483,i_0_1498,i_0_1499,i_0_1543,i_0_1544,i_0_1561,i_0_1562,i_0_1563,i_0_1564,i_0_1588,i_0_1589,i_0_1603,i_0_1653,i_0_1679,i_0_1682,i_0_1705,i_0_1717,i_0_1241,i_0_1257,i_0_1524,i_0_1525,i_0_1546,i_0_1240,i_0_1256,i_0_2027,i_0_2029,i_0_2035,i_0_1558,i_0_1300,i_0_1458,i_0_1459,i_0_1560,i_0_1619,i_0_1683,i_0_1790,i_0_1913,i_0_1557,i_0_1399,i_0_1412,i_0_1442,i_0_1533,i_0_1612]) ).

cnf(i_0_2622,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
    | X2 = X1 ),
    inference(rename_variables,[],[i_0_1612]) ).

cnf(i_0_2623,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = esk45_2(c_Set_Oinsert(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),v_F)))
    | c_Set_Oinsert(tc_Arrow__Order__Mirabelle_Oindi,X3,c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oindi,c_COMBI(tc_Arrow__Order__Mirabelle_Oindi),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)) ),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2344,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2046,i_0_2573,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_2555,i_0_1670,i_0_2272,i_0_1849,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_2480,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_2488,i_0_2500,i_0_2508,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_2523,i_0_2562,i_0_1759,i_0_2545,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_2469,i_0_2514,i_0_2517,i_0_2520,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_2497,i_0_2614,i_0_1714,i_0_2390,i_0_1821,i_0_2537,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_2377,i_0_2532,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_2212,i_0_1669,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_2491,i_0_1470,i_0_2190,i_0_2193,i_0_2494,i_0_2505,i_0_1528,i_0_1426,i_0_1428,i_0_1494,i_0_1495,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_2558,i_0_2563,i_0_2567,i_0_2578,i_0_2584,i_0_2577,i_0_1870,i_0_2340,i_0_2465,i_0_2474,i_0_2554,i_0_1685,i_0_1863,i_0_2159,i_0_1882,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1904,i_0_1905,i_0_1906,i_0_1908,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404,i_0_1439,i_0_1473,i_0_1483,i_0_1498,i_0_1499,i_0_1543,i_0_1544,i_0_1561,i_0_1562,i_0_1563,i_0_1564,i_0_1588,i_0_1589,i_0_1603,i_0_1653,i_0_1679,i_0_1682,i_0_1705,i_0_1717,i_0_1241,i_0_1257,i_0_1524,i_0_1525,i_0_1546,i_0_1240,i_0_1256,i_0_2027,i_0_2029,i_0_2035,i_0_1558,i_0_1300,i_0_1458,i_0_1459,i_0_1560,i_0_1619,i_0_1683,i_0_1790,i_0_1913,i_0_1557,i_0_1399,i_0_1412,i_0_1442,i_0_1533,i_0_1612,i_0_1661]) ).

cnf(i_0_2624,plain,
    ( c_Finite__Set_Ocard(X1,X2) != c_Finite__Set_Ocard(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
    | X2 = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))
    | ~ c_Finite__Set_Ofinite(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(rename_variables,[],[i_0_1661]) ).

cnf(i_0_2625,plain,
    ( c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) = c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Set_Oinsert(tc_Arrow__Order__Mirabelle_Oindi,X1,c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oindi,c_COMBI(tc_Arrow__Order__Mirabelle_Oindi),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))))
    | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = esk45_2(c_Set_Oinsert(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),v_F))) ),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2344,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2046,i_0_2573,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_2555,i_0_1670,i_0_2272,i_0_1849,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_2480,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_2488,i_0_2500,i_0_2508,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_2523,i_0_2562,i_0_1759,i_0_2545,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_2469,i_0_2514,i_0_2517,i_0_2520,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_2497,i_0_2614,i_0_1714,i_0_2390,i_0_1821,i_0_2537,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_2377,i_0_2532,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_2212,i_0_1669,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_2491,i_0_1470,i_0_2190,i_0_2193,i_0_2494,i_0_2505,i_0_1528,i_0_1426,i_0_1428,i_0_1494,i_0_1495,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_2558,i_0_2563,i_0_2567,i_0_2578,i_0_2584,i_0_2577,i_0_1870,i_0_2340,i_0_2465,i_0_2474,i_0_2554,i_0_1685,i_0_1863,i_0_2159,i_0_1882,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1904,i_0_1905,i_0_1906,i_0_1908,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404,i_0_1439,i_0_1473,i_0_1483,i_0_1498,i_0_1499,i_0_1543,i_0_1544,i_0_1561,i_0_1562,i_0_1563,i_0_1564,i_0_1588,i_0_1589,i_0_1603,i_0_1653,i_0_1679,i_0_1682,i_0_1705,i_0_1717,i_0_1241,i_0_1257,i_0_1524,i_0_1525,i_0_1546,i_0_1240,i_0_1256,i_0_2027,i_0_2029,i_0_2035,i_0_1558,i_0_1300,i_0_1458,i_0_1459,i_0_1560,i_0_1619,i_0_1683,i_0_1790,i_0_1913,i_0_1557,i_0_1399,i_0_1412,i_0_1442,i_0_1533,i_0_1612,i_0_1661,i_0_1686]) ).

cnf(i_0_2626,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1))
    | X1 = X2 ),
    inference(rename_variables,[],[i_0_1686]) ).

cnf(i_0_2627,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = esk45_2(c_Set_Oinsert(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),v_F)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),X5))))),X3)) ),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2344,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2046,i_0_2573,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_2555,i_0_1670,i_0_2272,i_0_1849,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_2480,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_2488,i_0_2500,i_0_2508,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_2523,i_0_2562,i_0_2566,i_0_1759,i_0_2545,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_2469,i_0_2514,i_0_2517,i_0_2520,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_2497,i_0_2614,i_0_1714,i_0_2390,i_0_1821,i_0_2537,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_2377,i_0_2532,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_2212,i_0_1669,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_2491,i_0_1470,i_0_2190,i_0_2193,i_0_2494,i_0_2505,i_0_1528,i_0_1426,i_0_1428,i_0_1494,i_0_1495,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_2558,i_0_2563,i_0_2567,i_0_2578,i_0_2584,i_0_2577,i_0_1870,i_0_2340,i_0_2465,i_0_2474,i_0_2554,i_0_1685,i_0_1863,i_0_2159,i_0_1882,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1904,i_0_1905,i_0_1906,i_0_1908,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404,i_0_1439,i_0_1473,i_0_1483,i_0_1498,i_0_1499,i_0_1543,i_0_1544,i_0_1561,i_0_1562,i_0_1563,i_0_1564,i_0_1588,i_0_1589,i_0_1603,i_0_1653,i_0_1679,i_0_1682,i_0_1705,i_0_1717,i_0_1241,i_0_1257,i_0_1524,i_0_1525,i_0_1546,i_0_1240,i_0_1256,i_0_2027,i_0_2029,i_0_2035,i_0_1558,i_0_1300,i_0_1458,i_0_1459,i_0_1560,i_0_1619,i_0_1683,i_0_1790,i_0_1913,i_0_1557,i_0_1399,i_0_1412,i_0_1442,i_0_1533,i_0_1612,i_0_1661,i_0_1686,i_0_1389]) ).

cnf(i_0_2628,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
    inference(rename_variables,[],[i_0_1785]) ).

cnf(i_0_2629,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X5))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(rename_variables,[],[i_0_1389]) ).

cnf(i_0_2630,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = esk45_2(c_Set_Oinsert(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),v_F)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,esk11_0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) ),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2344,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2587,i_0_2046,i_0_2573,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_2555,i_0_1670,i_0_2272,i_0_1849,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_2480,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_2488,i_0_2500,i_0_2508,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_2523,i_0_2562,i_0_2566,i_0_1759,i_0_2545,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_2469,i_0_2514,i_0_2517,i_0_2520,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_2497,i_0_2614,i_0_1714,i_0_2390,i_0_1821,i_0_2537,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_2377,i_0_2532,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_2212,i_0_1669,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_2491,i_0_1470,i_0_2190,i_0_2193,i_0_2494,i_0_2505,i_0_1528,i_0_1426,i_0_1428,i_0_1494,i_0_1495,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_2558,i_0_2563,i_0_2567,i_0_2578,i_0_2584,i_0_2588,i_0_2577,i_0_1870,i_0_2340,i_0_2465,i_0_2474,i_0_2554,i_0_2581,i_0_1685,i_0_1863,i_0_2159,i_0_1866,i_0_1882,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1904,i_0_1905,i_0_1906,i_0_1908,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404,i_0_1439,i_0_1473,i_0_1483,i_0_1498,i_0_1499,i_0_1543,i_0_1544,i_0_1561,i_0_1562,i_0_1563,i_0_1564,i_0_1588,i_0_1589,i_0_1603,i_0_1653,i_0_1679,i_0_1682,i_0_1705,i_0_1717,i_0_1241,i_0_1257,i_0_1524,i_0_1525,i_0_1546,i_0_1240,i_0_1256,i_0_2027,i_0_2029,i_0_2035,i_0_1558,i_0_1300,i_0_1458,i_0_1459,i_0_1560,i_0_1619,i_0_1683,i_0_1790,i_0_1913,i_0_1557,i_0_1399,i_0_1412,i_0_1442,i_0_1533,i_0_1612,i_0_1661,i_0_1686,i_0_1389,i_0_2030]) ).

cnf(i_0_2631,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X3),X1))),
    inference(rename_variables,[],[i_0_2045]) ).

cnf(i_0_2632,plain,
    X1 != hAPP(c_Nat_OSuc,X1),
    inference(rename_variables,[],[i_0_1870]) ).

cnf(i_0_2633,plain,
    hAPP(c_Nat_OSuc,X1) != X1,
    inference(rename_variables,[],[i_0_1869]) ).

cnf(i_0_2634,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
    inference(rename_variables,[],[i_0_1866]) ).

cnf(i_0_2635,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1),X4),X3)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X4)),X1))
    | X2 = X3
    | X4 = X3
    | X2 = X4 ),
    inference(rename_variables,[],[i_0_2030]) ).

cnf(i_0_2636,plain,
    ( c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) != esk45_2(c_Set_Oinsert(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),v_F)))
    | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = esk45_2(c_Set_Oinsert(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),v_F))) ),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2344,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2587,i_0_2046,i_0_2573,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_2555,i_0_1670,i_0_2272,i_0_1849,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_2480,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_2488,i_0_2500,i_0_2508,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_2523,i_0_2562,i_0_2566,i_0_1759,i_0_2545,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_2469,i_0_2514,i_0_2517,i_0_2520,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_2497,i_0_2614,i_0_1714,i_0_2390,i_0_1821,i_0_2537,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_2377,i_0_2532,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_2212,i_0_1669,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_2491,i_0_1470,i_0_2190,i_0_2193,i_0_2494,i_0_2505,i_0_1528,i_0_1426,i_0_1428,i_0_1494,i_0_1495,i_0_1363,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_2558,i_0_2563,i_0_2567,i_0_2578,i_0_2584,i_0_2588,i_0_2577,i_0_1870,i_0_2340,i_0_2465,i_0_2474,i_0_2554,i_0_2581,i_0_1685,i_0_1863,i_0_2159,i_0_1866,i_0_1882,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1904,i_0_1905,i_0_1906,i_0_1908,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404,i_0_1439,i_0_1473,i_0_1483,i_0_1498,i_0_1499,i_0_1543,i_0_1544,i_0_1561,i_0_1562,i_0_1563,i_0_1564,i_0_1588,i_0_1589,i_0_1603,i_0_1653,i_0_1679,i_0_1682,i_0_1705,i_0_1717,i_0_1241,i_0_1257,i_0_1524,i_0_1525,i_0_1546,i_0_1240,i_0_1256,i_0_2027,i_0_2029,i_0_2035,i_0_1558,i_0_1300,i_0_1458,i_0_1459,i_0_1560,i_0_1619,i_0_1683,i_0_1790,i_0_1913,i_0_1557,i_0_1399,i_0_1412,i_0_1442,i_0_1533,i_0_1612,i_0_1661,i_0_1686,i_0_1389,i_0_2030,i_0_1537]) ).

cnf(i_0_2637,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | X2 != X3 ),
    inference(rename_variables,[],[i_0_1537]) ).

cnf(i_0_2638,plain,
    ( c_Arrow__Order__Mirabelle_Odictator(v_F,X1)
    | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = esk45_2(c_Set_Oinsert(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),v_F)))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk14_2(X1,v_F)),c_Arrow__Order__Mirabelle_OProf)) ),
    inference(scs_inference,[],[i_0_2066,i_0_2059,i_0_2344,i_0_2045,i_0_2284,i_0_2287,i_0_2291,i_0_2587,i_0_2631,i_0_2046,i_0_2573,i_0_2077,i_0_2116,i_0_2280,i_0_2290,i_0_2300,i_0_1877,i_0_2297,i_0_2332,i_0_2434,i_0_2438,i_0_2440,i_0_2442,i_0_2444,i_0_2446,i_0_2448,i_0_2450,i_0_2452,i_0_2455,i_0_2457,i_0_2459,i_0_2461,i_0_2555,i_0_1670,i_0_2272,i_0_1849,i_0_1817,i_0_1842,i_0_1568,i_0_2121,i_0_2317,i_0_2325,i_0_2352,i_0_2480,i_0_1831,i_0_2177,i_0_2215,i_0_2281,i_0_2314,i_0_2470,i_0_2488,i_0_2500,i_0_2508,i_0_1765,i_0_2471,i_0_1785,i_0_2162,i_0_2165,i_0_2196,i_0_2523,i_0_2562,i_0_2566,i_0_1759,i_0_2545,i_0_1745,i_0_2138,i_0_2147,i_0_2267,i_0_1776,i_0_2152,i_0_2380,i_0_2391,i_0_2469,i_0_2514,i_0_2517,i_0_2520,i_0_1646,i_0_2349,i_0_2353,i_0_2358,i_0_2383,i_0_2497,i_0_2614,i_0_1714,i_0_2390,i_0_1821,i_0_2537,i_0_1657,i_0_2204,i_0_2207,i_0_2230,i_0_2260,i_0_2377,i_0_2532,i_0_1351,i_0_1668,i_0_2180,i_0_2183,i_0_2199,i_0_2212,i_0_1669,i_0_1616,i_0_1615,i_0_1614,i_0_1325,i_0_1469,i_0_2251,i_0_2254,i_0_2374,i_0_2401,i_0_2406,i_0_2491,i_0_1470,i_0_2190,i_0_2193,i_0_2494,i_0_2505,i_0_1528,i_0_1426,i_0_1428,i_0_1494,i_0_1495,i_0_1363,i_0_1171,i_0_1671,i_0_2294,i_0_2301,i_0_2326,i_0_2341,i_0_1869,i_0_2394,i_0_2421,i_0_2477,i_0_2558,i_0_2563,i_0_2567,i_0_2578,i_0_2584,i_0_2588,i_0_2577,i_0_1870,i_0_2340,i_0_2465,i_0_2474,i_0_2554,i_0_2581,i_0_1685,i_0_1863,i_0_2159,i_0_1866,i_0_1882,i_0_1887,i_0_1889,i_0_1891,i_0_1894,i_0_1897,i_0_1898,i_0_1899,i_0_1900,i_0_1902,i_0_1903,i_0_1904,i_0_1905,i_0_1906,i_0_1908,i_0_1798,i_0_1462,i_0_1846,i_0_1286,i_0_1292,i_0_1353,i_0_1391,i_0_1403,i_0_1531,i_0_1698,i_0_1718,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1332,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1438,i_0_1440,i_0_1454,i_0_1455,i_0_1480,i_0_1539,i_0_1550,i_0_1552,i_0_1570,i_0_1571,i_0_1573,i_0_1575,i_0_1577,i_0_1581,i_0_1585,i_0_1599,i_0_1601,i_0_1630,i_0_1631,i_0_1639,i_0_1659,i_0_1662,i_0_1689,i_0_1691,i_0_1697,i_0_1726,i_0_1729,i_0_1763,i_0_1764,i_0_1769,i_0_1770,i_0_1771,i_0_1779,i_0_1782,i_0_1791,i_0_1805,i_0_1828,i_0_1854,i_0_2043,i_0_1910,i_0_1912,i_0_1349,i_0_1868,i_0_1990,i_0_1243,i_0_1276,i_0_1302,i_0_1303,i_0_1306,i_0_1307,i_0_1362,i_0_1383,i_0_1513,i_0_1587,i_0_1604,i_0_1645,i_0_1174,i_0_1313,i_0_1322,i_0_1327,i_0_1329,i_0_1330,i_0_1334,i_0_1365,i_0_1373,i_0_1380,i_0_1400,i_0_1416,i_0_1503,i_0_1509,i_0_1516,i_0_1518,i_0_1521,i_0_1567,i_0_1591,i_0_1592,i_0_1596,i_0_1598,i_0_1613,i_0_1621,i_0_1622,i_0_1624,i_0_1628,i_0_1629,i_0_1647,i_0_1654,i_0_1665,i_0_1667,i_0_1709,i_0_1723,i_0_1728,i_0_1732,i_0_1734,i_0_1735,i_0_1736,i_0_1749,i_0_1753,i_0_1804,i_0_1814,i_0_1815,i_0_1816,i_0_2040,i_0_2042,i_0_1911,i_0_2000,i_0_2001,i_0_2007,i_0_2008,i_0_2015,i_0_2016,i_0_2018,i_0_2019,i_0_2020,i_0_2021,i_0_2022,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1998,i_0_1384,i_0_1600,i_0_2031,i_0_2036,i_0_1235,i_0_1288,i_0_1299,i_0_1376,i_0_1397,i_0_1398,i_0_1404,i_0_1439,i_0_1473,i_0_1483,i_0_1498,i_0_1499,i_0_1543,i_0_1544,i_0_1561,i_0_1562,i_0_1563,i_0_1564,i_0_1588,i_0_1589,i_0_1603,i_0_1653,i_0_1679,i_0_1682,i_0_1705,i_0_1717,i_0_1241,i_0_1257,i_0_1524,i_0_1525,i_0_1546,i_0_1240,i_0_1256,i_0_2027,i_0_2029,i_0_2035,i_0_1558,i_0_1300,i_0_1458,i_0_1459,i_0_1560,i_0_1619,i_0_1683,i_0_1790,i_0_1913,i_0_1557,i_0_1399,i_0_1412,i_0_1442,i_0_1533,i_0_1612,i_0_1661,i_0_1686,i_0_1389,i_0_2030,i_0_1537,i_0_1158]) ).

cnf(i_0_2639,plain,
    c_Finite__Set_Ofinite(X1,c_Set_Oimage(X2,X1,hAPP(c_COMBB(tc_Arrow__Order__Mirabelle_Oindi,X1,X2,X3),X4),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))),
    inference(scs_inference,[],[i_0_2382,i_0_1255]) ).

cnf(i_0_2640,plain,
    c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,X1),
    inference(rename_variables,[],[i_0_2382]) ).

cnf(i_0_2641,plain,
    ( ~ c_Finite__Set_Ofinite(X1,c_Set_Oimage(X2,X1,X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))
    | c_Finite__Set_Ofinite(X4,c_Set_Oimage(X2,X4,hAPP(c_COMBB(X1,X4,X2,X5),X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))) ),
    inference(rename_variables,[],[i_0_1255]) ).

cnf(i_0_2642,plain,
    hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4)) = X4,
    inference(scs_inference,[],[i_0_2144,i_0_2382,i_0_1255,i_0_1778]) ).

cnf(i_0_2643,plain,
    hAPP(X1,hAPP(c_Hilbert__Choice_Oinv__into(X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),X1),hAPP(X1,X4))) = hAPP(X1,X4),
    inference(rename_variables,[],[i_0_2144]) ).

cnf(i_0_2644,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)
    | X2 = X3 ),
    inference(rename_variables,[],[i_0_1778]) ).

cnf(i_0_2645,plain,
    c_FunDef_Oin__rel(X1,X2,c_Set_Oinsert(tc_prod(X1,X2),X3,c_Set_Oinsert(tc_prod(X1,X2),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X5),X6)),X4,X5),
    inference(scs_inference,[],[i_0_2120,i_0_2144,i_0_2382,i_0_1255,i_0_1778,i_0_1292]) ).

cnf(i_0_2646,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X3,c_Set_Oinsert(X1,X2,X4)))),
    inference(rename_variables,[],[i_0_2120]) ).

cnf(i_0_2647,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5))
    | c_FunDef_Oin__rel(X1,X2,X5,X3,X4) ),
    inference(rename_variables,[],[i_0_1292]) ).

cnf(i_0_2648,plain,
    hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),c_Set_Oimage(X4,X1,X2,c_Set_Oinsert(X4,X5,c_Set_Oinsert(X4,X3,X6))))),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2144,i_0_2382,i_0_1255,i_0_1778,i_0_1292,i_0_1353]) ).

cnf(i_0_2649,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hBOOL(hAPP(hAPP(c_member(X4),hAPP(X5,X2)),c_Set_Oimage(X1,X4,X5,X3))) ),
    inference(rename_variables,[],[i_0_1353]) ).

cnf(i_0_2650,plain,
    c_Set_Oinsert(X1,hAPP(X2,X3),c_Set_Oimage(X4,X1,X2,c_Set_Oinsert(X4,X5,c_Set_Oinsert(X4,X3,X6)))) = c_Set_Oimage(X4,X1,X2,c_Set_Oinsert(X4,X5,c_Set_Oinsert(X4,X3,X6))),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2144,i_0_2382,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403]) ).

cnf(i_0_2651,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | c_Set_Oinsert(X4,hAPP(X5,X2),c_Set_Oimage(X1,X4,X5,X3)) = c_Set_Oimage(X1,X4,X5,X3) ),
    inference(rename_variables,[],[i_0_1403]) ).

cnf(i_0_2652,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X3,c_Set_Oinsert(X1,X4,c_Set_Oinsert(X1,X2,X5))))),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2144,i_0_2382,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531]) ).

cnf(i_0_2653,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X4,X3))) ),
    inference(rename_variables,[],[i_0_1531]) ).

cnf(i_0_2654,plain,
    c_Set_Oinsert(X1,X2,c_Set_Oinsert(X1,X3,c_Set_Oinsert(X1,X2,X4))) = c_Set_Oinsert(X1,X3,c_Set_Oinsert(X1,X2,X4)),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2144,i_0_2382,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698]) ).

cnf(i_0_2655,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | c_Set_Oinsert(X1,X2,X3) = X3 ),
    inference(rename_variables,[],[i_0_1698]) ).

cnf(i_0_2656,plain,
    ~ hBOOL(hAPP(c_Set_Oimage(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_COMBI(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1),X2)),hAPP(c_COMBI(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)))),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2144,i_0_2382,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762]) ).

cnf(i_0_2657,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(rename_variables,[],[i_0_1762]) ).

cnf(i_0_2658,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1,X2,X3)),X3)),c_Wellfounded_Ofinite__psubset(X1))),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2144,i_0_2343,i_0_2382,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199]) ).

cnf(i_0_2659,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),X3)),c_Wellfounded_Ofinite__psubset(X1))) ),
    inference(rename_variables,[],[i_0_1199]) ).

cnf(i_0_2660,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),c_Set_Oimage(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),v_F,c_Arrow__Order__Mirabelle_OProf)),c_Arrow__Order__Mirabelle_OLin)),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2144,i_0_2343,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203]) ).

cnf(i_0_2661,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X1,X2,X4,hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X5))))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),c_Set_Oimage(X1,X2,X3,X4)),X5)) ),
    inference(rename_variables,[],[i_0_1203]) ).

cnf(i_0_2662,plain,
    c_Set_Oimage(X1,X2,X3,X4) = c_Set_Oimage(X1,X2,X3,esk37_5(c_Set_Oinsert(X1,X5,X4),X3,X1,c_Set_Oimage(X1,X2,X3,X4),X2)),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2144,i_0_2343,i_0_2142,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221]) ).

cnf(i_0_2663,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Set_Oimage(X3,X1,X4,X5)))
    | X2 = c_Set_Oimage(X3,X1,X4,esk37_5(X5,X4,X3,X2,X1)) ),
    inference(rename_variables,[],[i_0_1221]) ).

cnf(i_0_2664,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(tc_fun(X1,X2),X3),tc_HOL_Obool),c_FuncSet_OPi(tc_fun(X1,X2),X3,c_FuncSet_OPi(X1,X2,X4,X5),X6)),c_FuncSet_OPi(tc_fun(X1,X2),X3,c_FuncSet_OPi(X1,X2,c_Set_Oinsert(X1,X7,X4),X5),X6))),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2144,i_0_2343,i_0_2140,i_0_2142,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248]) ).

cnf(i_0_2665,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,X4),tc_HOL_Obool),c_FuncSet_OPi(X1,X4,X3,X5)),c_FuncSet_OPi(X1,X4,X2,X5))) ),
    inference(rename_variables,[],[i_0_1248]) ).

cnf(i_0_2666,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(tc_fun(X2,X3),X1,X4,c_FuncSet_OPi(X2,X3,c_Set_Oinsert(X2,X5,X6),X7))),c_Set_Oimage(tc_fun(X2,X3),X1,X4,c_FuncSet_OPi(X2,X3,X6,X7)))),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2144,i_0_2343,i_0_2140,i_0_2142,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271]) ).

cnf(i_0_2667,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Set_Oimage(X1,X4,X5,X2)),c_Set_Oimage(X1,X4,X5,X3))) ),
    inference(rename_variables,[],[i_0_1271]) ).

cnf(i_0_2668,plain,
    hAPP(X1,hAPP(c_Hilbert__Choice_Oinv__into(X2,X3,hAPP(c_fequal,X4),X1),hAPP(X1,X4))) = hAPP(X1,X4),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2118,i_0_2144,i_0_2343,i_0_2140,i_0_2142,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296]) ).

cnf(i_0_2669,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oimage(X3,X1,X4,X5)))
    | hAPP(X4,hAPP(c_Hilbert__Choice_Oinv__into(X3,X1,X5,X4),X2)) = X2 ),
    inference(rename_variables,[],[i_0_1296]) ).

cnf(i_0_2670,plain,
    hAPP(c_Nat_OSuc,hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Nat_OSuc),esk38_3(c_Nat_OSuc,X2,X1))) != esk38_3(c_Nat_OSuc,X2,X1),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2118,i_0_2144,i_0_2343,i_0_2140,i_0_2142,i_0_2158,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300]) ).

cnf(i_0_2671,plain,
    ( c_Set_Oimage(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))
    | hAPP(X3,hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3),esk38_3(X3,X2,X1))) != esk38_3(X3,X2,X1) ),
    inference(rename_variables,[],[i_0_1300]) ).

cnf(i_0_2672,plain,
    c_Fun_Oinj__on(X1,X2,c_Hilbert__Choice_Oinv__into(X2,X1,c_Set_Oinsert(X2,X3,X4),X5),c_Set_Oimage(X2,X1,X5,X4)),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2118,i_0_2144,i_0_2343,i_0_2140,i_0_2142,i_0_2158,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301]) ).

cnf(i_0_2673,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Set_Oimage(X3,X1,X4,X5)))
    | c_Fun_Oinj__on(X1,X3,c_Hilbert__Choice_Oinv__into(X3,X1,X5,X4),X2) ),
    inference(rename_variables,[],[i_0_1301]) ).

cnf(i_0_2674,plain,
    hAPP(X1,X2) = hAPP(X1,esk36_4(hAPP(c_fequal,X2),X1,X3,hAPP(X1,X2))),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2118,i_0_2144,i_0_2343,i_0_2140,i_0_2142,i_0_2158,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318]) ).

cnf(i_0_2675,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oimage(X3,X1,X4,X5)))
    | X2 = hAPP(X4,esk36_4(X5,X4,X3,X2)) ),
    inference(rename_variables,[],[i_0_1318]) ).

cnf(i_0_2676,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(c_Nat_OSuc,X2)),X2)),c_Wellfounded_Omeasure(X1,c_Nat_OSuc))),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2118,i_0_2144,i_0_2343,i_0_2140,i_0_2142,i_0_2365,i_0_2158,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328]) ).

cnf(i_0_2677,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X1)),
    inference(rename_variables,[],[i_0_2365]) ).

cnf(i_0_2678,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1,X2)),hAPP(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_Wellfounded_Omeasure(X4,X1))) ),
    inference(rename_variables,[],[i_0_1328]) ).

cnf(i_0_2679,plain,
    hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,v_Lab____),X1)),c_Arrow__Order__Mirabelle_OLin)),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2118,i_0_1497,i_0_2144,i_0_2343,i_0_2140,i_0_2142,i_0_2365,i_0_2158,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331]) ).

cnf(i_0_2680,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1),X2)),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(rename_variables,[],[i_0_1331]) ).

cnf(i_0_2681,plain,
    c_Set_Oimage(X1,X2,hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X3)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2118,i_0_1497,i_0_2144,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2365,i_0_2158,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339]) ).

cnf(i_0_2682,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2) != X1,
    inference(rename_variables,[],[i_0_2253]) ).

cnf(i_0_2683,plain,
    ( hAPP(X1,hAPP(c_Hilbert__Choice_Oinv__into(X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),X1),X4)) = X4
    | c_Set_Oimage(X2,X3,X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)) ),
    inference(rename_variables,[],[i_0_1339]) ).

cnf(i_0_2684,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X2)))),c_Wellfounded_Omlex__prod(X1,c_Nat_OSuc,X3))),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2118,i_0_1497,i_0_2144,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2365,i_0_2195,i_0_2158,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340]) ).

cnf(i_0_2685,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)))),
    inference(rename_variables,[],[i_0_2195]) ).

cnf(i_0_2686,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1,X2)),hAPP(X1,X3)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_Wellfounded_Omlex__prod(X4,X1,X5))) ),
    inference(rename_variables,[],[i_0_1340]) ).

cnf(i_0_2687,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X2)))),c_Wellfounded_Omeasure(X1,c_Nat_OSuc))),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2118,i_0_1497,i_0_2144,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2365,i_0_2195,i_0_2685,i_0_2158,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346]) ).

cnf(i_0_2688,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)))),
    inference(rename_variables,[],[i_0_2195]) ).

cnf(i_0_2689,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1,X2)),hAPP(X1,X3)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_Wellfounded_Omeasure(X4,X1))) ),
    inference(rename_variables,[],[i_0_1346]) ).

cnf(i_0_2690,plain,
    X1 = esk36_4(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),hAPP(c_COMBC(X3,tc_fun(X3,tc_HOL_Obool),tc_HOL_Obool),c_member(X3)),X2,hAPP(hAPP(c_COMBC(X3,tc_fun(X3,tc_HOL_Obool),tc_HOL_Obool),c_member(X3)),X1)),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2118,i_0_1497,i_0_2144,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2365,i_0_2195,i_0_2685,i_0_2158,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381]) ).

cnf(i_0_2691,plain,
    hAPP(X1,X2) = hAPP(X1,esk36_4(c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)),X1,X3,hAPP(X1,X2))),
    inference(rename_variables,[],[i_0_2149]) ).

cnf(i_0_2692,plain,
    ( hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2) != hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)
    | X2 = X3 ),
    inference(rename_variables,[],[i_0_1381]) ).

cnf(i_0_2693,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,X2),tc_HOL_Obool),c_Set_Oinsert(tc_fun(X1,X2),X3,c_FuncSet_OPi(X1,X2,c_Set_Oinsert(X1,X4,X5),X6))),c_Set_Oinsert(tc_fun(X1,X2),X3,c_FuncSet_OPi(X1,X2,X5,X6)))),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2118,i_0_1497,i_0_2144,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2365,i_0_2195,i_0_2685,i_0_2158,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387]) ).

cnf(i_0_2694,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1,X4,X2)),c_Set_Oinsert(X1,X4,X3))) ),
    inference(rename_variables,[],[i_0_1387]) ).

cnf(i_0_2695,plain,
    ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X1)),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2118,i_0_1497,i_0_2144,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2365,i_0_2203,i_0_2195,i_0_2685,i_0_2158,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402]) ).

cnf(i_0_2696,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2))
    | ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
    inference(rename_variables,[],[i_0_1402]) ).

cnf(i_0_2697,plain,
    hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X1))),X3))),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2118,i_0_1497,i_0_2144,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2365,i_0_2182,i_0_2203,i_0_2195,i_0_2685,i_0_2158,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440]) ).

cnf(i_0_2698,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)),X3))),
    inference(rename_variables,[],[i_0_2182]) ).

cnf(i_0_2699,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2))
    | hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
    inference(rename_variables,[],[i_0_1440]) ).

cnf(i_0_2700,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,X2),tc_HOL_Obool),c_FuncSet_OPi(X1,X2,c_Set_Oinsert(X1,X3,X4),X5)),c_Set_Oinsert(tc_fun(X1,X2),X6,c_FuncSet_OPi(X1,X2,X4,X5)))),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2118,i_0_1497,i_0_2144,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2365,i_0_2182,i_0_2203,i_0_2195,i_0_2685,i_0_2158,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480]) ).

cnf(i_0_2701,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Set_Oinsert(X1,X4,X3))) ),
    inference(rename_variables,[],[i_0_1480]) ).

cnf(i_0_2702,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Nat_OSuc,esk33_2(hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),v_F)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2468,i_0_2118,i_0_1497,i_0_2144,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2365,i_0_2182,i_0_2203,i_0_2195,i_0_2685,i_0_2158,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539]) ).

cnf(i_0_2703,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2))) ),
    inference(rename_variables,[],[i_0_1539]) ).

cnf(i_0_2704,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))),X2))),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2468,i_0_2118,i_0_1497,i_0_2144,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2211,i_0_2365,i_0_2182,i_0_2203,i_0_2195,i_0_2685,i_0_2158,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570]) ).

cnf(i_0_2705,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))),
    inference(rename_variables,[],[i_0_2211]) ).

cnf(i_0_2706,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(rename_variables,[],[i_0_1570]) ).

cnf(i_0_2707,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Nat_OSuc,X1))))),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2468,i_0_2118,i_0_1497,i_0_2144,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2211,i_0_2365,i_0_2405,i_0_2182,i_0_2203,i_0_2195,i_0_2685,i_0_2158,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573]) ).

cnf(i_0_2708,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2))) ),
    inference(rename_variables,[],[i_0_1573]) ).

cnf(i_0_2709,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))),X2)),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2468,i_0_2118,i_0_1497,i_0_2144,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2211,i_0_2365,i_0_2405,i_0_2493,i_0_2182,i_0_2203,i_0_2195,i_0_2685,i_0_2158,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575]) ).

cnf(i_0_2710,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)),X2)),
    inference(rename_variables,[],[i_0_2493]) ).

cnf(i_0_2711,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
    inference(rename_variables,[],[i_0_1575]) ).

cnf(i_0_2712,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))),X3)),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2468,i_0_2118,i_0_1497,i_0_2144,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2211,i_0_2365,i_0_2405,i_0_2493,i_0_2217,i_0_2182,i_0_2203,i_0_2195,i_0_2685,i_0_2158,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577]) ).

cnf(i_0_2713,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))),X2)),
    inference(rename_variables,[],[i_0_2217]) ).

cnf(i_0_2714,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3)) ),
    inference(rename_variables,[],[i_0_1577]) ).

cnf(i_0_2715,plain,
    hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk32_2(hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)),X1))),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2468,i_0_2118,i_0_1497,i_0_2144,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2211,i_0_2365,i_0_2405,i_0_2493,i_0_2217,i_0_2182,i_0_2203,i_0_2195,i_0_2685,i_0_2688,i_0_2158,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630]) ).

cnf(i_0_2716,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk32_2(X2,X1))) ),
    inference(rename_variables,[],[i_0_1630]) ).

cnf(i_0_2717,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),hAPP(c_Nat_OSuc,X3)))),X3)),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2468,i_0_2118,i_0_1497,i_0_2144,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2211,i_0_2365,i_0_2405,i_0_2504,i_0_2493,i_0_2217,i_0_2182,i_0_2203,i_0_2195,i_0_2685,i_0_2688,i_0_2158,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689]) ).

cnf(i_0_2718,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),X3))),X3)),
    inference(rename_variables,[],[i_0_2504]) ).

cnf(i_0_2719,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X2)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
    inference(rename_variables,[],[i_0_1689]) ).

cnf(i_0_2720,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1) = hAPP(c_Nat_OSuc,esk30_1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2468,i_0_2118,i_0_1497,i_0_2144,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2211,i_0_2705,i_0_2365,i_0_2405,i_0_2504,i_0_2493,i_0_2217,i_0_2182,i_0_2203,i_0_2195,i_0_2685,i_0_2688,i_0_2158,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729]) ).

cnf(i_0_2721,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))),
    inference(rename_variables,[],[i_0_2211]) ).

cnf(i_0_2722,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
    | X1 = hAPP(c_Nat_OSuc,esk30_1(X1)) ),
    inference(rename_variables,[],[i_0_1729]) ).

cnf(i_0_2723,plain,
    X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)),X3),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2468,i_0_2118,i_0_1497,i_0_2144,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2211,i_0_2705,i_0_2365,i_0_2405,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2203,i_0_2195,i_0_2685,i_0_2688,i_0_2158,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771]) ).

cnf(i_0_2724,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
    | X2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3) ),
    inference(rename_variables,[],[i_0_1771]) ).

cnf(i_0_2725,plain,
    c_Set_Oimage(X1,X2,X3,c_Set_Oimage(X2,X1,c_Hilbert__Choice_Oinv__into(X1,X2,c_Set_Oinsert(X1,X4,X5),X3),c_Set_Oimage(X1,X2,X3,X5))) = c_Set_Oimage(X1,X2,X3,X5),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2468,i_0_2118,i_0_1497,i_0_2144,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2211,i_0_2705,i_0_2365,i_0_2405,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2203,i_0_2195,i_0_2685,i_0_2688,i_0_2158,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043]) ).

cnf(i_0_2726,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Set_Oimage(X3,X1,X4,X5)))
    | c_Set_Oimage(X3,X1,X4,c_Set_Oimage(X1,X3,c_Hilbert__Choice_Oinv__into(X3,X1,X5,X4),X2)) = X2 ),
    inference(rename_variables,[],[i_0_2043]) ).

cnf(i_0_2727,plain,
    c_Finite__Set_Ofinite(esk37_5(tc_Product__Type_Ounit,c_Nat_OSuc,tc_Nat_Onat,c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,tc_Product__Type_Ounit),tc_Nat_Onat),X1),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2468,i_0_2118,i_0_1497,i_0_2144,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2211,i_0_2705,i_0_2365,i_0_2405,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2203,i_0_2195,i_0_2685,i_0_2688,i_0_2158,i_0_2435,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868]) ).

cnf(i_0_2728,plain,
    ( ~ class_Finite__Set_Ofinite(X1)
    | c_Finite__Set_Ofinite(X1,X2) ),
    inference(rename_variables,[],[i_0_1868]) ).

cnf(i_0_2729,plain,
    ~ c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,c_Arrow__Order__Mirabelle_Obelow(hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,esk11_0),hAPP(c_Nat_OSuc,X1)),X1,hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X1)),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2211,i_0_2705,i_0_2365,i_0_2405,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2203,i_0_2195,i_0_2685,i_0_2688,i_0_2158,i_0_2435,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286]) ).

cnf(i_0_2730,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5))
    | ~ c_FunDef_Oin__rel(X1,X2,X5,X3,X4) ),
    inference(rename_variables,[],[i_0_1286]) ).

cnf(i_0_2731,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Nat_OSuc,X1)))),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2211,i_0_2705,i_0_2365,i_0_2405,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2203,i_0_2195,i_0_2685,i_0_2688,i_0_2158,i_0_2435,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438]) ).

cnf(i_0_2732,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X3)) ),
    inference(rename_variables,[],[i_0_1438]) ).

cnf(i_0_2733,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2211,i_0_2705,i_0_2365,i_0_2405,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2203,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2158,i_0_2435,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454]) ).

cnf(i_0_2734,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3)) ),
    inference(rename_variables,[],[i_0_1454]) ).

cnf(i_0_2735,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)))),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2211,i_0_2705,i_0_2365,i_0_2405,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2203,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2214,i_0_2158,i_0_2435,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455]) ).

cnf(i_0_2736,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X1))),
    inference(rename_variables,[],[i_0_2214]) ).

cnf(i_0_2737,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3)) ),
    inference(rename_variables,[],[i_0_1455]) ).

cnf(i_0_2738,plain,
    X1 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2211,i_0_2705,i_0_2365,i_0_2677,i_0_2405,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2203,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2214,i_0_2158,i_0_2435,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662]) ).

cnf(i_0_2739,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X2 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)) ),
    inference(rename_variables,[],[i_0_1662]) ).

cnf(i_0_2740,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk18_2(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2),X1)),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2211,i_0_2705,i_0_2365,i_0_2677,i_0_2405,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2242,i_0_2203,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2214,i_0_2158,i_0_2435,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726]) ).

cnf(i_0_2741,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
    | X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk18_2(X2,X1)) ),
    inference(rename_variables,[],[i_0_1726]) ).

cnf(i_0_2742,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X1))),X3))),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2211,i_0_2705,i_0_2365,i_0_2677,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2242,i_0_2203,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2214,i_0_2158,i_0_2435,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764]) ).

cnf(i_0_2743,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
    inference(rename_variables,[],[i_0_1764]) ).

cnf(i_0_2744,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),X3)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2189,i_0_2211,i_0_2705,i_0_2365,i_0_2677,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2242,i_0_2203,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2214,i_0_2158,i_0_2435,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779]) ).

cnf(i_0_2745,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))),X2)),
    inference(rename_variables,[],[i_0_2189]) ).

cnf(i_0_2746,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(rename_variables,[],[i_0_1779]) ).

cnf(i_0_2747,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),X3)) != X2,
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2189,i_0_2745,i_0_2211,i_0_2705,i_0_2365,i_0_2677,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2242,i_0_2203,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2214,i_0_2158,i_0_2435,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782]) ).

cnf(i_0_2748,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))),X2)),
    inference(rename_variables,[],[i_0_2189]) ).

cnf(i_0_2749,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
    | X1 != X2 ),
    inference(rename_variables,[],[i_0_1782]) ).

cnf(i_0_2750,plain,
    hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,v_Lab____),X1)),c_Arrow__Order__Mirabelle_OLin)),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2189,i_0_2745,i_0_2211,i_0_2705,i_0_2365,i_0_2677,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2242,i_0_2203,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2214,i_0_2158,i_0_2435,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332]) ).

cnf(i_0_2751,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1),X2)),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(rename_variables,[],[i_0_1332]) ).

cnf(i_0_2752,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))),X1)),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2189,i_0_2745,i_0_2211,i_0_2705,i_0_2365,i_0_2677,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2242,i_0_2203,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2214,i_0_2158,i_0_2435,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550]) ).

cnf(i_0_2753,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X1)),
    inference(rename_variables,[],[i_0_2365]) ).

cnf(i_0_2754,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(rename_variables,[],[i_0_1550]) ).

cnf(i_0_2755,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))),X2)),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2189,i_0_2745,i_0_2211,i_0_2705,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2242,i_0_2203,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2214,i_0_2158,i_0_2435,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552]) ).

cnf(i_0_2756,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X1)),
    inference(rename_variables,[],[i_0_2365]) ).

cnf(i_0_2757,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X3)) ),
    inference(rename_variables,[],[i_0_1552]) ).

cnf(i_0_2758,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2189,i_0_2745,i_0_2211,i_0_2705,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2242,i_0_2203,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2158,i_0_2435,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581]) ).

cnf(i_0_2759,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X1))) ),
    inference(rename_variables,[],[i_0_1581]) ).

cnf(i_0_2760,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X1))),X3))),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2189,i_0_2745,i_0_2211,i_0_2705,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2242,i_0_2203,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2158,i_0_2435,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585]) ).

cnf(i_0_2761,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)),X3))),
    inference(rename_variables,[],[i_0_2182]) ).

cnf(i_0_2762,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(rename_variables,[],[i_0_1585]) ).

cnf(i_0_2763,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)))),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2189,i_0_2745,i_0_2211,i_0_2705,i_0_2721,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2242,i_0_2203,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2158,i_0_2435,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639]) ).

cnf(i_0_2764,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))) ),
    inference(rename_variables,[],[i_0_1639]) ).

cnf(i_0_2765,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Nat_OSuc,X1)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2189,i_0_2745,i_0_2211,i_0_2705,i_0_2721,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2242,i_0_2203,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2158,i_0_2435,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763]) ).

cnf(i_0_2766,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(rename_variables,[],[i_0_1763]) ).

cnf(i_0_2767,plain,
    hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))) != X2,
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2189,i_0_2745,i_0_2211,i_0_2705,i_0_2721,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2242,i_0_2203,i_0_2173,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2158,i_0_2435,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769]) ).

cnf(i_0_2768,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X2 != X1 ),
    inference(rename_variables,[],[i_0_1769]) ).

cnf(i_0_2769,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Nat_OSuc,X1)),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2189,i_0_2745,i_0_2211,i_0_2705,i_0_2721,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2242,i_0_2203,i_0_2173,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2158,i_0_2435,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770]) ).

cnf(i_0_2770,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X1 != X2 ),
    inference(rename_variables,[],[i_0_1770]) ).

cnf(i_0_2771,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))),X3) != X2,
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2189,i_0_2745,i_0_2211,i_0_2705,i_0_2721,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2242,i_0_2203,i_0_2173,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2158,i_0_2435,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828]) ).

cnf(i_0_2772,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
    | X1 != X2 ),
    inference(rename_variables,[],[i_0_1828]) ).

cnf(i_0_2773,plain,
    hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Nat_OSuc),hAPP(c_Nat_OSuc,X3)) = X3,
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2189,i_0_2745,i_0_2211,i_0_2705,i_0_2721,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2242,i_0_2203,i_0_2173,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2158,i_0_2435,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854]) ).

cnf(i_0_2774,plain,
    hAPP(X1,hAPP(c_Hilbert__Choice_Oinv__into(X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),X1),hAPP(X1,X4))) = hAPP(X1,X4),
    inference(rename_variables,[],[i_0_2144]) ).

cnf(i_0_2775,plain,
    ( hAPP(c_Nat_OSuc,X1) != hAPP(c_Nat_OSuc,X2)
    | X1 = X2 ),
    inference(rename_variables,[],[i_0_1854]) ).

cnf(i_0_2776,plain,
    hBOOL(hAPP(c_Set_Oinsert(X1,X2,c_Set_Oinsert(X1,X3,X4)),X3)),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2189,i_0_2745,i_0_2211,i_0_2705,i_0_2721,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2242,i_0_2203,i_0_2173,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2158,i_0_2435,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718]) ).

cnf(i_0_2777,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hBOOL(hAPP(X3,X2)) ),
    inference(rename_variables,[],[i_0_1718]) ).

cnf(i_0_2778,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X3)))),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2189,i_0_2745,i_0_2211,i_0_2705,i_0_2721,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2242,i_0_2203,i_0_2173,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2158,i_0_2435,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599]) ).

cnf(i_0_2779,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)))),
    inference(rename_variables,[],[i_0_2221]) ).

cnf(i_0_2780,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
    inference(rename_variables,[],[i_0_1599]) ).

cnf(i_0_2781,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),X3))),X2)),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2242,i_0_2203,i_0_2173,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2158,i_0_2435,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659]) ).

cnf(i_0_2782,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))),X2)),
    inference(rename_variables,[],[i_0_2189]) ).

cnf(i_0_2783,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
    inference(rename_variables,[],[i_0_1659]) ).

cnf(i_0_2784,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3))))),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2242,i_0_2203,i_0_2173,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2158,i_0_2435,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659,i_0_1697]) ).

cnf(i_0_2785,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
    inference(rename_variables,[],[i_0_1697]) ).

cnf(i_0_2786,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))),X3)),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2242,i_0_2203,i_0_2173,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2158,i_0_2435,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659,i_0_1697,i_0_1459]) ).

cnf(i_0_2787,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3)) ),
    inference(rename_variables,[],[i_0_1459]) ).

cnf(i_0_2788,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))),X2)),X1)),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2242,i_0_2203,i_0_2173,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2158,i_0_2435,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659,i_0_1697,i_0_1459,i_0_1571]) ).

cnf(i_0_2789,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))),
    inference(rename_variables,[],[i_0_2242]) ).

cnf(i_0_2790,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
    inference(rename_variables,[],[i_0_1571]) ).

cnf(i_0_2791,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X1)))),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2242,i_0_2203,i_0_2173,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2606,i_0_2158,i_0_2435,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659,i_0_1697,i_0_1459,i_0_1571,i_0_1560]) ).

cnf(i_0_2792,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))),
    inference(rename_variables,[],[i_0_2606]) ).

cnf(i_0_2793,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2)))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
    inference(rename_variables,[],[i_0_1560]) ).

cnf(i_0_2794,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X3)))),X3)),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2242,i_0_2203,i_0_2522,i_0_2173,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2606,i_0_2158,i_0_2435,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659,i_0_1697,i_0_1459,i_0_1571,i_0_1560,i_0_1601]) ).

cnf(i_0_2795,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))),X3)),
    inference(rename_variables,[],[i_0_2522]) ).

cnf(i_0_2796,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
    inference(rename_variables,[],[i_0_1601]) ).

cnf(i_0_2797,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk33_2(hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),v_F)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2242,i_0_2203,i_0_2522,i_0_2173,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2606,i_0_2158,i_0_2435,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659,i_0_1697,i_0_1459,i_0_1571,i_0_1560,i_0_1601,i_0_1691]) ).

cnf(i_0_2798,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X1))) ),
    inference(rename_variables,[],[i_0_1691]) ).

cnf(i_0_2799,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)))),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2242,i_0_2203,i_0_2522,i_0_2173,i_0_2232,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2606,i_0_2158,i_0_2435,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659,i_0_1697,i_0_1459,i_0_1571,i_0_1560,i_0_1601,i_0_1691,i_0_1631]) ).

cnf(i_0_2800,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
    inference(rename_variables,[],[i_0_1631]) ).

cnf(i_0_2801,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),v_F)))),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2242,i_0_2203,i_0_2519,i_0_2522,i_0_2173,i_0_2232,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2606,i_0_2158,i_0_2435,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659,i_0_1697,i_0_1459,i_0_1571,i_0_1560,i_0_1601,i_0_1691,i_0_1631,i_0_1683]) ).

cnf(i_0_2802,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
    inference(rename_variables,[],[i_0_1683]) ).

cnf(i_0_2803,plain,
    X1 = hAPP(c_Hilbert__Choice_Oinv__into(X2,X2,hAPP(c_fequal,X1),c_COMBI(X2)),hAPP(c_COMBI(X2),X1)),
    inference(scs_inference,[],[i_0_2120,i_0_2646,i_0_2293,i_0_2299,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2242,i_0_2203,i_0_2519,i_0_2522,i_0_2173,i_0_2232,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2606,i_0_2158,i_0_2435,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659,i_0_1697,i_0_1459,i_0_1571,i_0_1560,i_0_1601,i_0_1691,i_0_1631,i_0_1683,i_0_1910]) ).

cnf(i_0_2804,plain,
    c_Set_Oinsert(X1,X2,X3) != hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),X2),
    inference(scs_inference,[],[i_0_2276,i_0_2120,i_0_2646,i_0_2293,i_0_2299,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2242,i_0_2203,i_0_2519,i_0_2522,i_0_2173,i_0_2232,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2606,i_0_2158,i_0_2435,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659,i_0_1697,i_0_1459,i_0_1571,i_0_1560,i_0_1601,i_0_1691,i_0_1631,i_0_1683,i_0_1910,i_0_1912]) ).

cnf(i_0_2805,plain,
    hAPP(c_Set_Oinsert(X1,X2,X3),X2) != hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),X5),X5),
    inference(rename_variables,[],[i_0_2276]) ).

cnf(i_0_2806,plain,
    hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)) != X2,
    inference(scs_inference,[],[i_0_2276,i_0_2120,i_0_2646,i_0_2293,i_0_2299,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2427,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2242,i_0_2203,i_0_2519,i_0_2522,i_0_2173,i_0_2232,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2606,i_0_2158,i_0_2435,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659,i_0_1697,i_0_1459,i_0_1571,i_0_1560,i_0_1601,i_0_1691,i_0_1631,i_0_1683,i_0_1910,i_0_1912,i_0_1913]) ).

cnf(i_0_2807,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)) != X2,
    inference(rename_variables,[],[i_0_2427]) ).

cnf(i_0_2808,plain,
    ~ c_Finite__Set_Ofolding__image__simple(X1,X2,X3,X4,X5,hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Finite__Set_Ofold__image(X1,X2,X3,X5,X4,c_Set_Oimage(tc_Nat_Onat,X2,X6,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X7,X8)))))),
    inference(scs_inference,[],[i_0_2276,i_0_2120,i_0_2646,i_0_2293,i_0_2299,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2682,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2427,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2328,i_0_2242,i_0_2203,i_0_2519,i_0_2522,i_0_2173,i_0_2232,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2606,i_0_2158,i_0_2435,i_0_2382,i_0_1171,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659,i_0_1697,i_0_1459,i_0_1571,i_0_1560,i_0_1601,i_0_1691,i_0_1631,i_0_1683,i_0_1910,i_0_1912,i_0_1913,i_0_1163]) ).

cnf(i_0_2809,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2) != X1,
    inference(rename_variables,[],[i_0_2253]) ).

cnf(i_0_2810,plain,
    ( hAPP(X1,X2) = c_Finite__Set_Ofold__image(X3,X4,X5,X6,X7,X2)
    | ~ c_Finite__Set_Ofolding__image__simple(X3,X4,X5,X7,X6,X1)
    | ~ c_Finite__Set_Ofinite(X4,X2) ),
    inference(rename_variables,[],[i_0_1163]) ).

cnf(i_0_2811,plain,
    hAPP(c_Hilbert__Choice_Oinv__into(X1,X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_COMBI(X1)),X2) = hAPP(c_Hilbert__Choice_Oinv__into(X1,X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_COMBI(X1)),esk34_4(hAPP(c_Hilbert__Choice_Oinv__into(X1,X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_COMBI(X1)),X2),c_Hilbert__Choice_Oinv__into(X1,X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_COMBI(X1)),X1,X1)),
    inference(scs_inference,[],[i_0_2276,i_0_2120,i_0_2646,i_0_2293,i_0_2299,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2682,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2427,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2328,i_0_2242,i_0_2203,i_0_2519,i_0_2522,i_0_2173,i_0_2232,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2606,i_0_2158,i_0_2435,i_0_2382,i_0_1351,i_0_1171,i_0_2271,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659,i_0_1697,i_0_1459,i_0_1571,i_0_1560,i_0_1601,i_0_1691,i_0_1631,i_0_1683,i_0_1910,i_0_1912,i_0_1913,i_0_1163,i_0_1282]) ).

cnf(i_0_2812,plain,
    hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),c_Set_Oimage(X4,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))),
    inference(rename_variables,[],[i_0_1351]) ).

cnf(i_0_2813,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oimage(X3,X1,X4,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))))
    | X2 = hAPP(X4,esk34_4(X2,X4,X1,X3))
    | ~ c_Fun_Oinj__on(X3,X1,X4,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))) ),
    inference(rename_variables,[],[i_0_1282]) ).

cnf(i_0_2814,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
    inference(scs_inference,[],[i_0_2276,i_0_2120,i_0_2646,i_0_2293,i_0_2299,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2682,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2427,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2328,i_0_2242,i_0_2203,i_0_2519,i_0_2522,i_0_2173,i_0_2232,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2606,i_0_2158,i_0_2435,i_0_2382,i_0_1351,i_0_1171,i_0_2271,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659,i_0_1697,i_0_1459,i_0_1571,i_0_1560,i_0_1601,i_0_1691,i_0_1631,i_0_1683,i_0_1910,i_0_1912,i_0_1913,i_0_1163,i_0_1282,i_0_1478]) ).

cnf(i_0_2815,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
    inference(rename_variables,[],[i_0_1478]) ).

cnf(i_0_2816,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(scs_inference,[],[i_0_2276,i_0_2120,i_0_2646,i_0_2293,i_0_2299,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2682,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2427,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2328,i_0_2242,i_0_2203,i_0_2519,i_0_2522,i_0_2173,i_0_2232,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2606,i_0_2158,i_0_2435,i_0_2382,i_0_1351,i_0_1171,i_0_2271,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659,i_0_1697,i_0_1459,i_0_1571,i_0_1560,i_0_1601,i_0_1691,i_0_1631,i_0_1683,i_0_1910,i_0_1912,i_0_1913,i_0_1163,i_0_1282,i_0_1478,i_0_1809]) ).

cnf(i_0_2817,plain,
    hAPP(c_Hilbert__Choice_Oinv__into(X1,X1,hAPP(c_fequal,X2),c_COMBI(X1)),hAPP(c_COMBI(X1),X2)) = X2,
    inference(rename_variables,[],[i_0_2299]) ).

cnf(i_0_2818,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(rename_variables,[],[i_0_1809]) ).

cnf(i_0_2819,plain,
    X1 = esk34_4(hAPP(c_Hilbert__Choice_Oinv__into(X2,X2,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),c_COMBI(X2)),X1),c_Hilbert__Choice_Oinv__into(X2,X2,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),c_COMBI(X2)),X2,X2),
    inference(scs_inference,[],[i_0_2276,i_0_2120,i_0_2646,i_0_2293,i_0_2299,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2140,i_0_2142,i_0_2253,i_0_2682,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2427,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2328,i_0_2242,i_0_2203,i_0_2519,i_0_2522,i_0_2173,i_0_2232,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2606,i_0_2158,i_0_2435,i_0_2382,i_0_1351,i_0_2812,i_0_1171,i_0_2271,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659,i_0_1697,i_0_1459,i_0_1571,i_0_1560,i_0_1601,i_0_1691,i_0_1631,i_0_1683,i_0_1910,i_0_1912,i_0_1913,i_0_1163,i_0_1282,i_0_1478,i_0_1809,i_0_2041]) ).

cnf(i_0_2820,plain,
    c_Fun_Oinj__on(X1,X1,c_Hilbert__Choice_Oinv__into(X1,X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_COMBI(X1)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),
    inference(rename_variables,[],[i_0_2271]) ).

cnf(i_0_2821,plain,
    hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),c_Set_Oimage(X4,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))),
    inference(rename_variables,[],[i_0_1351]) ).

cnf(i_0_2822,plain,
    ( ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
    | ~ hBOOL(hAPP(hAPP(c_member(X2),hAPP(X3,X4)),c_Set_Oimage(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))))
    | X4 = esk34_4(hAPP(X3,X4),X3,X2,X1) ),
    inference(rename_variables,[],[i_0_2041]) ).

cnf(i_0_2823,plain,
    class_Groups_Ocomm__monoid__add(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),tc_Nat_Onat),esk18_2(tc_Nat_Onat,tc_Nat_Onat))),
    inference(scs_inference,[],[i_0_2276,i_0_2120,i_0_2646,i_0_2293,i_0_2299,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2236,i_0_2140,i_0_2142,i_0_2253,i_0_2682,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2427,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2328,i_0_2242,i_0_2203,i_0_2519,i_0_2522,i_0_2173,i_0_2232,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2606,i_0_2158,i_0_2435,i_0_2382,i_0_1351,i_0_2812,i_0_1171,i_0_2271,i_0_1885,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659,i_0_1697,i_0_1459,i_0_1571,i_0_1560,i_0_1601,i_0_1691,i_0_1631,i_0_1683,i_0_1910,i_0_1912,i_0_1913,i_0_1163,i_0_1282,i_0_1478,i_0_1809,i_0_2041,i_0_2002]) ).

cnf(i_0_2824,plain,
    X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk18_2(X1,X1)),
    inference(rename_variables,[],[i_0_2236]) ).

cnf(i_0_2825,plain,
    class_Groups_Omonoid__add(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),tc_Nat_Onat),esk18_2(tc_Nat_Onat,tc_Nat_Onat))),
    inference(scs_inference,[],[i_0_2276,i_0_2120,i_0_2646,i_0_2293,i_0_2299,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2236,i_0_2824,i_0_2140,i_0_2142,i_0_2253,i_0_2682,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2427,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2328,i_0_2242,i_0_2203,i_0_2519,i_0_2522,i_0_2173,i_0_2232,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2606,i_0_2158,i_0_2435,i_0_2382,i_0_1351,i_0_2812,i_0_1171,i_0_2271,i_0_1885,i_0_1886,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659,i_0_1697,i_0_1459,i_0_1571,i_0_1560,i_0_1601,i_0_1691,i_0_1631,i_0_1683,i_0_1910,i_0_1912,i_0_1913,i_0_1163,i_0_1282,i_0_1478,i_0_1809,i_0_2041,i_0_2002,i_0_2003]) ).

cnf(i_0_2826,plain,
    X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk18_2(X1,X1)),
    inference(rename_variables,[],[i_0_2236]) ).

cnf(i_0_2827,plain,
    class_Rings_Ozero__neq__one(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),tc_Nat_Onat),esk18_2(tc_Nat_Onat,tc_Nat_Onat))),
    inference(scs_inference,[],[i_0_2276,i_0_2120,i_0_2646,i_0_2293,i_0_2299,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2236,i_0_2824,i_0_2826,i_0_2140,i_0_2142,i_0_2253,i_0_2682,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2427,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2328,i_0_2242,i_0_2203,i_0_2519,i_0_2522,i_0_2173,i_0_2232,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2606,i_0_2158,i_0_2435,i_0_2382,i_0_1351,i_0_2812,i_0_1171,i_0_2271,i_0_1884,i_0_1885,i_0_1886,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659,i_0_1697,i_0_1459,i_0_1571,i_0_1560,i_0_1601,i_0_1691,i_0_1631,i_0_1683,i_0_1910,i_0_1912,i_0_1913,i_0_1163,i_0_1282,i_0_1478,i_0_1809,i_0_2041,i_0_2002,i_0_2003,i_0_2004]) ).

cnf(i_0_2828,plain,
    X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk18_2(X1,X1)),
    inference(rename_variables,[],[i_0_2236]) ).

cnf(i_0_2829,plain,
    class_Groups_Ozero(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),tc_Nat_Onat),esk18_2(tc_Nat_Onat,tc_Nat_Onat))),
    inference(scs_inference,[],[i_0_2276,i_0_2120,i_0_2646,i_0_2293,i_0_2299,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2236,i_0_2824,i_0_2826,i_0_2828,i_0_2140,i_0_2142,i_0_2253,i_0_2682,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2427,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2328,i_0_2242,i_0_2203,i_0_2519,i_0_2522,i_0_2173,i_0_2232,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2606,i_0_2158,i_0_2435,i_0_2382,i_0_1351,i_0_2812,i_0_1171,i_0_2271,i_0_1883,i_0_1884,i_0_1885,i_0_1886,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659,i_0_1697,i_0_1459,i_0_1571,i_0_1560,i_0_1601,i_0_1691,i_0_1631,i_0_1683,i_0_1910,i_0_1912,i_0_1913,i_0_1163,i_0_1282,i_0_1478,i_0_1809,i_0_2041,i_0_2002,i_0_2003,i_0_2004,i_0_2005]) ).

cnf(i_0_2830,plain,
    X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk18_2(X1,X1)),
    inference(rename_variables,[],[i_0_2236]) ).

cnf(i_0_2831,plain,
    class_Groups_Oone(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),tc_Nat_Onat),esk18_2(tc_Nat_Onat,tc_Nat_Onat))),
    inference(scs_inference,[],[i_0_2276,i_0_2120,i_0_2646,i_0_2293,i_0_2299,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2236,i_0_2824,i_0_2826,i_0_2828,i_0_2830,i_0_2140,i_0_2142,i_0_2253,i_0_2682,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2427,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2328,i_0_2242,i_0_2203,i_0_2519,i_0_2522,i_0_2173,i_0_2232,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2606,i_0_2158,i_0_2435,i_0_2382,i_0_1351,i_0_2812,i_0_1171,i_0_2271,i_0_1883,i_0_1884,i_0_1885,i_0_1886,i_0_1892,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659,i_0_1697,i_0_1459,i_0_1571,i_0_1560,i_0_1601,i_0_1691,i_0_1631,i_0_1683,i_0_1910,i_0_1912,i_0_1913,i_0_1163,i_0_1282,i_0_1478,i_0_1809,i_0_2041,i_0_2002,i_0_2003,i_0_2004,i_0_2005,i_0_2006]) ).

cnf(i_0_2832,plain,
    X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk18_2(X1,X1)),
    inference(rename_variables,[],[i_0_2236]) ).

cnf(i_0_2833,plain,
    ~ c_Finite__Set_Ofolding__image__simple(hAPP(c_Hilbert__Choice_Oinv__into(X1,X1,hAPP(c_fequal,X2),c_COMBI(X1)),hAPP(c_COMBI(X1),X2)),X3,X4,X5,X6,hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Finite__Set_Ofold__image(X2,X3,X4,X6,X5,c_Set_Oimage(tc_Nat_Onat,X3,X7,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X8,X9)))))),
    inference(scs_inference,[],[i_0_2276,i_0_2120,i_0_2646,i_0_2293,i_0_2299,i_0_2817,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2236,i_0_2824,i_0_2826,i_0_2828,i_0_2830,i_0_2140,i_0_2142,i_0_2253,i_0_2682,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2427,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2328,i_0_2242,i_0_2203,i_0_2519,i_0_2522,i_0_2173,i_0_2232,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2606,i_0_2158,i_0_2435,i_0_2382,i_0_1351,i_0_2812,i_0_1171,i_0_2271,i_0_1883,i_0_1884,i_0_1885,i_0_1886,i_0_1892,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659,i_0_1697,i_0_1459,i_0_1571,i_0_1560,i_0_1601,i_0_1691,i_0_1631,i_0_1683,i_0_1910,i_0_1912,i_0_1913,i_0_1163,i_0_1282,i_0_1478,i_0_1809,i_0_2041,i_0_2002,i_0_2003,i_0_2004,i_0_2005,i_0_2006,i_0_2009]) ).

cnf(i_0_2834,plain,
    ~ c_Finite__Set_Ofolding__image__simple(X1,hAPP(c_Hilbert__Choice_Oinv__into(X2,X2,hAPP(c_fequal,X1),c_COMBI(X2)),hAPP(c_COMBI(X2),X1)),X3,X4,X5,hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Finite__Set_Ofold__image(X1,X1,X3,X5,X4,c_Set_Oimage(tc_Nat_Onat,X1,X6,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X7,X8)))))),
    inference(scs_inference,[],[i_0_2276,i_0_2120,i_0_2646,i_0_2293,i_0_2299,i_0_2817,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2236,i_0_2824,i_0_2826,i_0_2828,i_0_2830,i_0_2140,i_0_2142,i_0_2253,i_0_2682,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2427,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2328,i_0_2242,i_0_2203,i_0_2519,i_0_2522,i_0_2173,i_0_2232,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2606,i_0_2158,i_0_2435,i_0_2382,i_0_1351,i_0_2812,i_0_1171,i_0_2271,i_0_1883,i_0_1884,i_0_1885,i_0_1886,i_0_1892,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659,i_0_1697,i_0_1459,i_0_1571,i_0_1560,i_0_1601,i_0_1691,i_0_1631,i_0_1683,i_0_1910,i_0_1912,i_0_1913,i_0_1163,i_0_1282,i_0_1478,i_0_1809,i_0_2041,i_0_2002,i_0_2003,i_0_2004,i_0_2005,i_0_2006,i_0_2009,i_0_2010]) ).

cnf(i_0_2835,plain,
    ~ c_Finite__Set_Ofolding__image__simple(X1,X1,hAPP(c_Hilbert__Choice_Oinv__into(X2,X2,hAPP(c_fequal,X1),c_COMBI(X2)),hAPP(c_COMBI(X2),X1)),X3,X4,hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Finite__Set_Ofold__image(X1,X1,X1,X4,X3,c_Set_Oimage(tc_Nat_Onat,X1,X5,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X6,X7)))))),
    inference(scs_inference,[],[i_0_2276,i_0_2120,i_0_2646,i_0_2293,i_0_2299,i_0_2817,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2236,i_0_2824,i_0_2826,i_0_2828,i_0_2830,i_0_2140,i_0_2142,i_0_2253,i_0_2682,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2427,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2328,i_0_2242,i_0_2203,i_0_2519,i_0_2522,i_0_2173,i_0_2232,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2606,i_0_2158,i_0_2435,i_0_2382,i_0_1351,i_0_2812,i_0_1171,i_0_2271,i_0_1883,i_0_1884,i_0_1885,i_0_1886,i_0_1892,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659,i_0_1697,i_0_1459,i_0_1571,i_0_1560,i_0_1601,i_0_1691,i_0_1631,i_0_1683,i_0_1910,i_0_1912,i_0_1913,i_0_1163,i_0_1282,i_0_1478,i_0_1809,i_0_2041,i_0_2002,i_0_2003,i_0_2004,i_0_2005,i_0_2006,i_0_2009,i_0_2010,i_0_2011]) ).

cnf(i_0_2836,plain,
    ~ c_Finite__Set_Ofolding__image__simple(X1,X1,X1,hAPP(c_Hilbert__Choice_Oinv__into(X2,X2,hAPP(c_fequal,X1),c_COMBI(X2)),hAPP(c_COMBI(X2),X1)),X3,hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Finite__Set_Ofold__image(X1,X1,X1,X3,X1,c_Set_Oimage(tc_Nat_Onat,X1,X4,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X5,X6)))))),
    inference(scs_inference,[],[i_0_2276,i_0_2120,i_0_2646,i_0_2293,i_0_2299,i_0_2817,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2236,i_0_2824,i_0_2826,i_0_2828,i_0_2830,i_0_2140,i_0_2142,i_0_2253,i_0_2682,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2427,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2328,i_0_2242,i_0_2203,i_0_2519,i_0_2522,i_0_2173,i_0_2232,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2606,i_0_2158,i_0_2435,i_0_2382,i_0_1351,i_0_2812,i_0_1171,i_0_2271,i_0_1883,i_0_1884,i_0_1885,i_0_1886,i_0_1892,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659,i_0_1697,i_0_1459,i_0_1571,i_0_1560,i_0_1601,i_0_1691,i_0_1631,i_0_1683,i_0_1910,i_0_1912,i_0_1913,i_0_1163,i_0_1282,i_0_1478,i_0_1809,i_0_2041,i_0_2002,i_0_2003,i_0_2004,i_0_2005,i_0_2006,i_0_2009,i_0_2010,i_0_2011,i_0_2012]) ).

cnf(i_0_2837,plain,
    ~ c_Finite__Set_Ofolding__image__simple(X1,X1,X1,X1,hAPP(c_Hilbert__Choice_Oinv__into(X2,X2,hAPP(c_fequal,X1),c_COMBI(X2)),hAPP(c_COMBI(X2),X1)),hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Finite__Set_Ofold__image(X1,X1,X1,X1,X1,c_Set_Oimage(tc_Nat_Onat,X1,X3,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X4,X5)))))),
    inference(scs_inference,[],[i_0_2276,i_0_2120,i_0_2646,i_0_2293,i_0_2299,i_0_2817,i_0_2468,i_0_2575,i_0_2118,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2236,i_0_2824,i_0_2826,i_0_2828,i_0_2830,i_0_2140,i_0_2142,i_0_2253,i_0_2682,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2427,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2328,i_0_2242,i_0_2203,i_0_2519,i_0_2522,i_0_2173,i_0_2232,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2606,i_0_2158,i_0_2435,i_0_2382,i_0_1351,i_0_2812,i_0_1171,i_0_2271,i_0_1883,i_0_1884,i_0_1885,i_0_1886,i_0_1892,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659,i_0_1697,i_0_1459,i_0_1571,i_0_1560,i_0_1601,i_0_1691,i_0_1631,i_0_1683,i_0_1910,i_0_1912,i_0_1913,i_0_1163,i_0_1282,i_0_1478,i_0_1809,i_0_2041,i_0_2002,i_0_2003,i_0_2004,i_0_2005,i_0_2006,i_0_2009,i_0_2010,i_0_2011,i_0_2012,i_0_2013]) ).

cnf(i_0_2838,plain,
    ~ c_Finite__Set_Ofolding__image__simple(X1,X1,X1,X1,X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Finite__Set_Ofold__image(X1,X1,X1,X1,X1,c_Set_Oimage(tc_Nat_Onat,X1,X2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3,X4))))))),
    inference(scs_inference,[],[i_0_2276,i_0_2120,i_0_2646,i_0_2293,i_0_2299,i_0_2817,i_0_2468,i_0_2575,i_0_2118,i_0_1847,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2236,i_0_2824,i_0_2826,i_0_2828,i_0_2830,i_0_2140,i_0_2142,i_0_2253,i_0_2682,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2427,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2328,i_0_2242,i_0_2203,i_0_2519,i_0_2522,i_0_2173,i_0_2232,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2606,i_0_2158,i_0_2435,i_0_2382,i_0_1351,i_0_2812,i_0_1171,i_0_2271,i_0_1883,i_0_1884,i_0_1885,i_0_1886,i_0_1892,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659,i_0_1697,i_0_1459,i_0_1571,i_0_1560,i_0_1601,i_0_1691,i_0_1631,i_0_1683,i_0_1910,i_0_1912,i_0_1913,i_0_1163,i_0_1282,i_0_1478,i_0_1809,i_0_2041,i_0_2002,i_0_2003,i_0_2004,i_0_2005,i_0_2006,i_0_2009,i_0_2010,i_0_2011,i_0_2012,i_0_2013,i_0_2014]) ).

cnf(i_0_2839,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) = X1,
    inference(rename_variables,[],[i_0_1847]) ).

cnf(i_0_2840,plain,
    class_Orderings_Oord(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),tc_Nat_Onat),esk18_2(tc_Nat_Onat,tc_Nat_Onat))),
    inference(scs_inference,[],[i_0_2276,i_0_2120,i_0_2646,i_0_2293,i_0_2299,i_0_2817,i_0_2468,i_0_2575,i_0_2118,i_0_1847,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2236,i_0_2824,i_0_2826,i_0_2828,i_0_2830,i_0_2832,i_0_2140,i_0_2142,i_0_2253,i_0_2682,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2427,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2328,i_0_2242,i_0_2203,i_0_2519,i_0_2522,i_0_2173,i_0_2232,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2606,i_0_2158,i_0_2435,i_0_2382,i_0_1351,i_0_2812,i_0_1171,i_0_2271,i_0_1883,i_0_1884,i_0_1885,i_0_1886,i_0_1892,i_0_1899,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659,i_0_1697,i_0_1459,i_0_1571,i_0_1560,i_0_1601,i_0_1691,i_0_1631,i_0_1683,i_0_1910,i_0_1912,i_0_1913,i_0_1163,i_0_1282,i_0_1478,i_0_1809,i_0_2041,i_0_2002,i_0_2003,i_0_2004,i_0_2005,i_0_2006,i_0_2009,i_0_2010,i_0_2011,i_0_2012,i_0_2013,i_0_2014,i_0_2017]) ).

cnf(i_0_2841,plain,
    X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk18_2(X1,X1)),
    inference(rename_variables,[],[i_0_2236]) ).

cnf(i_0_2842,plain,
    class_Orderings_Olinorder(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),tc_Nat_Onat),esk18_2(tc_Nat_Onat,tc_Nat_Onat))),
    inference(scs_inference,[],[i_0_2276,i_0_2120,i_0_2646,i_0_2293,i_0_2299,i_0_2817,i_0_2468,i_0_2575,i_0_2118,i_0_1847,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2236,i_0_2824,i_0_2826,i_0_2828,i_0_2830,i_0_2832,i_0_2841,i_0_2140,i_0_2142,i_0_2253,i_0_2682,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2427,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2328,i_0_2242,i_0_2203,i_0_2519,i_0_2522,i_0_2173,i_0_2232,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2606,i_0_2158,i_0_2435,i_0_2382,i_0_1351,i_0_2812,i_0_1171,i_0_2271,i_0_1883,i_0_1884,i_0_1885,i_0_1886,i_0_1892,i_0_1899,i_0_1900,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659,i_0_1697,i_0_1459,i_0_1571,i_0_1560,i_0_1601,i_0_1691,i_0_1631,i_0_1683,i_0_1910,i_0_1912,i_0_1913,i_0_1163,i_0_1282,i_0_1478,i_0_1809,i_0_2041,i_0_2002,i_0_2003,i_0_2004,i_0_2005,i_0_2006,i_0_2009,i_0_2010,i_0_2011,i_0_2012,i_0_2013,i_0_2014,i_0_2017,i_0_1982]) ).

cnf(i_0_2843,plain,
    X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk18_2(X1,X1)),
    inference(rename_variables,[],[i_0_2236]) ).

cnf(i_0_2844,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),tc_Nat_Onat),esk18_2(tc_Nat_Onat,tc_Nat_Onat))),
    inference(scs_inference,[],[i_0_2276,i_0_2120,i_0_2646,i_0_2293,i_0_2299,i_0_2817,i_0_2468,i_0_2575,i_0_2118,i_0_1847,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2236,i_0_2824,i_0_2826,i_0_2828,i_0_2830,i_0_2832,i_0_2841,i_0_2843,i_0_2140,i_0_2142,i_0_2253,i_0_2682,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2427,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2328,i_0_2242,i_0_2203,i_0_2519,i_0_2522,i_0_2173,i_0_2232,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2606,i_0_2158,i_0_2435,i_0_2382,i_0_1351,i_0_2812,i_0_1171,i_0_2271,i_0_1883,i_0_1884,i_0_1885,i_0_1886,i_0_1892,i_0_1891,i_0_1899,i_0_1900,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659,i_0_1697,i_0_1459,i_0_1571,i_0_1560,i_0_1601,i_0_1691,i_0_1631,i_0_1683,i_0_1910,i_0_1912,i_0_1913,i_0_1163,i_0_1282,i_0_1478,i_0_1809,i_0_2041,i_0_2002,i_0_2003,i_0_2004,i_0_2005,i_0_2006,i_0_2009,i_0_2010,i_0_2011,i_0_2012,i_0_2013,i_0_2014,i_0_2017,i_0_1982,i_0_1983]) ).

cnf(i_0_2845,plain,
    X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk18_2(X1,X1)),
    inference(rename_variables,[],[i_0_2236]) ).

cnf(i_0_2846,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),tc_Nat_Onat),esk18_2(tc_Nat_Onat,tc_Nat_Onat))),
    inference(scs_inference,[],[i_0_2276,i_0_2120,i_0_2646,i_0_2293,i_0_2299,i_0_2817,i_0_2468,i_0_2575,i_0_2118,i_0_1847,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2236,i_0_2824,i_0_2826,i_0_2828,i_0_2830,i_0_2832,i_0_2841,i_0_2843,i_0_2845,i_0_2140,i_0_2142,i_0_2253,i_0_2682,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2427,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2328,i_0_2242,i_0_2203,i_0_2519,i_0_2522,i_0_2173,i_0_2232,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2606,i_0_2158,i_0_2435,i_0_2382,i_0_1351,i_0_2812,i_0_1171,i_0_2271,i_0_1883,i_0_1884,i_0_1885,i_0_1886,i_0_1892,i_0_1891,i_0_1899,i_0_1903,i_0_1900,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659,i_0_1697,i_0_1459,i_0_1571,i_0_1560,i_0_1601,i_0_1691,i_0_1631,i_0_1683,i_0_1910,i_0_1912,i_0_1913,i_0_1163,i_0_1282,i_0_1478,i_0_1809,i_0_2041,i_0_2002,i_0_2003,i_0_2004,i_0_2005,i_0_2006,i_0_2009,i_0_2010,i_0_2011,i_0_2012,i_0_2013,i_0_2014,i_0_2017,i_0_1982,i_0_1983,i_0_1984]) ).

cnf(i_0_2847,plain,
    X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk18_2(X1,X1)),
    inference(rename_variables,[],[i_0_2236]) ).

cnf(i_0_2848,plain,
    class_Groups_Oordered__ab__semigroup__add(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),tc_Nat_Onat),esk18_2(tc_Nat_Onat,tc_Nat_Onat))),
    inference(scs_inference,[],[i_0_2276,i_0_2120,i_0_2646,i_0_2293,i_0_2299,i_0_2817,i_0_2468,i_0_2575,i_0_2118,i_0_1847,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2236,i_0_2824,i_0_2826,i_0_2828,i_0_2830,i_0_2832,i_0_2841,i_0_2843,i_0_2845,i_0_2847,i_0_2140,i_0_2142,i_0_2253,i_0_2682,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2427,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2328,i_0_2242,i_0_2203,i_0_2519,i_0_2522,i_0_2173,i_0_2232,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2606,i_0_2158,i_0_2435,i_0_2382,i_0_1351,i_0_2812,i_0_1171,i_0_2271,i_0_1883,i_0_1884,i_0_1885,i_0_1886,i_0_1890,i_0_1892,i_0_1891,i_0_1899,i_0_1903,i_0_1900,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659,i_0_1697,i_0_1459,i_0_1571,i_0_1560,i_0_1601,i_0_1691,i_0_1631,i_0_1683,i_0_1910,i_0_1912,i_0_1913,i_0_1163,i_0_1282,i_0_1478,i_0_1809,i_0_2041,i_0_2002,i_0_2003,i_0_2004,i_0_2005,i_0_2006,i_0_2009,i_0_2010,i_0_2011,i_0_2012,i_0_2013,i_0_2014,i_0_2017,i_0_1982,i_0_1983,i_0_1984,i_0_1985]) ).

cnf(i_0_2849,plain,
    X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk18_2(X1,X1)),
    inference(rename_variables,[],[i_0_2236]) ).

cnf(i_0_2850,plain,
    class_Groups_Oordered__comm__monoid__add(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),tc_Nat_Onat),esk18_2(tc_Nat_Onat,tc_Nat_Onat))),
    inference(scs_inference,[],[i_0_2276,i_0_2120,i_0_2646,i_0_2293,i_0_2299,i_0_2817,i_0_2468,i_0_2575,i_0_2118,i_0_1847,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2236,i_0_2824,i_0_2826,i_0_2828,i_0_2830,i_0_2832,i_0_2841,i_0_2843,i_0_2845,i_0_2847,i_0_2849,i_0_2140,i_0_2142,i_0_2253,i_0_2682,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2427,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2328,i_0_2242,i_0_2203,i_0_2519,i_0_2522,i_0_2173,i_0_2232,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2606,i_0_2158,i_0_2435,i_0_2382,i_0_1351,i_0_2812,i_0_1171,i_0_2271,i_0_1883,i_0_1884,i_0_1885,i_0_1886,i_0_1890,i_0_1892,i_0_1891,i_0_1899,i_0_1903,i_0_1882,i_0_1900,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659,i_0_1697,i_0_1459,i_0_1571,i_0_1560,i_0_1601,i_0_1691,i_0_1631,i_0_1683,i_0_1910,i_0_1912,i_0_1913,i_0_1163,i_0_1282,i_0_1478,i_0_1809,i_0_2041,i_0_2002,i_0_2003,i_0_2004,i_0_2005,i_0_2006,i_0_2009,i_0_2010,i_0_2011,i_0_2012,i_0_2013,i_0_2014,i_0_2017,i_0_1982,i_0_1983,i_0_1984,i_0_1985,i_0_1987]) ).

cnf(i_0_2851,plain,
    X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk18_2(X1,X1)),
    inference(rename_variables,[],[i_0_2236]) ).

cnf(i_0_2852,plain,
    class_Rings_Ocomm__semiring__1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),tc_Nat_Onat),esk18_2(tc_Nat_Onat,tc_Nat_Onat))),
    inference(scs_inference,[],[i_0_2276,i_0_2120,i_0_2646,i_0_2293,i_0_2299,i_0_2817,i_0_2468,i_0_2575,i_0_2118,i_0_1847,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2236,i_0_2824,i_0_2826,i_0_2828,i_0_2830,i_0_2832,i_0_2841,i_0_2843,i_0_2845,i_0_2847,i_0_2849,i_0_2851,i_0_2140,i_0_2142,i_0_2253,i_0_2682,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2427,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2328,i_0_2242,i_0_2203,i_0_2519,i_0_2522,i_0_2173,i_0_2232,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2606,i_0_2158,i_0_2435,i_0_2382,i_0_1351,i_0_2812,i_0_1171,i_0_2271,i_0_1881,i_0_1883,i_0_1884,i_0_1885,i_0_1886,i_0_1890,i_0_1892,i_0_1891,i_0_1899,i_0_1903,i_0_1882,i_0_1900,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659,i_0_1697,i_0_1459,i_0_1571,i_0_1560,i_0_1601,i_0_1691,i_0_1631,i_0_1683,i_0_1910,i_0_1912,i_0_1913,i_0_1163,i_0_1282,i_0_1478,i_0_1809,i_0_2041,i_0_2002,i_0_2003,i_0_2004,i_0_2005,i_0_2006,i_0_2009,i_0_2010,i_0_2011,i_0_2012,i_0_2013,i_0_2014,i_0_2017,i_0_1982,i_0_1983,i_0_1984,i_0_1985,i_0_1987,i_0_1989]) ).

cnf(i_0_2853,plain,
    X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk18_2(X1,X1)),
    inference(rename_variables,[],[i_0_2236]) ).

cnf(i_0_2854,plain,
    class_Rings_Olinordered__semidom(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),tc_Nat_Onat),esk18_2(tc_Nat_Onat,tc_Nat_Onat))),
    inference(scs_inference,[],[i_0_2276,i_0_2120,i_0_2646,i_0_2293,i_0_2299,i_0_2817,i_0_2468,i_0_2575,i_0_2118,i_0_1847,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2236,i_0_2824,i_0_2826,i_0_2828,i_0_2830,i_0_2832,i_0_2841,i_0_2843,i_0_2845,i_0_2847,i_0_2849,i_0_2851,i_0_2853,i_0_2140,i_0_2142,i_0_2253,i_0_2682,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2427,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2328,i_0_2242,i_0_2203,i_0_2519,i_0_2522,i_0_2173,i_0_2232,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2606,i_0_2158,i_0_2435,i_0_2382,i_0_1351,i_0_2812,i_0_1171,i_0_2271,i_0_1881,i_0_1883,i_0_1884,i_0_1885,i_0_1886,i_0_1890,i_0_1892,i_0_1891,i_0_1899,i_0_1904,i_0_1903,i_0_1882,i_0_1900,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659,i_0_1697,i_0_1459,i_0_1571,i_0_1560,i_0_1601,i_0_1691,i_0_1631,i_0_1683,i_0_1910,i_0_1912,i_0_1913,i_0_1163,i_0_1282,i_0_1478,i_0_1809,i_0_2041,i_0_2002,i_0_2003,i_0_2004,i_0_2005,i_0_2006,i_0_2009,i_0_2010,i_0_2011,i_0_2012,i_0_2013,i_0_2014,i_0_2017,i_0_1982,i_0_1983,i_0_1984,i_0_1985,i_0_1987,i_0_1989,i_0_1991]) ).

cnf(i_0_2855,plain,
    X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk18_2(X1,X1)),
    inference(rename_variables,[],[i_0_2236]) ).

cnf(i_0_2856,plain,
    class_Orderings_Opreorder(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),tc_HOL_Obool),esk18_2(tc_HOL_Obool,tc_HOL_Obool))),
    inference(scs_inference,[],[i_0_2276,i_0_2120,i_0_2646,i_0_2293,i_0_2299,i_0_2817,i_0_2468,i_0_2575,i_0_2118,i_0_1847,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2236,i_0_2824,i_0_2826,i_0_2828,i_0_2830,i_0_2832,i_0_2841,i_0_2843,i_0_2845,i_0_2847,i_0_2849,i_0_2851,i_0_2853,i_0_2855,i_0_2140,i_0_2142,i_0_2253,i_0_2682,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2427,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2328,i_0_2242,i_0_2203,i_0_2519,i_0_2522,i_0_2173,i_0_2232,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2606,i_0_2158,i_0_2435,i_0_2382,i_0_1351,i_0_2812,i_0_1171,i_0_2271,i_0_1881,i_0_1883,i_0_1884,i_0_1885,i_0_1886,i_0_1890,i_0_1892,i_0_1901,i_0_1891,i_0_1899,i_0_1904,i_0_1903,i_0_1882,i_0_1900,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659,i_0_1697,i_0_1459,i_0_1571,i_0_1560,i_0_1601,i_0_1691,i_0_1631,i_0_1683,i_0_1910,i_0_1912,i_0_1913,i_0_1163,i_0_1282,i_0_1478,i_0_1809,i_0_2041,i_0_2002,i_0_2003,i_0_2004,i_0_2005,i_0_2006,i_0_2009,i_0_2010,i_0_2011,i_0_2012,i_0_2013,i_0_2014,i_0_2017,i_0_1982,i_0_1983,i_0_1984,i_0_1985,i_0_1987,i_0_1989,i_0_1991,i_0_1993]) ).

cnf(i_0_2857,plain,
    X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk18_2(X1,X1)),
    inference(rename_variables,[],[i_0_2236]) ).

cnf(i_0_2858,plain,
    class_Orderings_Oorder(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),tc_HOL_Obool),esk18_2(tc_HOL_Obool,tc_HOL_Obool))),
    inference(scs_inference,[],[i_0_2276,i_0_2120,i_0_2646,i_0_2293,i_0_2299,i_0_2817,i_0_2468,i_0_2575,i_0_2118,i_0_1847,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2236,i_0_2824,i_0_2826,i_0_2828,i_0_2830,i_0_2832,i_0_2841,i_0_2843,i_0_2845,i_0_2847,i_0_2849,i_0_2851,i_0_2853,i_0_2855,i_0_2857,i_0_2140,i_0_2142,i_0_2253,i_0_2682,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2427,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2328,i_0_2242,i_0_2203,i_0_2519,i_0_2522,i_0_2173,i_0_2232,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2606,i_0_2158,i_0_2435,i_0_2382,i_0_1351,i_0_2812,i_0_1171,i_0_2271,i_0_1881,i_0_1883,i_0_1884,i_0_1885,i_0_1886,i_0_1890,i_0_1892,i_0_1896,i_0_1901,i_0_1891,i_0_1899,i_0_1904,i_0_1903,i_0_1882,i_0_1900,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659,i_0_1697,i_0_1459,i_0_1571,i_0_1560,i_0_1601,i_0_1691,i_0_1631,i_0_1683,i_0_1910,i_0_1912,i_0_1913,i_0_1163,i_0_1282,i_0_1478,i_0_1809,i_0_2041,i_0_2002,i_0_2003,i_0_2004,i_0_2005,i_0_2006,i_0_2009,i_0_2010,i_0_2011,i_0_2012,i_0_2013,i_0_2014,i_0_2017,i_0_1982,i_0_1983,i_0_1984,i_0_1985,i_0_1987,i_0_1989,i_0_1991,i_0_1993,i_0_1994]) ).

cnf(i_0_2859,plain,
    X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk18_2(X1,X1)),
    inference(rename_variables,[],[i_0_2236]) ).

cnf(i_0_2860,plain,
    class_Groups_Oab__semigroup__add(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),tc_Nat_Onat),esk18_2(tc_Nat_Onat,tc_Nat_Onat))),
    inference(scs_inference,[],[i_0_2276,i_0_2120,i_0_2646,i_0_2293,i_0_2299,i_0_2817,i_0_2468,i_0_2575,i_0_2118,i_0_1847,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2236,i_0_2824,i_0_2826,i_0_2828,i_0_2830,i_0_2832,i_0_2841,i_0_2843,i_0_2845,i_0_2847,i_0_2849,i_0_2851,i_0_2853,i_0_2855,i_0_2857,i_0_2859,i_0_2140,i_0_2142,i_0_2253,i_0_2682,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2427,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2328,i_0_2242,i_0_2203,i_0_2519,i_0_2522,i_0_2173,i_0_2232,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2606,i_0_2158,i_0_2435,i_0_2382,i_0_1351,i_0_2812,i_0_1171,i_0_2271,i_0_1881,i_0_1883,i_0_1884,i_0_1885,i_0_1886,i_0_1890,i_0_1892,i_0_1893,i_0_1896,i_0_1901,i_0_1891,i_0_1899,i_0_1904,i_0_1903,i_0_1882,i_0_1900,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659,i_0_1697,i_0_1459,i_0_1571,i_0_1560,i_0_1601,i_0_1691,i_0_1631,i_0_1683,i_0_1910,i_0_1912,i_0_1913,i_0_1163,i_0_1282,i_0_1478,i_0_1809,i_0_2041,i_0_2002,i_0_2003,i_0_2004,i_0_2005,i_0_2006,i_0_2009,i_0_2010,i_0_2011,i_0_2012,i_0_2013,i_0_2014,i_0_2017,i_0_1982,i_0_1983,i_0_1984,i_0_1985,i_0_1987,i_0_1989,i_0_1991,i_0_1993,i_0_1994,i_0_1995]) ).

cnf(i_0_2861,plain,
    X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk18_2(X1,X1)),
    inference(rename_variables,[],[i_0_2236]) ).

cnf(i_0_2862,plain,
    class_Groups_Ocancel__semigroup__add(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),tc_Nat_Onat),esk18_2(tc_Nat_Onat,tc_Nat_Onat))),
    inference(scs_inference,[],[i_0_2276,i_0_2120,i_0_2646,i_0_2293,i_0_2299,i_0_2817,i_0_2468,i_0_2575,i_0_2118,i_0_1847,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2236,i_0_2824,i_0_2826,i_0_2828,i_0_2830,i_0_2832,i_0_2841,i_0_2843,i_0_2845,i_0_2847,i_0_2849,i_0_2851,i_0_2853,i_0_2855,i_0_2857,i_0_2859,i_0_2861,i_0_2140,i_0_2142,i_0_2253,i_0_2682,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2427,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2328,i_0_2242,i_0_2203,i_0_2519,i_0_2522,i_0_2173,i_0_2232,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2606,i_0_2158,i_0_2435,i_0_2382,i_0_1351,i_0_2812,i_0_1171,i_0_2271,i_0_1881,i_0_1883,i_0_1884,i_0_1885,i_0_1886,i_0_1890,i_0_1892,i_0_1893,i_0_1895,i_0_1896,i_0_1901,i_0_1891,i_0_1899,i_0_1904,i_0_1903,i_0_1882,i_0_1900,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659,i_0_1697,i_0_1459,i_0_1571,i_0_1560,i_0_1601,i_0_1691,i_0_1631,i_0_1683,i_0_1910,i_0_1912,i_0_1913,i_0_1163,i_0_1282,i_0_1478,i_0_1809,i_0_2041,i_0_2002,i_0_2003,i_0_2004,i_0_2005,i_0_2006,i_0_2009,i_0_2010,i_0_2011,i_0_2012,i_0_2013,i_0_2014,i_0_2017,i_0_1982,i_0_1983,i_0_1984,i_0_1985,i_0_1987,i_0_1989,i_0_1991,i_0_1993,i_0_1994,i_0_1995,i_0_1996]) ).

cnf(i_0_2863,plain,
    X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk18_2(X1,X1)),
    inference(rename_variables,[],[i_0_2236]) ).

cnf(i_0_2864,plain,
    class_Groups_Ocancel__ab__semigroup__add(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),tc_Nat_Onat),esk18_2(tc_Nat_Onat,tc_Nat_Onat))),
    inference(scs_inference,[],[i_0_2276,i_0_2120,i_0_2646,i_0_2293,i_0_2299,i_0_2817,i_0_2468,i_0_2575,i_0_2118,i_0_1847,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2236,i_0_2824,i_0_2826,i_0_2828,i_0_2830,i_0_2832,i_0_2841,i_0_2843,i_0_2845,i_0_2847,i_0_2849,i_0_2851,i_0_2853,i_0_2855,i_0_2857,i_0_2859,i_0_2861,i_0_2863,i_0_2140,i_0_2142,i_0_2253,i_0_2682,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2427,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2328,i_0_2242,i_0_2203,i_0_2519,i_0_2522,i_0_2173,i_0_2232,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2606,i_0_2158,i_0_2435,i_0_2382,i_0_1351,i_0_2812,i_0_1171,i_0_2271,i_0_1881,i_0_1883,i_0_1884,i_0_1885,i_0_1886,i_0_1890,i_0_1892,i_0_1893,i_0_1895,i_0_1896,i_0_1901,i_0_1891,i_0_1894,i_0_1899,i_0_1904,i_0_1903,i_0_1882,i_0_1900,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659,i_0_1697,i_0_1459,i_0_1571,i_0_1560,i_0_1601,i_0_1691,i_0_1631,i_0_1683,i_0_1910,i_0_1912,i_0_1913,i_0_1163,i_0_1282,i_0_1478,i_0_1809,i_0_2041,i_0_2002,i_0_2003,i_0_2004,i_0_2005,i_0_2006,i_0_2009,i_0_2010,i_0_2011,i_0_2012,i_0_2013,i_0_2014,i_0_2017,i_0_1982,i_0_1983,i_0_1984,i_0_1985,i_0_1987,i_0_1989,i_0_1991,i_0_1993,i_0_1994,i_0_1995,i_0_1996,i_0_1997]) ).

cnf(i_0_2865,plain,
    X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk18_2(X1,X1)),
    inference(rename_variables,[],[i_0_2236]) ).

cnf(i_0_2866,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),tc_Nat_Onat),esk18_2(tc_Nat_Onat,tc_Nat_Onat))),
    inference(scs_inference,[],[i_0_2276,i_0_2120,i_0_2646,i_0_2293,i_0_2299,i_0_2817,i_0_2468,i_0_2575,i_0_2118,i_0_1847,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2236,i_0_2824,i_0_2826,i_0_2828,i_0_2830,i_0_2832,i_0_2841,i_0_2843,i_0_2845,i_0_2847,i_0_2849,i_0_2851,i_0_2853,i_0_2855,i_0_2857,i_0_2859,i_0_2861,i_0_2863,i_0_2865,i_0_2140,i_0_2142,i_0_2253,i_0_2682,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2427,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2328,i_0_2242,i_0_2203,i_0_2519,i_0_2522,i_0_2173,i_0_2232,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2606,i_0_2158,i_0_2435,i_0_2382,i_0_1351,i_0_2812,i_0_1171,i_0_2271,i_0_1880,i_0_1881,i_0_1883,i_0_1884,i_0_1885,i_0_1886,i_0_1890,i_0_1892,i_0_1893,i_0_1895,i_0_1896,i_0_1901,i_0_1891,i_0_1894,i_0_1899,i_0_1904,i_0_1903,i_0_1882,i_0_1900,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659,i_0_1697,i_0_1459,i_0_1571,i_0_1560,i_0_1601,i_0_1691,i_0_1631,i_0_1683,i_0_1910,i_0_1912,i_0_1913,i_0_1163,i_0_1282,i_0_1478,i_0_1809,i_0_2041,i_0_2002,i_0_2003,i_0_2004,i_0_2005,i_0_2006,i_0_2009,i_0_2010,i_0_2011,i_0_2012,i_0_2013,i_0_2014,i_0_2017,i_0_1982,i_0_1983,i_0_1984,i_0_1985,i_0_1987,i_0_1989,i_0_1991,i_0_1993,i_0_1994,i_0_1995,i_0_1996,i_0_1997,i_0_1999]) ).

cnf(i_0_2867,plain,
    X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk18_2(X1,X1)),
    inference(rename_variables,[],[i_0_2236]) ).

cnf(i_0_2868,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))))),
    inference(scs_inference,[],[i_0_2276,i_0_2120,i_0_2646,i_0_2293,i_0_2299,i_0_2817,i_0_2468,i_0_2575,i_0_2118,i_0_1847,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2236,i_0_2824,i_0_2826,i_0_2828,i_0_2830,i_0_2832,i_0_2841,i_0_2843,i_0_2845,i_0_2847,i_0_2849,i_0_2851,i_0_2853,i_0_2855,i_0_2857,i_0_2859,i_0_2861,i_0_2863,i_0_2865,i_0_2140,i_0_2142,i_0_2253,i_0_2682,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2427,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2328,i_0_2242,i_0_2203,i_0_2519,i_0_2522,i_0_2173,i_0_2232,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2606,i_0_2158,i_0_2435,i_0_2382,i_0_1351,i_0_2812,i_0_1171,i_0_2271,i_0_1880,i_0_1881,i_0_1883,i_0_1884,i_0_1885,i_0_1886,i_0_1890,i_0_1892,i_0_1893,i_0_1895,i_0_1896,i_0_1901,i_0_1891,i_0_1894,i_0_1899,i_0_1904,i_0_1903,i_0_1882,i_0_1900,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659,i_0_1697,i_0_1459,i_0_1571,i_0_1560,i_0_1601,i_0_1691,i_0_1631,i_0_1683,i_0_1910,i_0_1912,i_0_1913,i_0_1163,i_0_1282,i_0_1478,i_0_1809,i_0_2041,i_0_2002,i_0_2003,i_0_2004,i_0_2005,i_0_2006,i_0_2009,i_0_2010,i_0_2011,i_0_2012,i_0_2013,i_0_2014,i_0_2017,i_0_1982,i_0_1983,i_0_1984,i_0_1985,i_0_1987,i_0_1989,i_0_1991,i_0_1993,i_0_1994,i_0_1995,i_0_1996,i_0_1997,i_0_1999,i_0_1367]) ).

cnf(i_0_2869,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
    inference(rename_variables,[],[i_0_1367]) ).

cnf(i_0_2870,plain,
    hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_OSuc,esk33_2(hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),v_F)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(scs_inference,[],[i_0_2276,i_0_2120,i_0_2646,i_0_2293,i_0_2299,i_0_2817,i_0_2468,i_0_2575,i_0_2118,i_0_1847,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2236,i_0_2824,i_0_2826,i_0_2828,i_0_2830,i_0_2832,i_0_2841,i_0_2843,i_0_2845,i_0_2847,i_0_2849,i_0_2851,i_0_2853,i_0_2855,i_0_2857,i_0_2859,i_0_2861,i_0_2863,i_0_2865,i_0_2140,i_0_2142,i_0_2253,i_0_2682,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2427,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2328,i_0_2242,i_0_2203,i_0_2519,i_0_2522,i_0_2173,i_0_2232,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2606,i_0_2158,i_0_2435,i_0_2382,i_0_1351,i_0_2812,i_0_1171,i_0_1765,i_0_2271,i_0_1880,i_0_1881,i_0_1883,i_0_1884,i_0_1885,i_0_1886,i_0_1890,i_0_1892,i_0_1893,i_0_1895,i_0_1896,i_0_1901,i_0_1891,i_0_1894,i_0_1899,i_0_1904,i_0_1903,i_0_1882,i_0_1900,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659,i_0_1697,i_0_1459,i_0_1571,i_0_1560,i_0_1601,i_0_1691,i_0_1631,i_0_1683,i_0_1910,i_0_1912,i_0_1913,i_0_1163,i_0_1282,i_0_1478,i_0_1809,i_0_2041,i_0_2002,i_0_2003,i_0_2004,i_0_2005,i_0_2006,i_0_2009,i_0_2010,i_0_2011,i_0_2012,i_0_2013,i_0_2014,i_0_2017,i_0_1982,i_0_1983,i_0_1984,i_0_1985,i_0_1987,i_0_1989,i_0_1991,i_0_1993,i_0_1994,i_0_1995,i_0_1996,i_0_1997,i_0_1999,i_0_1367,i_0_1590]) ).

cnf(i_0_2871,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X1))),
    inference(rename_variables,[],[i_0_1765]) ).

cnf(i_0_2872,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | hAPP(c_Nat_OSuc,X1) = X2 ),
    inference(rename_variables,[],[i_0_1590]) ).

cnf(i_0_2873,plain,
    ~ c_Finite__Set_Ofinite(tc_Nat_Onat,c_Set_Oimage(X1,tc_Nat_Onat,hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
    inference(scs_inference,[],[i_0_2276,i_0_2120,i_0_2646,i_0_2293,i_0_2299,i_0_2817,i_0_2468,i_0_2575,i_0_2118,i_0_1847,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2236,i_0_2824,i_0_2826,i_0_2828,i_0_2830,i_0_2832,i_0_2841,i_0_2843,i_0_2845,i_0_2847,i_0_2849,i_0_2851,i_0_2853,i_0_2855,i_0_2857,i_0_2859,i_0_2861,i_0_2863,i_0_2865,i_0_2140,i_0_2142,i_0_2253,i_0_2682,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2427,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2718,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2328,i_0_2242,i_0_2203,i_0_2519,i_0_2522,i_0_2173,i_0_2232,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2606,i_0_2158,i_0_2435,i_0_2382,i_0_1351,i_0_2812,i_0_2821,i_0_1171,i_0_1765,i_0_2271,i_0_1880,i_0_1881,i_0_1883,i_0_1884,i_0_1885,i_0_1886,i_0_1890,i_0_1892,i_0_1893,i_0_1895,i_0_1896,i_0_1901,i_0_1891,i_0_1894,i_0_1899,i_0_1904,i_0_1903,i_0_1882,i_0_1900,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659,i_0_1697,i_0_1459,i_0_1571,i_0_1560,i_0_1601,i_0_1691,i_0_1631,i_0_1683,i_0_1910,i_0_1912,i_0_1913,i_0_1163,i_0_1282,i_0_1478,i_0_1809,i_0_2041,i_0_2002,i_0_2003,i_0_2004,i_0_2005,i_0_2006,i_0_2009,i_0_2010,i_0_2011,i_0_2012,i_0_2013,i_0_2014,i_0_2017,i_0_1982,i_0_1983,i_0_1984,i_0_1985,i_0_1987,i_0_1989,i_0_1991,i_0_1993,i_0_1994,i_0_1995,i_0_1996,i_0_1997,i_0_1999,i_0_1367,i_0_1590,i_0_1663]) ).

cnf(i_0_2874,plain,
    hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),c_Set_Oimage(X4,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))),
    inference(rename_variables,[],[i_0_1351]) ).

cnf(i_0_2875,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),X3))),X3)),
    inference(rename_variables,[],[i_0_2504]) ).

cnf(i_0_2876,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),X2))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),esk43_1(X2)))
    | ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X2) ),
    inference(rename_variables,[],[i_0_1663]) ).

cnf(i_0_2877,plain,
    esk18_2(X1,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(scs_inference,[],[i_0_2276,i_0_2120,i_0_2646,i_0_2293,i_0_2299,i_0_2817,i_0_2468,i_0_2575,i_0_2118,i_0_1847,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2343,i_0_2236,i_0_2824,i_0_2826,i_0_2828,i_0_2830,i_0_2832,i_0_2841,i_0_2843,i_0_2845,i_0_2847,i_0_2849,i_0_2851,i_0_2853,i_0_2855,i_0_2857,i_0_2859,i_0_2861,i_0_2863,i_0_2865,i_0_2867,i_0_2140,i_0_2142,i_0_2253,i_0_2682,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2427,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2718,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2328,i_0_2242,i_0_2203,i_0_2519,i_0_2522,i_0_2173,i_0_2232,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2606,i_0_2158,i_0_2435,i_0_2382,i_0_1351,i_0_2812,i_0_2821,i_0_1171,i_0_1765,i_0_2271,i_0_1880,i_0_1881,i_0_1883,i_0_1884,i_0_1885,i_0_1886,i_0_1890,i_0_1892,i_0_1893,i_0_1895,i_0_1896,i_0_1901,i_0_1891,i_0_1894,i_0_1899,i_0_1904,i_0_1903,i_0_1882,i_0_1900,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659,i_0_1697,i_0_1459,i_0_1571,i_0_1560,i_0_1601,i_0_1691,i_0_1631,i_0_1683,i_0_1910,i_0_1912,i_0_1913,i_0_1163,i_0_1282,i_0_1478,i_0_1809,i_0_2041,i_0_2002,i_0_2003,i_0_2004,i_0_2005,i_0_2006,i_0_2009,i_0_2010,i_0_2011,i_0_2012,i_0_2013,i_0_2014,i_0_2017,i_0_1982,i_0_1983,i_0_1984,i_0_1985,i_0_1987,i_0_1989,i_0_1991,i_0_1993,i_0_1994,i_0_1995,i_0_1996,i_0_1997,i_0_1999,i_0_1367,i_0_1590,i_0_1663,i_0_1808]) ).

cnf(i_0_2878,plain,
    ( X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X3)
    | X3 = c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ),
    inference(rename_variables,[],[i_0_1808]) ).

cnf(i_0_2879,plain,
    X1 = esk36_4(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),
    inference(scs_inference,[],[i_0_2276,i_0_2120,i_0_2646,i_0_2293,i_0_2299,i_0_2817,i_0_2468,i_0_2575,i_0_2118,i_0_1847,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2691,i_0_2343,i_0_2236,i_0_2824,i_0_2826,i_0_2828,i_0_2830,i_0_2832,i_0_2841,i_0_2843,i_0_2845,i_0_2847,i_0_2849,i_0_2851,i_0_2853,i_0_2855,i_0_2857,i_0_2859,i_0_2861,i_0_2863,i_0_2865,i_0_2867,i_0_2140,i_0_2142,i_0_2253,i_0_2682,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2427,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2718,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2328,i_0_2242,i_0_2203,i_0_2519,i_0_2522,i_0_2173,i_0_2232,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2606,i_0_2158,i_0_2435,i_0_2382,i_0_1351,i_0_2812,i_0_2821,i_0_1171,i_0_1765,i_0_2271,i_0_1880,i_0_1881,i_0_1883,i_0_1884,i_0_1885,i_0_1886,i_0_1890,i_0_1892,i_0_1893,i_0_1895,i_0_1896,i_0_1901,i_0_1891,i_0_1894,i_0_1899,i_0_1904,i_0_1903,i_0_1882,i_0_1900,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659,i_0_1697,i_0_1459,i_0_1571,i_0_1560,i_0_1601,i_0_1691,i_0_1631,i_0_1683,i_0_1910,i_0_1912,i_0_1913,i_0_1163,i_0_1282,i_0_1478,i_0_1809,i_0_2041,i_0_2002,i_0_2003,i_0_2004,i_0_2005,i_0_2006,i_0_2009,i_0_2010,i_0_2011,i_0_2012,i_0_2013,i_0_2014,i_0_2017,i_0_1982,i_0_1983,i_0_1984,i_0_1985,i_0_1987,i_0_1989,i_0_1991,i_0_1993,i_0_1994,i_0_1995,i_0_1996,i_0_1997,i_0_1999,i_0_1367,i_0_1590,i_0_1663,i_0_1808,i_0_1751]) ).

cnf(i_0_2880,plain,
    hAPP(X1,X2) = hAPP(X1,esk36_4(c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)),X1,X3,hAPP(X1,X2))),
    inference(rename_variables,[],[i_0_2149]) ).

cnf(i_0_2881,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)
    | X3 = X4
    | ~ class_Groups_Ocancel__semigroup__add(X1) ),
    inference(rename_variables,[],[i_0_1751]) ).

cnf(i_0_2882,plain,
    esk32_2(hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(scs_inference,[],[i_0_2276,i_0_2120,i_0_2646,i_0_2293,i_0_2299,i_0_2817,i_0_2468,i_0_2575,i_0_2118,i_0_1847,i_0_1497,i_0_2144,i_0_2643,i_0_2149,i_0_2691,i_0_2343,i_0_2236,i_0_2824,i_0_2826,i_0_2828,i_0_2830,i_0_2832,i_0_2841,i_0_2843,i_0_2845,i_0_2847,i_0_2849,i_0_2851,i_0_2853,i_0_2855,i_0_2857,i_0_2859,i_0_2861,i_0_2863,i_0_2865,i_0_2867,i_0_2140,i_0_2142,i_0_2253,i_0_2682,i_0_2264,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2427,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2718,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2328,i_0_2242,i_0_2203,i_0_2519,i_0_2522,i_0_2173,i_0_2232,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2606,i_0_2158,i_0_2435,i_0_2382,i_0_1351,i_0_2812,i_0_2821,i_0_1171,i_0_1765,i_0_2271,i_0_1880,i_0_1881,i_0_1883,i_0_1884,i_0_1885,i_0_1886,i_0_1890,i_0_1892,i_0_1893,i_0_1895,i_0_1896,i_0_1901,i_0_1870,i_0_1891,i_0_1894,i_0_1899,i_0_1904,i_0_1903,i_0_1882,i_0_1900,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659,i_0_1697,i_0_1459,i_0_1571,i_0_1560,i_0_1601,i_0_1691,i_0_1631,i_0_1683,i_0_1910,i_0_1912,i_0_1913,i_0_1163,i_0_1282,i_0_1478,i_0_1809,i_0_2041,i_0_2002,i_0_2003,i_0_2004,i_0_2005,i_0_2006,i_0_2009,i_0_2010,i_0_2011,i_0_2012,i_0_2013,i_0_2014,i_0_2017,i_0_1982,i_0_1983,i_0_1984,i_0_1985,i_0_1987,i_0_1989,i_0_1991,i_0_1993,i_0_1994,i_0_1995,i_0_1996,i_0_1997,i_0_1999,i_0_1367,i_0_1590,i_0_1663,i_0_1808,i_0_1751,i_0_1789]) ).

cnf(i_0_2883,plain,
    X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk32_2(hAPP(c_Nat_OSuc,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(rename_variables,[],[i_0_2264]) ).

cnf(i_0_2884,plain,
    X1 != hAPP(c_Nat_OSuc,X1),
    inference(rename_variables,[],[i_0_1870]) ).

cnf(i_0_2885,plain,
    ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)
    | X2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(rename_variables,[],[i_0_1789]) ).

cnf(i_0_2886,plain,
    $false,
    inference(scs_inference,[],[i_0_2276,i_0_2120,i_0_2646,i_0_2293,i_0_2299,i_0_2817,i_0_2468,i_0_2575,i_0_2118,i_0_1847,i_0_1497,i_0_2146,i_0_2144,i_0_2643,i_0_2149,i_0_2691,i_0_2343,i_0_2236,i_0_2824,i_0_2826,i_0_2828,i_0_2830,i_0_2832,i_0_2841,i_0_2843,i_0_2845,i_0_2847,i_0_2849,i_0_2851,i_0_2853,i_0_2855,i_0_2857,i_0_2859,i_0_2861,i_0_2863,i_0_2865,i_0_2867,i_0_2140,i_0_2142,i_0_2253,i_0_2682,i_0_2264,i_0_2189,i_0_2745,i_0_2748,i_0_2211,i_0_2705,i_0_2721,i_0_2427,i_0_2365,i_0_2677,i_0_2753,i_0_2405,i_0_2534,i_0_2504,i_0_2718,i_0_2198,i_0_2493,i_0_2217,i_0_2182,i_0_2698,i_0_2221,i_0_2328,i_0_2242,i_0_2203,i_0_2519,i_0_2522,i_0_2173,i_0_2232,i_0_2602,i_0_2195,i_0_2685,i_0_2688,i_0_2201,i_0_2214,i_0_2606,i_0_2158,i_0_2435,i_0_2382,i_0_2640,i_0_1351,i_0_2812,i_0_2821,i_0_1171,i_0_1765,i_0_2271,i_0_1880,i_0_1881,i_0_1883,i_0_1884,i_0_1885,i_0_1886,i_0_1890,i_0_1892,i_0_1893,i_0_1895,i_0_1896,i_0_1901,i_0_1870,i_0_1891,i_0_1894,i_0_1899,i_0_1904,i_0_1903,i_0_1882,i_0_1900,i_0_1255,i_0_1778,i_0_1292,i_0_1353,i_0_1403,i_0_1531,i_0_1698,i_0_1762,i_0_1199,i_0_1203,i_0_1221,i_0_1248,i_0_1271,i_0_1296,i_0_1300,i_0_1301,i_0_1318,i_0_1328,i_0_1331,i_0_1339,i_0_1340,i_0_1346,i_0_1381,i_0_1387,i_0_1402,i_0_1440,i_0_1480,i_0_1539,i_0_1570,i_0_1573,i_0_1575,i_0_1577,i_0_1630,i_0_1689,i_0_1729,i_0_1771,i_0_2043,i_0_1868,i_0_1286,i_0_1438,i_0_1454,i_0_1455,i_0_1662,i_0_1726,i_0_1764,i_0_1779,i_0_1782,i_0_1332,i_0_1550,i_0_1552,i_0_1581,i_0_1585,i_0_1639,i_0_1763,i_0_1769,i_0_1770,i_0_1828,i_0_1854,i_0_1718,i_0_1599,i_0_1659,i_0_1697,i_0_1459,i_0_1571,i_0_1560,i_0_1601,i_0_1691,i_0_1631,i_0_1683,i_0_1910,i_0_1912,i_0_1913,i_0_1163,i_0_1282,i_0_1478,i_0_1809,i_0_2041,i_0_2002,i_0_2003,i_0_2004,i_0_2005,i_0_2006,i_0_2009,i_0_2010,i_0_2011,i_0_2012,i_0_2013,i_0_2014,i_0_2017,i_0_1982,i_0_1983,i_0_1984,i_0_1985,i_0_1987,i_0_1989,i_0_1991,i_0_1993,i_0_1994,i_0_1995,i_0_1996,i_0_1997,i_0_1999,i_0_1367,i_0_1590,i_0_1663,i_0_1808,i_0_1751,i_0_1789,i_0_1370]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SCT167+1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.12  % Command    : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.33  % Computer : n029.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33  % CPULimit   : 300
% 0.14/0.33  % WCLimit    : 300
% 0.14/0.33  % DateTime   : Tue May  5 01:59:59 EDT 2026
% 0.14/0.33  % CPUTime    : 
% 0.14/0.34  % start to proof: theBenchmark
% 6.16/5.77  % Version  : CSE_E---1.7
% 6.16/5.77  % Problem  : theBenchmark.p
% 6.16/5.77  % SZS status Theorem for theBenchmark.p
% 6.16/5.77  % SZS output start CNFRefutation
% See solution above
% 15.42/15.07  % Total time : 5.420s
%------------------------------------------------------------------------------