CSE_E---1.7.THM-CRf.s

%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : SCT165+1 : TPTP v9.2.1. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d

% Computer : n019.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 05:06:11 PM UTC 2026

% Result   : Theorem 5.46s 5.80s
% Output   : CNFRefutation 15.27s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named 1130)

% Comments : 
%------------------------------------------------------------------------------
fof(fact__096_091_124_Ac_A_126_061_Ae_059_Aa_A_126_061_Ab_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_A_L_A1_Athen_ALab_Aelse_ALba_J_A_058_AProf_059_AALL_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_A_124_093_061_061_062_A_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_A_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,
    ( v_c____ != v_e____
   => ( v_a____ != v_b____
     => ( 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____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),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_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____)) ) ) )
           => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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/sandbox/benchmark/theBenchmark.p',fact__096_091_124_Ac_A_126_061_Ae_059_Aa_A_126_061_Ab_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_A_L_A1_Athen_ALab_Aelse_ALba_J_A_058_AProf_059_AALL_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_A_124_093_061_061_062_A_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_A_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(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_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/sandbox/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,
    ~ ! [X42] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),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),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),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),X42),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))) ) ),
    file('/export/starexec/sandbox/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,X15,X46,X1,X6,X2,X18,X12] :
      ( c_Finite__Set_Ofolding__image__simple(X12,X18,X2,X6,X1,X46)
     => ( c_Finite__Set_Ofinite(X18,X15)
       => ( ~ hBOOL(hAPP(hAPP(c_member(X18),X9),X15))
         => hAPP(X46,c_Set_Oinsert(X18,X9,X15)) = hAPP(hAPP(X2,hAPP(X1,X9)),hAPP(X46,X15)) ) ) ),
    file('/export/starexec/sandbox/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/sandbox/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/sandbox/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,
    ! [X15,X2,X18,X12] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X12,c_Set_Oimage(X18,X12,X2,X15))),c_Finite__Set_Ocard(X18,X15)))
     => ~ c_Fun_Oinj__on(X18,X12,X2,X15) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pigeonhole) ).

fof(fact_card__def,axiom,
    ! [X15,X12] :
      ( ( c_Finite__Set_Ofinite(X12,X15)
       => c_Finite__Set_Ocard(X12,X15) = 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),X15) )
      & ( ~ c_Finite__Set_Ofinite(X12,X15)
       => c_Finite__Set_Ocard(X12,X15) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_notin__Lin__iff) ).

fof(fact_Lin__irrefl,axiom,
    ! [X28,X29,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),X29),X28)),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),X28),X29)),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Lin__irrefl) ).

fof(fact_PiE,axiom,
    ! [X9,X14,X15,X2,X18,X12] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(X12,X18)),X2),c_FuncSet_OPi(X12,X18,X15,X14)))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X18),hAPP(X2,X9)),hAPP(X14,X9)))
       => ~ hBOOL(hAPP(hAPP(c_member(X12),X9),X15)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_PiE) ).

fof(fact_subset__insert,axiom,
    ! [X14,X15,X9,X12] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X12),X9),X15))
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X15),c_Set_Oinsert(X12,X9,X14)))
      <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X15),X14)) ) ),
    file('/export/starexec/sandbox/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,
    ~ ! [X45] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),X45))
       => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X45),c_Arrow__Order__Mirabelle_OLin)) ),
    file('/export/starexec/sandbox/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,
    ~ ! [X44] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____)),X44))
       => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X44),c_Arrow__Order__Mirabelle_OLin)) ),
    file('/export/starexec/sandbox/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,X18] :
      ( class_Orderings_Oord(X18)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12,X18)),X2),X1))
      <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,X18),X2),X1))
          & ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,X18),X1),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__fun__def) ).

fof(fact_add__leE,axiom,
    ! [X24,X25,X23] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23),X25)),X24))
     => ~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X23),X24))
         => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X25),X24)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leE) ).

fof(fact_not__add__less1,axiom,
    ! [X19,X20] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),X19)),X20)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less1) ).

fof(fact_not__add__less2,axiom,
    ! [X20,X19] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X20)),X20)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less2) ).

fof(fact_ex__least__nat__less,axiom,
    ! [X10,X32] :
      ( ~ hBOOL(hAPP(X32,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
     => ( hBOOL(hAPP(X32,X10))
       => ? [X27] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X27),X10))
            & ! [X4] :
                ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),X27))
               => ~ hBOOL(hAPP(X32,X4)) )
            & hBOOL(hAPP(X32,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__least__nat__less) ).

fof(fact_insertCI,axiom,
    ! [X28,X14,X29,X12] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X12),X29),X14))
       => X29 = X28 )
     => hBOOL(hAPP(hAPP(c_member(X12),X29),c_Set_Oinsert(X12,X28,X14))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertCI) ).

fof(fact_insert__ident,axiom,
    ! [X14,X15,X9,X12] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X12),X9),X15))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X12),X9),X14))
       => ( c_Set_Oinsert(X12,X9,X15) = c_Set_Oinsert(X12,X9,X14)
        <=> X15 = X14 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__ident) ).

fof(fact_not__less__eq__eq,axiom,
    ! [X10,X21] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21),X10))
    <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X10)),X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).

fof(fact_not__less__eq,axiom,
    ! [X10,X21] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X10))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10),hAPP(c_Nat_OSuc,X21))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq) ).

fof(fact_xt1_I9_J,axiom,
    ! [X11,X41,X12] :
      ( class_Orderings_Oorder(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X41),X11))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X11),X41)) ) ),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).

fof(fact_order__less__asym,axiom,
    ! [X30,X31,X12] :
      ( class_Orderings_Opreorder(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X31),X30))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X30),X31)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__asym) ).

fof(fact_order__less__asym_H,axiom,
    ! [X41,X11,X12] :
      ( class_Orderings_Opreorder(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X11),X41))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X41),X11)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__asym_H) ).

fof(fact_order__less__imp__not__less,axiom,
    ! [X30,X31,X12] :
      ( class_Orderings_Opreorder(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X31),X30))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X30),X31)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__less) ).

fof(fact_order__less__not__sym,axiom,
    ! [X30,X31,X12] :
      ( class_Orderings_Opreorder(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X31),X30))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X30),X31)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__not__sym) ).

fof(fact_card_Oinsert,axiom,
    ! [X9,X15,X12] :
      ( c_Finite__Set_Ofinite(X12,X15)
     => ( ~ hBOOL(hAPP(hAPP(c_member(X12),X9),X15))
       => c_Finite__Set_Ocard(X12,c_Set_Oinsert(X12,X9,X15)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Finite__Set_Ocard(X12,X15)) ) ),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_less__le__not__le) ).

fof(fact_card__insert__if,axiom,
    ! [X9,X15,X12] :
      ( c_Finite__Set_Ofinite(X12,X15)
     => ( ( hBOOL(hAPP(hAPP(c_member(X12),X9),X15))
         => c_Finite__Set_Ocard(X12,c_Set_Oinsert(X12,X9,X15)) = c_Finite__Set_Ocard(X12,X15) )
        & ( ~ hBOOL(hAPP(hAPP(c_member(X12),X9),X15))
         => c_Finite__Set_Ocard(X12,c_Set_Oinsert(X12,X9,X15)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X12,X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__insert__if) ).

fof(fact_not__less__less__Suc__eq,axiom,
    ! [X21,X10] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10),X21))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10),hAPP(c_Nat_OSuc,X21)))
      <=> X10 = X21 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).

fof(fact_less__antisym,axiom,
    ! [X23,X24] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X23))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),hAPP(c_Nat_OSuc,X23)))
       => X23 = X24 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__antisym) ).

fof(fact_less__SucE,axiom,
    ! [X24,X23] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23),hAPP(c_Nat_OSuc,X24)))
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23),X24))
       => X23 = X24 ) ),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv2) ).

fof(fact_leD,axiom,
    ! [X31,X30,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X30),X31))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X31),X30)) ) ),
    file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_linorder__not__le) ).

fof(fact_card__insert__disjoint,axiom,
    ! [X9,X15,X12] :
      ( c_Finite__Set_Ofinite(X12,X15)
     => ( ~ hBOOL(hAPP(hAPP(c_member(X12),X9),X15))
       => c_Finite__Set_Ocard(X12,c_Set_Oinsert(X12,X9,X15)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X12,X15)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__insert__disjoint) ).

fof(fact_le__SucE,axiom,
    ! [X24,X23] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X23),hAPP(c_Nat_OSuc,X24)))
     => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X23),X24))
       => X23 = hAPP(c_Nat_OSuc,X24) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SucE) ).

fof(fact_Suc__n__not__le__n,axiom,
    ! [X24] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X24)),X24)),
    file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_not__one__less__zero) ).

fof(fact_linorder__cases,axiom,
    ! [X30,X31,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X31),X30))
       => ( X31 != X30
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X30),X31)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__cases) ).

fof(fact_linorder__neqE,axiom,
    ! [X30,X31,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( X31 != X30
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X31),X30))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X30),X31)) ) ) ),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv3) ).

fof(fact_linorder__neqE__linordered__idom,axiom,
    ! [X30,X31,X12] :
      ( class_Rings_Olinordered__idom(X12)
     => ( X31 != X30
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X31),X30))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X30),X31)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).

fof(fact_not__leE,axiom,
    ! [X31,X30,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X30),X31))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X31),X30)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__leE) ).

fof(fact_leI,axiom,
    ! [X30,X31,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X31),X30))
       => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X30),X31)) ) ),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_not__one__le__zero) ).

fof(fact_linorder__neqE__nat,axiom,
    ! [X30,X31] :
      ( X31 != X30
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31),X30))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30),X31)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).

fof(fact_equalityE,axiom,
    ! [X12,X14,X15] :
      ( X15 = X14
     => ~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X15),X14))
         => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X14),X15)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityE) ).

fof(fact_order__less__irrefl,axiom,
    ! [X31,X12] :
      ( class_Orderings_Opreorder(X12)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X31),X31)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__irrefl) ).

fof(fact_linorder__le__cases,axiom,
    ! [X30,X31,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X31),X30))
       => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X30),X31)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__le__cases) ).

fof(fact_less__nat__zero__code,axiom,
    ! [X24] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__nat__zero__code) ).

fof(fact_not__less0,axiom,
    ! [X24] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less0) ).

fof(fact_less__zeroE,axiom,
    ! [X24] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__zeroE) ).

fof(fact_less__not__refl,axiom,
    ! [X24] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X24)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl) ).

fof(fact_less__irrefl__nat,axiom,
    ! [X24] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X24)),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',help_c__fequal__1) ).

fof(fact_card__infinite,axiom,
    ! [X15,X12] :
      ( ~ c_Finite__Set_Ofinite(X12,X15)
     => c_Finite__Set_Ocard(X12,X15) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__infinite) ).

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/sandbox/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,
    ? [X42] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),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),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),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),X42),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))) ),
    file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_n_I2_J) ).

fof(fact_pred__subset__eq2,axiom,
    ! [X16,X17,X18,X12] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_fun(X18,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X12,tc_fun(tc_prod(X12,X18),tc_HOL_Obool),tc_fun(X18,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X18,tc_fun(tc_fun(tc_prod(X12,X18),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X12,X18),tc_HOL_Obool),tc_fun(X18,tc_HOL_Obool)),X12,c_COMBC(X18,tc_fun(tc_prod(X12,X18),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X18,tc_prod(X12,X18)),tc_fun(X18,tc_fun(tc_fun(tc_prod(X12,X18),tc_HOL_Obool),tc_HOL_Obool)),X12,c_COMBB(tc_prod(X12,X18),tc_fun(tc_fun(tc_prod(X12,X18),tc_HOL_Obool),tc_HOL_Obool),X18,c_member(tc_prod(X12,X18)))),c_Product__Type_OPair(X12,X18)))),X17)),hAPP(hAPP(c_COMBC(X12,tc_fun(tc_prod(X12,X18),tc_HOL_Obool),tc_fun(X18,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X18,tc_fun(tc_fun(tc_prod(X12,X18),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X12,X18),tc_HOL_Obool),tc_fun(X18,tc_HOL_Obool)),X12,c_COMBC(X18,tc_fun(tc_prod(X12,X18),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X18,tc_prod(X12,X18)),tc_fun(X18,tc_fun(tc_fun(tc_prod(X12,X18),tc_HOL_Obool),tc_HOL_Obool)),X12,c_COMBB(tc_prod(X12,X18),tc_fun(tc_fun(tc_prod(X12,X18),tc_HOL_Obool),tc_HOL_Obool),X18,c_member(tc_prod(X12,X18)))),c_Product__Type_OPair(X12,X18)))),X16)))
    <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X12,X18),tc_HOL_Obool),X17),X16)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__subset__eq2) ).

fof(fact__C2_C,axiom,
    ! [X36,X32,X37,X38,X28,X29] :
      ( X29 != X28
     => ( X38 != X37
       => ( X29 != X37
         => ( X28 != 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))),X32),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))),X36),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),X29),X28)),hAPP(X32,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),X38),X37)),hAPP(X36,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),X29),X28)),hAPP(v_F,X32)))
                  <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X38),X37)),hAPP(v_F,X36))) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__C2_C) ).

fof(fact__C1_C,axiom,
    ! [X36,X32,X37,X38,X28,X29] :
      ( X29 != X28
     => ( X38 != X37
       => ( X29 != X37
         => ( X28 != 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))),X32),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))),X36),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),X29),X28)),hAPP(X32,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),X38),X37)),hAPP(X36,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),X29),X28)),hAPP(v_F,X32)))
                   => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X38),X37)),hAPP(v_F,X36))) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__C1_C) ).

fof(fact_pairwise__neutrality,axiom,
    ! [X36,X32,X37,X38,X28,X29] :
      ( X29 != X28
     => ( X38 != X37
       => ( 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))),X32),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))),X36),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),X29),X28)),hAPP(X32,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),X38),X37)),hAPP(X36,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),X29),X28)),hAPP(v_F,X32)))
              <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X38),X37)),hAPP(v_F,X36))) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pairwise__neutrality) ).

fof(fact_pred__equals__eq2,axiom,
    ! [X16,X17,X18,X12] :
      ( hAPP(hAPP(c_COMBC(X12,tc_fun(tc_prod(X12,X18),tc_HOL_Obool),tc_fun(X18,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X18,tc_fun(tc_fun(tc_prod(X12,X18),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X12,X18),tc_HOL_Obool),tc_fun(X18,tc_HOL_Obool)),X12,c_COMBC(X18,tc_fun(tc_prod(X12,X18),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X18,tc_prod(X12,X18)),tc_fun(X18,tc_fun(tc_fun(tc_prod(X12,X18),tc_HOL_Obool),tc_HOL_Obool)),X12,c_COMBB(tc_prod(X12,X18),tc_fun(tc_fun(tc_prod(X12,X18),tc_HOL_Obool),tc_HOL_Obool),X18,c_member(tc_prod(X12,X18)))),c_Product__Type_OPair(X12,X18)))),X17) = hAPP(hAPP(c_COMBC(X12,tc_fun(tc_prod(X12,X18),tc_HOL_Obool),tc_fun(X18,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X18,tc_fun(tc_fun(tc_prod(X12,X18),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X12,X18),tc_HOL_Obool),tc_fun(X18,tc_HOL_Obool)),X12,c_COMBC(X18,tc_fun(tc_prod(X12,X18),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X18,tc_prod(X12,X18)),tc_fun(X18,tc_fun(tc_fun(tc_prod(X12,X18),tc_HOL_Obool),tc_HOL_Obool)),X12,c_COMBB(tc_prod(X12,X18),tc_fun(tc_fun(tc_prod(X12,X18),tc_HOL_Obool),tc_HOL_Obool),X18,c_member(tc_prod(X12,X18)))),c_Product__Type_OPair(X12,X18)))),X16)
    <=> X17 = X16 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__equals__eq2) ).

fof(fact_Pi__mono,axiom,
    ! [X43,X14,X18,X15,X12] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X12),X3),X15))
         => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18,tc_HOL_Obool),hAPP(X14,X3)),hAPP(X43,X3))) )
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X12,X18),tc_HOL_Obool),c_FuncSet_OPi(X12,X18,X15,X14)),c_FuncSet_OPi(X12,X18,X15,X43))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__mono) ).

fof(fact_Pi__I,axiom,
    ! [X14,X2,X18,X15,X12] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X12),X3),X15))
         => hBOOL(hAPP(hAPP(c_member(X18),hAPP(X2,X3)),hAPP(X14,X3))) )
     => hBOOL(hAPP(hAPP(c_member(tc_fun(X12,X18)),X2),c_FuncSet_OPi(X12,X18,X15,X14))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__I) ).

fof(fact_IIA__def,axiom,
    ! [X46] :
      ( c_Arrow__Order__Mirabelle_OIIA(X46)
    <=> ! [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))
         => ! [X49] :
              ( 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))),X49),c_Arrow__Order__Mirabelle_OProf))
             => ! [X47,X48] :
                  ( ! [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),X47),X48)),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),X47),X48)),hAPP(X49,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),X47),X48)),hAPP(X46,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),X47),X48)),hAPP(X46,X49))) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IIA__def) ).

fof(fact__C4_C,axiom,
    ! [X36,X32,X13,X28,X29] :
      ( X29 != X28
     => ( X28 != X13
       => ( X29 != X13
         => ( 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))),X32),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))),X36),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),X29),X28)),hAPP(X32,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),X28),X13)),hAPP(X36,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),X29),X28)),hAPP(v_F,X32)))
                <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X28),X13)),hAPP(v_F,X36))) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__C4_C) ).

fof(fact_dictatorI,axiom,
    ! [X54,X46] :
      ( 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))),X46),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))
           => ! [X47,X48] :
                ( X47 != X48
               => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X47),X48)),hAPP(X3,X54)))
                 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X47),X48)),hAPP(X46,X3))) ) ) )
       => c_Arrow__Order__Mirabelle_Odictator(X46,X54) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dictatorI) ).

fof(fact_in__lex__prod,axiom,
    ! [X57,X58,X37,X38,X28,X29,X18,X12] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X12,X18),tc_prod(X12,X18))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X12,X18),tc_prod(X12,X18)),hAPP(hAPP(c_Product__Type_OPair(X12,X18),X29),X28)),hAPP(hAPP(c_Product__Type_OPair(X12,X18),X38),X37))),c_Wellfounded_Olex__prod(X12,X18,X58,X57)))
    <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X12,X12)),hAPP(hAPP(c_Product__Type_OPair(X12,X12),X29),X38)),X58))
        | ( X29 = X38
          & hBOOL(hAPP(hAPP(c_member(tc_prod(X18,X18)),hAPP(hAPP(c_Product__Type_OPair(X18,X18),X28),X37)),X57)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__lex__prod) ).

fof(fact__C3_C,axiom,
    ! [X36,X32,X28,X29] :
      ( X29 != X28
     => ( 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))),X32),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))),X36),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),X29),X28)),hAPP(X32,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),X28),X29)),hAPP(X36,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),X29),X28)),hAPP(v_F,X32)))
            <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X28),X29)),hAPP(v_F,X36))) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__C3_C) ).

fof(fact_folding__image__simple_Oeq__fold__g,axiom,
    ! [X15,X46,X1,X6,X2,X18,X12] :
      ( c_Finite__Set_Ofolding__image__simple(X12,X18,X2,X6,X1,X46)
     => ( c_Finite__Set_Ofinite(X18,X15)
       => hAPP(X46,X15) = c_Finite__Set_Ofold__image(X12,X18,X2,X1,X6,X15) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Oeq__fold__g) ).

fof(fact_subset__image__iff,axiom,
    ! [X15,X2,X18,X14,X12] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X14),c_Set_Oimage(X18,X12,X2,X15)))
    <=> ? [X67] :
          ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18,tc_HOL_Obool),X67),X15))
          & X14 = c_Set_Oimage(X18,X12,X2,X67) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__image__iff) ).

fof(fact_same__fstI,axiom,
    ! [X12,X17,X8,X56,X18,X9,X32] :
      ( hBOOL(hAPP(X32,X9))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X18,X18)),hAPP(hAPP(c_Product__Type_OPair(X18,X18),X56),X8)),hAPP(X17,X9)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X12,X18),tc_prod(X12,X18))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X12,X18),tc_prod(X12,X18)),hAPP(hAPP(c_Product__Type_OPair(X12,X18),X9),X56)),hAPP(hAPP(c_Product__Type_OPair(X12,X18),X9),X8))),c_Recdef_Osame__fst(X12,X18,X32,X17))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_same__fstI) ).

fof(fact_le__fun__def,axiom,
    ! [X1,X2,X12,X18] :
      ( class_Orderings_Oord(X18)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,X18),X2),X1))
      <=> ! [X3] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X18,hAPP(X2,X3)),hAPP(X1,X3))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__fun__def) ).

fof(fact_folding__image__simple__idem_Osubset__idem,axiom,
    ! [X14,X15,X46,X1,X6,X2,X18,X12] :
      ( c_Finite__Set_Ofolding__image__simple__idem(X12,X18,X2,X6,X1,X46)
     => ( c_Finite__Set_Ofinite(X18,X15)
       => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18,tc_HOL_Obool),X14),X15))
         => hAPP(hAPP(X2,hAPP(X46,X14)),hAPP(X46,X15)) = hAPP(X46,X15) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Osubset__idem) ).

fof(fact_folding__image__simple__idem_Oin__idem,axiom,
    ! [X9,X15,X46,X1,X6,X2,X18,X12] :
      ( c_Finite__Set_Ofolding__image__simple__idem(X12,X18,X2,X6,X1,X46)
     => ( c_Finite__Set_Ofinite(X18,X15)
       => ( hBOOL(hAPP(hAPP(c_member(X18),X9),X15))
         => hAPP(hAPP(X2,hAPP(X1,X9)),hAPP(X46,X15)) = hAPP(X46,X15) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oin__idem) ).

fof(fact_folding__image__simple__idem_Oinsert__idem,axiom,
    ! [X9,X15,X46,X1,X6,X2,X18,X12] :
      ( c_Finite__Set_Ofolding__image__simple__idem(X12,X18,X2,X6,X1,X46)
     => ( c_Finite__Set_Ofinite(X18,X15)
       => hAPP(X46,c_Set_Oinsert(X18,X9,X15)) = hAPP(hAPP(X2,hAPP(X1,X9)),hAPP(X46,X15)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oinsert__idem) ).

fof(fact_folding__image__simple__idem_Oidem,axiom,
    ! [X9,X46,X1,X6,X2,X18,X12] :
      ( c_Finite__Set_Ofolding__image__simple__idem(X12,X18,X2,X6,X1,X46)
     => hAPP(hAPP(X2,X9),X9) = X9 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oidem) ).

fof(fact_card__bij__eq,axiom,
    ! [X1,X14,X15,X2,X18,X12] :
      ( c_Fun_Oinj__on(X12,X18,X2,X15)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18,tc_HOL_Obool),c_Set_Oimage(X12,X18,X2,X15)),X14))
       => ( c_Fun_Oinj__on(X18,X12,X1,X14)
         => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),c_Set_Oimage(X18,X12,X1,X14)),X15))
           => ( c_Finite__Set_Ofinite(X12,X15)
             => ( c_Finite__Set_Ofinite(X18,X14)
               => c_Finite__Set_Ocard(X12,X15) = c_Finite__Set_Ocard(X18,X14) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__bij__eq) ).

fof(fact_unanimity__def,axiom,
    ! [X46] :
      ( c_Arrow__Order__Mirabelle_Ounanimity(X46)
    <=> ! [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))
         => ! [X47,X48] :
              ( ! [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),X47),X48)),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),X47),X48)),hAPP(X46,X3))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unanimity__def) ).

fof(fact_card__bij,axiom,
    ! [X1,X14,X15,X2,X18,X12] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(X12,X18)),X2),c_FuncSet_OPi(X12,X18,X15,hAPP(c_COMBK(tc_fun(X18,tc_HOL_Obool),X12),X14))))
     => ( c_Fun_Oinj__on(X12,X18,X2,X15)
       => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X18,X12)),X1),c_FuncSet_OPi(X18,X12,X14,hAPP(c_COMBK(tc_fun(X12,tc_HOL_Obool),X18),X15))))
         => ( c_Fun_Oinj__on(X18,X12,X1,X14)
           => ( c_Finite__Set_Ofinite(X12,X15)
             => ( c_Finite__Set_Ofinite(X18,X14)
               => c_Finite__Set_Ocard(X12,X15) = c_Finite__Set_Ocard(X18,X14) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__bij) ).

fof(fact_pred__subset__eq,axiom,
    ! [X16,X17,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)),X17)),hAPP(hAPP(c_COMBC(X12,tc_fun(X12,tc_HOL_Obool),tc_HOL_Obool),c_member(X12)),X16)))
    <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X17),X16)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__subset__eq) ).

fof(fact_inj__on__iff__card__le,axiom,
    ! [X14,X18,X15,X12] :
      ( c_Finite__Set_Ofinite(X12,X15)
     => ( c_Finite__Set_Ofinite(X18,X14)
       => ( ? [X74] :
              ( c_Fun_Oinj__on(X12,X18,X74,X15)
              & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18,tc_HOL_Obool),c_Set_Oimage(X12,X18,X74,X15)),X14)) )
        <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X12,X15)),c_Finite__Set_Ocard(X18,X14))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff__card__le) ).

fof(fact_in__above,axiom,
    ! [X8,X9,X7,X28,X29] :
      ( X29 != X28
     => ( 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),X29),X28)))
        <=> ( X9 != X8
            & ( X9 = 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),X29),X8)),X7)) )
            & ( X9 != X28
             => ( ( X8 = X28
                 => ( X9 = X29
                    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X29)),X7)) ) )
                & ( X8 != 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),X9),X8)),X7)) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__above) ).

fof(fact_in__below,axiom,
    ! [X8,X9,X7,X28,X29] :
      ( X29 != X28
     => ( 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,X29,X28)))
        <=> ( X9 != X8
            & ( X8 = X29
             => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X28)),X7)) )
            & ( X8 != X29
             => ( ( X9 = X29
                 => ( X8 = 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),X28),X8)),X7)) ) )
                & ( X9 != X29
                 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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/sandbox/benchmark/theBenchmark.p',fact_in__below) ).

fof(fact_card_Oeq__fold__g,axiom,
    ! [X15,X12] :
      ( c_Finite__Set_Ofinite(X12,X15)
     => c_Finite__Set_Ocard(X12,X15) = 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),X15) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oeq__fold__g) ).

fof(fact_inv__into__into,axiom,
    ! [X15,X2,X18,X9,X12] :
      ( hBOOL(hAPP(hAPP(c_member(X12),X9),c_Set_Oimage(X18,X12,X2,X15)))
     => hBOOL(hAPP(hAPP(c_member(X18),hAPP(c_Hilbert__Choice_Oinv__into(X18,X12,X15,X2),X9)),X15)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__into) ).

fof(fact_inj__image__subset__iff,axiom,
    ! [X14,X15,X2,X18,X12] :
      ( c_Fun_Oinj__on(X12,X18,X2,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18,tc_HOL_Obool),c_Set_Oimage(X12,X18,X2,X15)),c_Set_Oimage(X12,X18,X2,X14)))
      <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X15),X14)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__subset__iff) ).

fof(fact_in__finite__psubset,axiom,
    ! [X14,X15,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)),X15),X14)),c_Wellfounded_Ofinite__psubset(X12)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12,tc_HOL_Obool)),X15),X14))
        & c_Finite__Set_Ofinite(X12,X14) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__finite__psubset) ).

fof(fact_funcset__image,axiom,
    ! [X14,X15,X2,X18,X12] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(X12,X18)),X2),c_FuncSet_OPi(X12,X18,X15,hAPP(c_COMBK(tc_fun(X18,tc_HOL_Obool),X12),X14))))
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18,tc_HOL_Obool),c_Set_Oimage(X12,X18,X2,X15)),X14)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funcset__image) ).

fof(fact_inv__into__injective,axiom,
    ! [X8,X9,X2,X15,X18,X12] :
      ( hAPP(c_Hilbert__Choice_Oinv__into(X12,X18,X15,X2),X9) = hAPP(c_Hilbert__Choice_Oinv__into(X12,X18,X15,X2),X8)
     => ( hBOOL(hAPP(hAPP(c_member(X18),X9),c_Set_Oimage(X12,X18,X2,X15)))
       => ( hBOOL(hAPP(hAPP(c_member(X18),X8),c_Set_Oimage(X12,X18,X2,X15)))
         => X9 = X8 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__injective) ).

fof(fact_Ints__odd__less__0,axiom,
    ! [X29,X12] :
      ( class_Rings_Olinordered__idom(X12)
     => ( hBOOL(hAPP(hAPP(c_member(X12),X29),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)),X29)),X29)),c_Groups_Ozero__class_Ozero(X12)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X29),c_Groups_Ozero__class_Ozero(X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__odd__less__0) ).

fof(fact_range__ex1__eq,axiom,
    ! [X28,X2,X18,X12] :
      ( c_Fun_Oinj__on(X12,X18,X2,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))
     => ( hBOOL(hAPP(hAPP(c_member(X18),X28),c_Set_Oimage(X12,X18,X2,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))))
      <=> ? [X3] :
            ( X28 = hAPP(X2,X3)
            & ! [X71] :
                ( X28 = hAPP(X2,X71)
               => X71 = X3 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__ex1__eq) ).

fof(fact_card__image__le,axiom,
    ! [X2,X18,X15,X12] :
      ( c_Finite__Set_Ofinite(X12,X15)
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X18,c_Set_Oimage(X12,X18,X2,X15))),c_Finite__Set_Ocard(X12,X15))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__image__le) ).

fof(fact_inj__on__strict__subset,axiom,
    ! [X15,X14,X2,X18,X12] :
      ( c_Fun_Oinj__on(X12,X18,X2,X14)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12,tc_HOL_Obool)),X15),X14))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18,tc_HOL_Obool)),c_Set_Oimage(X12,X18,X2,X15)),c_Set_Oimage(X12,X18,X2,X14))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__strict__subset) ).

fof(fact_endo__inj__surj,axiom,
    ! [X2,X15,X12] :
      ( c_Finite__Set_Ofinite(X12,X15)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),c_Set_Oimage(X12,X12,X2,X15)),X15))
       => ( c_Fun_Oinj__on(X12,X12,X2,X15)
         => c_Set_Oimage(X12,X12,X2,X15) = X15 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_endo__inj__surj) ).

fof(fact_card__inj__on__le,axiom,
    ! [X14,X15,X2,X18,X12] :
      ( c_Fun_Oinj__on(X12,X18,X2,X15)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18,tc_HOL_Obool),c_Set_Oimage(X12,X18,X2,X15)),X14))
       => ( c_Finite__Set_Ofinite(X18,X14)
         => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X12,X15)),c_Finite__Set_Ocard(X18,X14))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__inj__on__le) ).

fof(fact_image__iff,axiom,
    ! [X15,X2,X18,X6,X12] :
      ( hBOOL(hAPP(hAPP(c_member(X12),X6),c_Set_Oimage(X18,X12,X2,X15)))
    <=> ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X18),X3),X15))
          & X6 = hAPP(X2,X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__iff) ).

fof(fact_card__inj,axiom,
    ! [X14,X15,X2,X18,X12] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(X12,X18)),X2),c_FuncSet_OPi(X12,X18,X15,hAPP(c_COMBK(tc_fun(X18,tc_HOL_Obool),X12),X14))))
     => ( c_Fun_Oinj__on(X12,X18,X2,X15)
       => ( c_Finite__Set_Ofinite(X18,X14)
         => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X12,X15)),c_Finite__Set_Ocard(X18,X14))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__inj) ).

fof(fact_Pi__anti__mono,axiom,
    ! [X14,X18,X15,X52,X12] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X52),X15))
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X12,X18),tc_HOL_Obool),c_FuncSet_OPi(X12,X18,X15,X14)),c_FuncSet_OPi(X12,X18,X52,X14))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__anti__mono) ).

fof(fact_finite__range__imageI,axiom,
    ! [X2,X53,X1,X18,X12] :
      ( c_Finite__Set_Ofinite(X12,c_Set_Oimage(X18,X12,X1,c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool))))
     => c_Finite__Set_Ofinite(X53,c_Set_Oimage(X18,X53,hAPP(c_COMBB(X12,X53,X18,X2),X1),c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool)))) ),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_const__Lin__Prof) ).

fof(fact_funcset__mem,axiom,
    ! [X9,X14,X15,X2,X18,X12] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(X12,X18)),X2),c_FuncSet_OPi(X12,X18,X15,hAPP(c_COMBK(tc_fun(X18,tc_HOL_Obool),X12),X14))))
     => ( hBOOL(hAPP(hAPP(c_member(X12),X9),X15))
       => hBOOL(hAPP(hAPP(c_member(X18),hAPP(X2,X9)),X14)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funcset__mem) ).

fof(fact_image__mono,axiom,
    ! [X2,X18,X14,X15,X12] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X15),X14))
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18,tc_HOL_Obool),c_Set_Oimage(X12,X18,X2,X15)),c_Set_Oimage(X12,X18,X2,X14))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__mono) ).

fof(fact_mlex__leq,axiom,
    ! [X17,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)),X17))
       => 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,X17))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mlex__leq) ).

fof(fact_in__rel__def,axiom,
    ! [X8,X9,X17,X18,X12] :
      ( c_FunDef_Oin__rel(X12,X18,X17,X9,X8)
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X12,X18)),hAPP(hAPP(c_Product__Type_OPair(X12,X18),X9),X8)),X17)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__rel__def) ).

fof(fact_f__inv__into__f,axiom,
    ! [X15,X2,X18,X8,X12] :
      ( hBOOL(hAPP(hAPP(c_member(X12),X8),c_Set_Oimage(X18,X12,X2,X15)))
     => hAPP(X2,hAPP(c_Hilbert__Choice_Oinv__into(X18,X12,X15,X2),X8)) = X8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_f__inv__into__f) ).

fof(fact_surj__iff__all,axiom,
    ! [X2,X12,X18] :
      ( c_Set_Oimage(X18,X12,X2,c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool))
    <=> ! [X3] : hAPP(X2,hAPP(c_Hilbert__Choice_Oinv__into(X18,X12,c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool)),X2),X3)) = X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__iff__all) ).

fof(fact_inj__on__inv__into,axiom,
    ! [X15,X2,X18,X14,X12] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X14),c_Set_Oimage(X18,X12,X2,X15)))
     => c_Fun_Oinj__on(X12,X18,c_Hilbert__Choice_Oinv__into(X18,X12,X15,X2),X14) ),
    file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_in__mktop) ).

fof(help_c__COMBS__1,axiom,
    ! [X17,X50,X32,X12,X53,X18] : hAPP(c_COMBS(X18,X53,X12,X32,X50),X17) = hAPP(hAPP(X32,X17),hAPP(X50,X17)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBS__1) ).

fof(fact_Pi__mem,axiom,
    ! [X9,X14,X15,X2,X18,X12] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(X12,X18)),X2),c_FuncSet_OPi(X12,X18,X15,X14)))
     => ( hBOOL(hAPP(hAPP(c_member(X12),X9),X15))
       => hBOOL(hAPP(hAPP(c_member(X18),hAPP(X2,X9)),hAPP(X14,X9))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__mem) ).

fof(fact_inj__image__mem__iff,axiom,
    ! [X15,X29,X2,X18,X12] :
      ( c_Fun_Oinj__on(X12,X18,X2,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))
     => ( hBOOL(hAPP(hAPP(c_member(X18),hAPP(X2,X29)),c_Set_Oimage(X12,X18,X2,X15)))
      <=> hBOOL(hAPP(hAPP(c_member(X12),X29),X15)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__mem__iff) ).

fof(fact_image__surj__f__inv__f,axiom,
    ! [X15,X2,X12,X18] :
      ( c_Set_Oimage(X18,X12,X2,c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool))
     => c_Set_Oimage(X18,X12,X2,c_Set_Oimage(X12,X18,c_Hilbert__Choice_Oinv__into(X18,X12,c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool)),X2),X15)) = X15 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__surj__f__inv__f) ).

fof(fact_image__inv__into__cancel,axiom,
    ! [X66,X52,X15,X2,X12,X18] :
      ( c_Set_Oimage(X18,X12,X2,X15) = X52
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X66),X52))
       => c_Set_Oimage(X18,X12,X2,c_Set_Oimage(X12,X18,c_Hilbert__Choice_Oinv__into(X18,X12,X15,X2),X66)) = X66 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__inv__into__cancel) ).

fof(fact_inj__on__def,axiom,
    ! [X15,X2,X18,X12] :
      ( c_Fun_Oinj__on(X12,X18,X2,X15)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X12),X3),X15))
         => ! [X49] :
              ( hBOOL(hAPP(hAPP(c_member(X12),X49),X15))
             => ( hAPP(X2,X3) = hAPP(X2,X49)
               => X3 = X49 ) ) ) ),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_above__Lin) ).

fof(fact_range__composition,axiom,
    ! [X1,X2,X53,X12,X18] : c_Set_Oimage(X18,X12,hAPP(c_COMBB(X53,X12,X18,X2),X1),c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool))) = c_Set_Oimage(X53,X12,X2,c_Set_Oimage(X18,X53,X1,c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__composition) ).

fof(fact_finite__surj__inj,axiom,
    ! [X2,X15,X12] :
      ( c_Finite__Set_Ofinite(X12,X15)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X15),c_Set_Oimage(X12,X12,X2,X15)))
       => c_Fun_Oinj__on(X12,X12,X2,X15) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__surj__inj) ).

fof(fact_dictator__def,axiom,
    ! [X54,X46] :
      ( c_Arrow__Order__Mirabelle_Odictator(X46,X54)
    <=> ! [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(X46,X3) = hAPP(X3,X54) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dictator__def) ).

fof(fact_inj__fun,axiom,
    ! [X53,X2,X18,X12] :
      ( c_Fun_Oinj__on(X12,X18,X2,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))
     => c_Fun_Oinj__on(X12,tc_fun(X53,X18),hAPP(c_COMBB(X18,tc_fun(X53,X18),X12,c_COMBK(X18,X53)),X2),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__fun) ).

fof(fact_funcset__id,axiom,
    ! [X15,X12] : hBOOL(hAPP(hAPP(c_member(tc_fun(X12,X12)),c_COMBI(X12)),c_FuncSet_OPi(X12,X12,X15,hAPP(c_COMBK(tc_fun(X12,tc_HOL_Obool),X12),X15)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funcset__id) ).

fof(fact_image__image,axiom,
    ! [X15,X1,X53,X2,X12,X18] : c_Set_Oimage(X18,X12,X2,c_Set_Oimage(X53,X18,X1,X15)) = c_Set_Oimage(X53,X12,hAPP(c_COMBB(X18,X12,X53,X2),X1),X15),
    file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_in__measure) ).

fof(fact_inv__into__image__cancel,axiom,
    ! [X16,X15,X2,X18,X12] :
      ( c_Fun_Oinj__on(X12,X18,X2,X15)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X16),X15))
       => c_Set_Oimage(X18,X12,c_Hilbert__Choice_Oinv__into(X12,X18,X15,X2),c_Set_Oimage(X12,X18,X2,X16)) = X16 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__image__cancel) ).

fof(fact_finite__surj,axiom,
    ! [X2,X14,X18,X15,X12] :
      ( c_Finite__Set_Ofinite(X12,X15)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18,tc_HOL_Obool),X14),c_Set_Oimage(X12,X18,X2,X15)))
       => c_Finite__Set_Ofinite(X18,X14) ) ),
    file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_mktop__Lin) ).

fof(fact_image__inv__f__f,axiom,
    ! [X15,X2,X18,X12] :
      ( c_Fun_Oinj__on(X12,X18,X2,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))
     => c_Set_Oimage(X18,X12,c_Hilbert__Choice_Oinv__into(X12,X18,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)),X2),c_Set_Oimage(X12,X18,X2,X15)) = X15 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__inv__f__f) ).

fof(fact_inv__image__comp,axiom,
    ! [X72,X2,X18,X12] :
      ( c_Fun_Oinj__on(X12,X18,X2,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))
     => c_Set_Oimage(X18,X12,c_Hilbert__Choice_Oinv__into(X12,X18,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)),X2),c_Set_Oimage(X12,X18,X2,X72)) = X72 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__image__comp) ).

fof(fact_surj__f__inv__f,axiom,
    ! [X8,X2,X12,X18] :
      ( c_Set_Oimage(X18,X12,X2,c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool))
     => hAPP(X2,hAPP(c_Hilbert__Choice_Oinv__into(X18,X12,c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool)),X2),X8)) = X8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__f__inv__f) ).

fof(fact_mlex__less,axiom,
    ! [X17,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,X17))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mlex__less) ).

fof(fact_subset__card__intvl__is__intvl,axiom,
    ! [X22,X15] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool),X15),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X22,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22),c_Finite__Set_Ocard(tc_Nat_Onat,X15)))))
     => X15 = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X22,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22),c_Finite__Set_Ocard(tc_Nat_Onat,X15))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__card__intvl__is__intvl) ).

fof(fact_atLeastLessThan__subset__iff,axiom,
    ! [X78,X13,X28,X29,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,X29,X28)),c_SetInterval_Oord__class_OatLeastLessThan(X12,X13,X78)))
       => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X28),X29))
          | ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X13),X29))
            & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X28),X78)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__subset__iff) ).

fof(fact_surj__imp__inj__inv,axiom,
    ! [X2,X12,X18] :
      ( c_Set_Oimage(X18,X12,X2,c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool))
     => c_Fun_Oinj__on(X12,X18,c_Hilbert__Choice_Oinv__into(X18,X12,c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__imp__inj__inv) ).

fof(fact_rangeI,axiom,
    ! [X18,X9,X2,X12] : hBOOL(hAPP(hAPP(c_member(X12),hAPP(X2,X9)),c_Set_Oimage(X18,X12,X2,c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rangeI) ).

fof(fact_inj__imp__surj__inv,axiom,
    ! [X2,X18,X12] :
      ( c_Fun_Oinj__on(X12,X18,X2,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))
     => c_Set_Oimage(X18,X12,c_Hilbert__Choice_Oinv__into(X12,X18,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__imp__surj__inv) ).

fof(fact_imageI,axiom,
    ! [X2,X18,X15,X9,X12] :
      ( hBOOL(hAPP(hAPP(c_member(X12),X9),X15))
     => hBOOL(hAPP(hAPP(c_member(X18),hAPP(X2,X9)),c_Set_Oimage(X12,X18,X2,X15))) ),
    file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact__096_Ia_M_Ab_J_A_126_058_ALba_096) ).

fof(fact_range__eqI,axiom,
    ! [X18,X12,X9,X2,X28] :
      ( X28 = hAPP(X2,X9)
     => hBOOL(hAPP(hAPP(c_member(X12),X28),c_Set_Oimage(X18,X12,X2,c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__eqI) ).

fof(fact_image__eqI,axiom,
    ! [X12,X15,X18,X9,X2,X28] :
      ( X28 = hAPP(X2,X9)
     => ( hBOOL(hAPP(hAPP(c_member(X18),X9),X15))
       => hBOOL(hAPP(hAPP(c_member(X12),X28),c_Set_Oimage(X18,X12,X2,X15))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__eqI) ).

fof(fact_rev__image__eqI,axiom,
    ! [X18,X2,X28,X15,X9,X12] :
      ( hBOOL(hAPP(hAPP(c_member(X12),X9),X15))
     => ( X28 = hAPP(X2,X9)
       => hBOOL(hAPP(hAPP(c_member(X18),X28),c_Set_Oimage(X12,X18,X2,X15))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__image__eqI) ).

fof(fact_inj__image__eq__iff,axiom,
    ! [X14,X15,X2,X18,X12] :
      ( c_Fun_Oinj__on(X12,X18,X2,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))
     => ( c_Set_Oimage(X12,X18,X2,X15) = c_Set_Oimage(X12,X18,X2,X14)
      <=> X15 = X14 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__eq__iff) ).

fof(fact_add__less__imp__less__right,axiom,
    ! [X41,X40,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),X40)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X41),X40)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X11),X41)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__imp__less__right) ).

fof(fact_add__less__cancel__right,axiom,
    ! [X28,X13,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),X13)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X28),X13)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X29),X28)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__cancel__right) ).

fof(fact_add__less__imp__less__left,axiom,
    ! [X41,X11,X40,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),X40),X11)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X40),X41)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X11),X41)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__imp__less__left) ).

fof(fact_add__less__cancel__left,axiom,
    ! [X28,X29,X13,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),X13),X29)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X13),X28)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X29),X28)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__cancel__left) ).

fof(fact_finite__imageD,axiom,
    ! [X15,X2,X18,X12] :
      ( c_Finite__Set_Ofinite(X12,c_Set_Oimage(X18,X12,X2,X15))
     => ( c_Fun_Oinj__on(X18,X12,X2,X15)
       => c_Finite__Set_Ofinite(X18,X15) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__imageD) ).

fof(fact_psubset__trans,axiom,
    ! [X43,X14,X15,X12] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12,tc_HOL_Obool)),X15),X14))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12,tc_HOL_Obool)),X14),X43))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12,tc_HOL_Obool)),X15),X43)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__trans) ).

fof(fact_add__le__imp__le__right,axiom,
    ! [X41,X40,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),X40)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X41),X40)))
       => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X11),X41)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__imp__le__right) ).

fof(fact_add__le__cancel__right,axiom,
    ! [X28,X13,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),X13)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X28),X13)))
      <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X29),X28)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__cancel__right) ).

fof(fact_add__le__imp__le__left,axiom,
    ! [X41,X11,X40,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),X40),X11)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X40),X41)))
       => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X11),X41)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__imp__le__left) ).

fof(fact_add__le__cancel__left,axiom,
    ! [X28,X29,X13,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),X13),X29)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X13),X28)))
      <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X29),X28)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__cancel__left) ).

fof(fact_insert__subset,axiom,
    ! [X14,X15,X9,X12] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),c_Set_Oinsert(X12,X9,X15)),X14))
    <=> ( hBOOL(hAPP(hAPP(c_member(X12),X9),X14))
        & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X15),X14)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__subset) ).

fof(fact_inv__f__f,axiom,
    ! [X9,X2,X18,X12] :
      ( c_Fun_Oinj__on(X12,X18,X2,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))
     => hAPP(c_Hilbert__Choice_Oinv__into(X12,X18,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)),X2),hAPP(X2,X9)) = X9 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__f__f) ).

fof(fact_inv__f__eq,axiom,
    ! [X8,X9,X2,X18,X12] :
      ( c_Fun_Oinj__on(X12,X18,X2,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))
     => ( hAPP(X2,X9) = X8
       => hAPP(c_Hilbert__Choice_Oinv__into(X12,X18,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)),X2),X8) = X9 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__f__eq) ).

fof(fact_pred__equals__eq,axiom,
    ! [X16,X17,X12] :
      ( hAPP(hAPP(c_COMBC(X12,tc_fun(X12,tc_HOL_Obool),tc_HOL_Obool),c_member(X12)),X17) = hAPP(hAPP(c_COMBC(X12,tc_fun(X12,tc_HOL_Obool),tc_HOL_Obool),c_member(X12)),X16)
    <=> X17 = X16 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__equals__eq) ).

fof(fact_nat__add__left__cancel__less,axiom,
    ! [X10,X21,X22] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22),X21)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22),X10)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X10)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).

fof(fact_inv__into__f__f,axiom,
    ! [X9,X15,X2,X18,X12] :
      ( c_Fun_Oinj__on(X12,X18,X2,X15)
     => ( hBOOL(hAPP(hAPP(c_member(X12),X9),X15))
       => hAPP(c_Hilbert__Choice_Oinv__into(X12,X18,X15,X2),hAPP(X2,X9)) = X9 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__f__f) ).

fof(fact_inv__into__f__eq,axiom,
    ! [X8,X9,X15,X2,X18,X12] :
      ( c_Fun_Oinj__on(X12,X18,X2,X15)
     => ( hBOOL(hAPP(hAPP(c_member(X12),X9),X15))
       => ( hAPP(X2,X9) = X8
         => hAPP(c_Hilbert__Choice_Oinv__into(X12,X18,X15,X2),X8) = X9 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__f__eq) ).

fof(fact_eq__card__imp__inj__on,axiom,
    ! [X2,X18,X15,X12] :
      ( c_Finite__Set_Ofinite(X12,X15)
     => ( c_Finite__Set_Ocard(X18,c_Set_Oimage(X12,X18,X2,X15)) = c_Finite__Set_Ocard(X12,X15)
       => c_Fun_Oinj__on(X12,X18,X2,X15) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__card__imp__inj__on) ).

fof(fact_inj__on__iff__eq__card,axiom,
    ! [X2,X18,X15,X12] :
      ( c_Finite__Set_Ofinite(X12,X15)
     => ( c_Fun_Oinj__on(X12,X18,X2,X15)
      <=> c_Finite__Set_Ocard(X18,c_Set_Oimage(X12,X18,X2,X15)) = c_Finite__Set_Ocard(X12,X15) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff__eq__card) ).

fof(fact_insert__mono,axiom,
    ! [X29,X55,X43,X12] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X43),X55))
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),c_Set_Oinsert(X12,X29,X43)),c_Set_Oinsert(X12,X29,X55))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__mono) ).

fof(help_c__COMBB__1,axiom,
    ! [X17,X50,X32,X53,X12,X18] : hAPP(hAPP(c_COMBB(X18,X12,X53,X32),X50),X17) = hAPP(X32,hAPP(X50,X17)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBB__1) ).

fof(fact_add__strict__mono,axiom,
    ! [X39,X40,X41,X11,X12] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X11),X41))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X40),X39))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X11),X40)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X41),X39))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__mono) ).

fof(fact_image__add__atLeastLessThan,axiom,
    ! [X77,X54,X22] : 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)),X22),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X54,X77)) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X54),X22),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X77),X22)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__add__atLeastLessThan) ).

fof(fact_nat__add__left__cancel__le,axiom,
    ! [X10,X21,X22] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22),X21)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22),X10)))
    <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21),X10)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).

fof(fact_add__le__less__mono,axiom,
    ! [X39,X40,X41,X11,X12] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X11),X41))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X40),X39))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X11),X40)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X41),X39))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__less__mono) ).

fof(fact_add__less__le__mono,axiom,
    ! [X39,X40,X41,X11,X12] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X11),X41))
       => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X40),X39))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X11),X40)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X41),X39))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__le__mono) ).

fof(fact_subset__psubset__trans,axiom,
    ! [X43,X14,X15,X12] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X15),X14))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12,tc_HOL_Obool)),X14),X43))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12,tc_HOL_Obool)),X15),X43)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__psubset__trans) ).

fof(fact_psubset__subset__trans,axiom,
    ! [X43,X14,X15,X12] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12,tc_HOL_Obool)),X15),X14))
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X14),X43))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12,tc_HOL_Obool)),X15),X43)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__subset__trans) ).

fof(fact_less__eq__nat_Osimps_I2_J,axiom,
    ! [X10,X21] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X21)),X10))
    <=> hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21),X10)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I2_J) ).

fof(fact_insert__image,axiom,
    ! [X2,X18,X15,X9,X12] :
      ( hBOOL(hAPP(hAPP(c_member(X12),X9),X15))
     => c_Set_Oinsert(X18,hAPP(X2,X9),c_Set_Oimage(X12,X18,X2,X15)) = c_Set_Oimage(X12,X18,X2,X15) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__image) ).

fof(fact_card__psubset,axiom,
    ! [X15,X14,X12] :
      ( c_Finite__Set_Ofinite(X12,X14)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X15),X14))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X12,X15)),c_Finite__Set_Ocard(X12,X14)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12,tc_HOL_Obool)),X15),X14)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__psubset) ).

fof(fact_add__mono,axiom,
    ! [X39,X40,X41,X11,X12] :
      ( class_Groups_Oordered__ab__semigroup__add(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X11),X41))
       => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X40),X39))
         => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X11),X40)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X41),X39))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mono) ).

fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
    ! [X29,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),X29),X29)),c_Groups_Ozero__class_Ozero(X12)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X29),c_Groups_Ozero__class_Ozero(X12))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).

fof(fact_even__less__0__iff,axiom,
    ! [X29,X12] :
      ( class_Rings_Olinordered__idom(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),X29)),c_Groups_Ozero__class_Ozero(X12)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X29),c_Groups_Ozero__class_Ozero(X12))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__less__0__iff) ).

fof(fact_add__less__mono,axiom,
    ! [X26,X25,X19,X20] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),X19))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),X26))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),X25)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X26))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono) ).

fof(fact_image__insert,axiom,
    ! [X14,X29,X2,X12,X18] : c_Set_Oimage(X18,X12,X2,c_Set_Oinsert(X18,X29,X14)) = c_Set_Oinsert(X12,hAPP(X2,X29),c_Set_Oimage(X18,X12,X2,X14)),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV__surj__inj) ).

fof(fact_subset__inj__on,axiom,
    ! [X15,X14,X2,X18,X12] :
      ( c_Fun_Oinj__on(X12,X18,X2,X14)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X15),X14))
       => c_Fun_Oinj__on(X12,X18,X2,X15) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__inj__on) ).

fof(fact_card__image,axiom,
    ! [X15,X2,X18,X12] :
      ( c_Fun_Oinj__on(X12,X18,X2,X15)
     => c_Finite__Set_Ocard(X18,c_Set_Oimage(X12,X18,X2,X15)) = c_Finite__Set_Ocard(X12,X15) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__image) ).

fof(fact_add__neg__neg,axiom,
    ! [X41,X11,X12] :
      ( class_Groups_Oordered__comm__monoid__add(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X11),c_Groups_Ozero__class_Ozero(X12)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X41),c_Groups_Ozero__class_Ozero(X12)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X11),X41)),c_Groups_Ozero__class_Ozero(X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__neg__neg) ).

fof(fact_Ints__add,axiom,
    ! [X28,X29,X12] :
      ( class_Rings_Oring__1(X12)
     => ( hBOOL(hAPP(hAPP(c_member(X12),X29),c_Int_Oring__1__class_OInts(X12)))
       => ( hBOOL(hAPP(hAPP(c_member(X12),X28),c_Int_Oring__1__class_OInts(X12)))
         => hBOOL(hAPP(hAPP(c_member(X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),X28)),c_Int_Oring__1__class_OInts(X12))) ) ) ),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV__inj__surj) ).

fof(fact_add__strict__right__mono,axiom,
    ! [X40,X41,X11,X12] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X11),X41))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X11),X40)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X41),X40))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).

fof(fact_add__strict__left__mono,axiom,
    ! [X40,X41,X11,X12] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X11),X41))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X40),X11)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X40),X41))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__left__mono) ).

fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
    ! [X29,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),X29),X29)),c_Groups_Ozero__class_Ozero(X12)))
      <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X29),c_Groups_Ozero__class_Ozero(X12))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).

fof(fact_add__nonpos__neg,axiom,
    ! [X41,X11,X12] :
      ( class_Groups_Oordered__comm__monoid__add(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X11),c_Groups_Ozero__class_Ozero(X12)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X41),c_Groups_Ozero__class_Ozero(X12)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X11),X41)),c_Groups_Ozero__class_Ozero(X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonpos__neg) ).

fof(fact_add__neg__nonpos,axiom,
    ! [X41,X11,X12] :
      ( class_Groups_Oordered__comm__monoid__add(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X11),c_Groups_Ozero__class_Ozero(X12)))
       => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X41),c_Groups_Ozero__class_Ozero(X12)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X11),X41)),c_Groups_Ozero__class_Ozero(X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__neg__nonpos) ).

fof(fact_add__le__mono,axiom,
    ! [X26,X25,X19,X20] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20),X19))
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X25),X26))
       => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),X25)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X26))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__mono) ).

fof(fact_finite__Plus__iff,axiom,
    ! [X14,X15,X18,X12] :
      ( c_Finite__Set_Ofinite(tc_sum(X12,X18),c_Sum__Type_OPlus(X12,X18,X15,X14))
    <=> ( c_Finite__Set_Ofinite(X12,X15)
        & c_Finite__Set_Ofinite(X18,X14) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Plus__iff) ).

fof(fact_finite__PlusD_I1_J,axiom,
    ! [X14,X15,X18,X12] :
      ( c_Finite__Set_Ofinite(tc_sum(X12,X18),c_Sum__Type_OPlus(X12,X18,X15,X14))
     => c_Finite__Set_Ofinite(X12,X15) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__PlusD_I1_J) ).

fof(fact_finite__PlusD_I2_J,axiom,
    ! [X14,X15,X18,X12] :
      ( c_Finite__Set_Ofinite(tc_sum(X12,X18),c_Sum__Type_OPlus(X12,X18,X15,X14))
     => c_Finite__Set_Ofinite(X18,X14) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__PlusD_I2_J) ).

fof(fact_add__right__mono,axiom,
    ! [X40,X41,X11,X12] :
      ( class_Groups_Oordered__ab__semigroup__add(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X11),X41))
       => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X11),X40)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X41),X40))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__mono) ).

fof(fact_add__left__mono,axiom,
    ! [X40,X41,X11,X12] :
      ( class_Groups_Oordered__ab__semigroup__add(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X11),X41))
       => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X40),X11)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X40),X41))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__mono) ).

fof(fact_add__lessD1,axiom,
    ! [X25,X19,X20] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),X19)),X25))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),X25)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__lessD1) ).

fof(fact_add__nonpos__nonpos,axiom,
    ! [X41,X11,X12] :
      ( class_Groups_Oordered__comm__monoid__add(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X11),c_Groups_Ozero__class_Ozero(X12)))
       => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X41),c_Groups_Ozero__class_Ozero(X12)))
         => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X11),X41)),c_Groups_Ozero__class_Ozero(X12))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonpos__nonpos) ).

fof(fact_predicate2D,axiom,
    ! [X8,X9,X50,X32,X18,X12] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_fun(X18,tc_HOL_Obool)),X32),X50))
     => ( hBOOL(hAPP(hAPP(X32,X9),X8))
       => hBOOL(hAPP(hAPP(X50,X9),X8)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_predicate2D) ).

fof(fact_rev__predicate2D,axiom,
    ! [X50,X18,X12,X8,X9,X32] :
      ( hBOOL(hAPP(hAPP(X32,X9),X8))
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_fun(X18,tc_HOL_Obool)),X32),X50))
       => hBOOL(hAPP(hAPP(X50,X9),X8)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__predicate2D) ).

fof(fact_add__less__mono1,axiom,
    ! [X25,X19,X20] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),X19))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),X25)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X25))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono1) ).

fof(fact_inj__on__iff,axiom,
    ! [X8,X9,X15,X2,X18,X12] :
      ( c_Fun_Oinj__on(X12,X18,X2,X15)
     => ( hBOOL(hAPP(hAPP(c_member(X12),X9),X15))
       => ( hBOOL(hAPP(hAPP(c_member(X12),X8),X15))
         => ( hAPP(X2,X9) = hAPP(X2,X8)
          <=> X9 = X8 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff) ).

fof(fact_inj__onD,axiom,
    ! [X8,X9,X15,X2,X18,X12] :
      ( c_Fun_Oinj__on(X12,X18,X2,X15)
     => ( hAPP(X2,X9) = hAPP(X2,X8)
       => ( hBOOL(hAPP(hAPP(c_member(X12),X9),X15))
         => ( hBOOL(hAPP(hAPP(c_member(X12),X8),X15))
           => X9 = X8 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__onD) ).

fof(fact_inj__on__contraD,axiom,
    ! [X8,X9,X15,X2,X18,X12] :
      ( c_Fun_Oinj__on(X12,X18,X2,X15)
     => ( X9 != X8
       => ( hBOOL(hAPP(hAPP(c_member(X12),X9),X15))
         => ( hBOOL(hAPP(hAPP(c_member(X12),X8),X15))
           => hAPP(X2,X9) != hAPP(X2,X8) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__contraD) ).

fof(fact_add__leD1,axiom,
    ! [X24,X25,X23] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23),X25)),X24))
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X23),X24)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leD1) ).

fof(fact_add__leD2,axiom,
    ! [X24,X25,X23] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23),X25)),X24))
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X25),X24)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leD2) ).

fof(fact_add__pos__pos,axiom,
    ! [X41,X11,X12] :
      ( class_Groups_Oordered__comm__monoid__add(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),c_Groups_Ozero__class_Ozero(X12)),X11))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),c_Groups_Ozero__class_Ozero(X12)),X41))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),c_Groups_Ozero__class_Ozero(X12)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X11),X41))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__pos__pos) ).

fof(fact_add__le__mono1,axiom,
    ! [X25,X19,X20] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20),X19))
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),X25)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X25))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__mono1) ).

fof(fact_psubsetD,axiom,
    ! [X13,X14,X15,X12] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12,tc_HOL_Obool)),X15),X14))
     => ( hBOOL(hAPP(hAPP(c_member(X12),X13),X15))
       => hBOOL(hAPP(hAPP(c_member(X12),X13),X14)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubsetD) ).

fof(fact_psubset__card__mono,axiom,
    ! [X15,X14,X12] :
      ( c_Finite__Set_Ofinite(X12,X14)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12,tc_HOL_Obool)),X15),X14))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X12,X15)),c_Finite__Set_Ocard(X12,X14))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__card__mono) ).

fof(fact_inj__on__add__nat,axiom,
    ! [X51,X22] : 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)),X22),X51),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__add__nat) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
    ! [X39,X40,X41,X11,X12] :
      ( class_Rings_Ocomm__semiring__1(X12)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X11),X41)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X40),X39)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X11),X40)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X41),X39)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).

fof(fact_subset__trans,axiom,
    ! [X43,X14,X15,X12] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X15),X14))
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X14),X43))
       => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X15),X43)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__trans) ).

fof(fact_add__nonneg__pos,axiom,
    ! [X41,X11,X12] :
      ( class_Groups_Oordered__comm__monoid__add(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,c_Groups_Ozero__class_Ozero(X12)),X11))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),c_Groups_Ozero__class_Ozero(X12)),X41))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),c_Groups_Ozero__class_Ozero(X12)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X11),X41))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__pos) ).

fof(fact_add__pos__nonneg,axiom,
    ! [X41,X11,X12] :
      ( class_Groups_Oordered__comm__monoid__add(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),c_Groups_Ozero__class_Ozero(X12)),X11))
       => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,c_Groups_Ozero__class_Ozero(X12)),X41))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),c_Groups_Ozero__class_Ozero(X12)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X11),X41))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__pos__nonneg) ).

fof(fact_card__Plus__conv__if,axiom,
    ! [X14,X18,X15,X12] :
      ( ( ( c_Finite__Set_Ofinite(X12,X15)
          & c_Finite__Set_Ofinite(X18,X14) )
       => c_Finite__Set_Ocard(tc_sum(X12,X18),c_Sum__Type_OPlus(X12,X18,X15,X14)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Finite__Set_Ocard(X12,X15)),c_Finite__Set_Ocard(X18,X14)) )
      & ( ~ ( c_Finite__Set_Ofinite(X12,X15)
            & c_Finite__Set_Ofinite(X18,X14) )
       => c_Finite__Set_Ocard(tc_sum(X12,X18),c_Sum__Type_OPlus(X12,X18,X15,X14)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Plus__conv__if) ).

fof(fact_card__Plus,axiom,
    ! [X14,X18,X15,X12] :
      ( c_Finite__Set_Ofinite(X12,X15)
     => ( c_Finite__Set_Ofinite(X18,X14)
       => c_Finite__Set_Ocard(tc_sum(X12,X18),c_Sum__Type_OPlus(X12,X18,X15,X14)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Finite__Set_Ocard(X12,X15)),c_Finite__Set_Ocard(X18,X14)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Plus) ).

fof(fact_pos__add__strict,axiom,
    ! [X40,X41,X11,X12] :
      ( class_Rings_Olinordered__semidom(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),c_Groups_Ozero__class_Ozero(X12)),X11))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X41),X40))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X41),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X11),X40))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__add__strict) ).

fof(fact_card__insert__le,axiom,
    ! [X9,X15,X12] :
      ( c_Finite__Set_Ofinite(X12,X15)
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X12,X15)),c_Finite__Set_Ocard(X12,c_Set_Oinsert(X12,X9,X15)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__insert__le) ).

fof(fact_Ints__odd__nonzero,axiom,
    ! [X29,X12] :
      ( class_Int_Oring__char__0(X12)
     => ( hBOOL(hAPP(hAPP(c_member(X12),X29),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)),X29)),X29) != c_Groups_Ozero__class_Ozero(X12) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__odd__nonzero) ).

fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
    ! [X29,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),X29),X29)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),c_Groups_Ozero__class_Ozero(X12)),X29)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).

fof(fact_add__gr__0,axiom,
    ! [X10,X21] :
      ( 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),X21),X10)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__gr__0) ).

fof(fact_card__seteq,axiom,
    ! [X15,X14,X12] :
      ( c_Finite__Set_Ofinite(X12,X14)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X15),X14))
       => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X12,X14)),c_Finite__Set_Ocard(X12,X15)))
         => X15 = X14 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__seteq) ).

fof(fact_subset__insertI2,axiom,
    ! [X28,X14,X15,X12] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X15),X14))
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X15),c_Set_Oinsert(X12,X28,X14))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insertI2) ).

fof(fact_add__strict__increasing2,axiom,
    ! [X40,X41,X11,X12] :
      ( class_Groups_Oordered__comm__monoid__add(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,c_Groups_Ozero__class_Ozero(X12)),X11))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X41),X40))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X41),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X11),X40))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__increasing2) ).

fof(fact_add__strict__increasing,axiom,
    ! [X40,X41,X11,X12] :
      ( class_Groups_Oordered__comm__monoid__add(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),c_Groups_Ozero__class_Ozero(X12)),X11))
       => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X41),X40))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X41),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X11),X40))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__increasing) ).

fof(fact_add__nonneg__nonneg,axiom,
    ! [X41,X11,X12] :
      ( class_Groups_Oordered__comm__monoid__add(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,c_Groups_Ozero__class_Ozero(X12)),X11))
       => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,c_Groups_Ozero__class_Ozero(X12)),X41))
         => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,c_Groups_Ozero__class_Ozero(X12)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X11),X41))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__nonneg) ).

fof(fact_psubset__imp__subset,axiom,
    ! [X14,X15,X12] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12,tc_HOL_Obool)),X15),X14))
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X15),X14)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__imp__subset) ).

fof(fact_subset__iff__psubset__eq,axiom,
    ! [X14,X15,X12] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X15),X14))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12,tc_HOL_Obool)),X15),X14))
        | X15 = X14 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__iff__psubset__eq) ).

fof(fact_psubset__eq,axiom,
    ! [X14,X15,X12] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12,tc_HOL_Obool)),X15),X14))
    <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X15),X14))
        & X15 != X14 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__eq) ).

fof(fact_insert__iff,axiom,
    ! [X15,X28,X29,X12] :
      ( hBOOL(hAPP(hAPP(c_member(X12),X29),c_Set_Oinsert(X12,X28,X15)))
    <=> ( X29 = X28
        | hBOOL(hAPP(hAPP(c_member(X12),X29),X15)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__iff) ).

fof(fact_insertE,axiom,
    ! [X15,X28,X29,X12] :
      ( hBOOL(hAPP(hAPP(c_member(X12),X29),c_Set_Oinsert(X12,X28,X15)))
     => ( X29 != X28
       => hBOOL(hAPP(hAPP(c_member(X12),X29),X15)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertE) ).

fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
    ! [X29,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),X29),X29)))
      <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,c_Groups_Ozero__class_Ozero(X12)),X29)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).

fof(fact_Pi__UNIV,axiom,
    ! [X15,X18,X12] : c_FuncSet_OPi(X12,X18,X15,hAPP(c_COMBK(tc_fun(X18,tc_HOL_Obool),X12),c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X12,X18),tc_HOL_Obool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__UNIV) ).

fof(fact_add__increasing,axiom,
    ! [X40,X41,X11,X12] :
      ( class_Groups_Oordered__comm__monoid__add(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,c_Groups_Ozero__class_Ozero(X12)),X11))
       => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X41),X40))
         => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X41),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X11),X40))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__increasing) ).

fof(fact_add__increasing2,axiom,
    ! [X11,X41,X40,X12] :
      ( class_Groups_Oordered__comm__monoid__add(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,c_Groups_Ozero__class_Ozero(X12)),X40))
       => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X41),X11))
         => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X41),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X11),X40))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__increasing2) ).

fof(fact_finite__Plus,axiom,
    ! [X14,X18,X15,X12] :
      ( c_Finite__Set_Ofinite(X12,X15)
     => ( c_Finite__Set_Ofinite(X18,X14)
       => c_Finite__Set_Ofinite(tc_sum(X12,X18),c_Sum__Type_OPlus(X12,X18,X15,X14)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Plus) ).

fof(help_c__COMBC__1,axiom,
    ! [X17,X50,X32,X12,X53,X18] : hAPP(hAPP(hAPP(c_COMBC(X18,X53,X12),X32),X50),X17) = hAPP(hAPP(X32,X17),X50),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBC__1) ).

fof(fact_set__eq__subset,axiom,
    ! [X12,X14,X15] :
      ( X15 = X14
    <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X15),X14))
        & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X14),X15)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__eq__subset) ).

fof(fact_equalityI,axiom,
    ! [X14,X15,X12] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X15),X14))
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X14),X15))
       => X15 = X14 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityI) ).

fof(fact_set__rev__mp,axiom,
    ! [X14,X15,X9,X12] :
      ( hBOOL(hAPP(hAPP(c_member(X12),X9),X15))
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X15),X14))
       => hBOOL(hAPP(hAPP(c_member(X12),X9),X14)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__rev__mp) ).

fof(fact_set__mp,axiom,
    ! [X9,X14,X15,X12] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X15),X14))
     => ( hBOOL(hAPP(hAPP(c_member(X12),X9),X15))
       => hBOOL(hAPP(hAPP(c_member(X12),X9),X14)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__mp) ).

fof(fact_in__mono,axiom,
    ! [X9,X14,X15,X12] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X15),X14))
     => ( hBOOL(hAPP(hAPP(c_member(X12),X9),X15))
       => hBOOL(hAPP(hAPP(c_member(X12),X9),X14)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__mono) ).

fof(fact_subsetD,axiom,
    ! [X13,X14,X15,X12] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X15),X14))
     => ( hBOOL(hAPP(hAPP(c_member(X12),X13),X15))
       => hBOOL(hAPP(hAPP(c_member(X12),X13),X14)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subsetD) ).

fof(fact_le__funD,axiom,
    ! [X9,X1,X2,X12,X18] :
      ( class_Orderings_Oord(X18)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,X18),X2),X1))
       => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X18,hAPP(X2,X9)),hAPP(X1,X9))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__funD) ).

fof(fact_le__funE,axiom,
    ! [X9,X1,X2,X12,X18] :
      ( class_Orderings_Oord(X18)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,X18),X2),X1))
       => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X18,hAPP(X2,X9)),hAPP(X1,X9))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__funE) ).

fof(fact_finite__imageI,axiom,
    ! [X65,X18,X46,X12] :
      ( c_Finite__Set_Ofinite(X12,X46)
     => c_Finite__Set_Ofinite(X18,c_Set_Oimage(X12,X18,X65,X46)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__imageI) ).

fof(fact_card__mono,axiom,
    ! [X15,X14,X12] :
      ( c_Finite__Set_Ofinite(X12,X14)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X15),X14))
       => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X12,X15)),c_Finite__Set_Ocard(X12,X14))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__mono) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
    ! [X40,X41,X11,X12] :
      ( class_Rings_Ocomm__semiring__1(X12)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X11),X41)),X40) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X11),X40)),X41) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).

fof(fact_inj__eq,axiom,
    ! [X8,X9,X2,X18,X12] :
      ( c_Fun_Oinj__on(X12,X18,X2,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))
     => ( hAPP(X2,X9) = hAPP(X2,X8)
      <=> X9 = X8 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__eq) ).

fof(fact_injD,axiom,
    ! [X8,X9,X2,X18,X12] :
      ( c_Fun_Oinj__on(X12,X18,X2,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))
     => ( hAPP(X2,X9) = hAPP(X2,X8)
       => X9 = X8 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_injD) ).

fof(fact_atLeastLessThan__eq__iff,axiom,
    ! [X78,X13,X28,X29,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X29),X28))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X13),X78))
         => ( c_SetInterval_Oord__class_OatLeastLessThan(X12,X29,X28) = c_SetInterval_Oord__class_OatLeastLessThan(X12,X13,X78)
          <=> ( X29 = X13
              & X28 = X78 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__eq__iff) ).

fof(fact_atLeastLessThan__inj_I1_J,axiom,
    ! [X78,X13,X28,X29,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( c_SetInterval_Oord__class_OatLeastLessThan(X12,X29,X28) = c_SetInterval_Oord__class_OatLeastLessThan(X12,X13,X78)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X29),X28))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X13),X78))
           => X29 = X13 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__inj_I1_J) ).

fof(fact_atLeastLessThan__inj_I2_J,axiom,
    ! [X78,X13,X28,X29,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( c_SetInterval_Oord__class_OatLeastLessThan(X12,X29,X28) = c_SetInterval_Oord__class_OatLeastLessThan(X12,X13,X78)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X29),X28))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X13),X78))
           => X28 = X78 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__inj_I2_J) ).

fof(fact_less__add__Suc1,axiom,
    ! [X23,X20] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),X23)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc1) ).

fof(fact_less__add__Suc2,axiom,
    ! [X23,X20] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23),X20)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc2) ).

fof(fact_insertI2,axiom,
    ! [X28,X14,X29,X12] :
      ( hBOOL(hAPP(hAPP(c_member(X12),X29),X14))
     => hBOOL(hAPP(hAPP(c_member(X12),X29),c_Set_Oinsert(X12,X28,X14))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertI2) ).

fof(fact_less__trans__Suc,axiom,
    ! [X25,X19,X20] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),X19))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19),X25))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20)),X25)) ) ),
    file('/export/starexec/sandbox/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/sandbox/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/sandbox/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,X21] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21)),hAPP(c_Nat_OSuc,X10)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X10)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__less__eq) ).

fof(fact_Suc__less__SucD,axiom,
    ! [X24,X23] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X23)),hAPP(c_Nat_OSuc,X24)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23),X24)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__less__SucD) ).

fof(fact_finite__fun__UNIVD1,axiom,
    ! [X18,X12] :
      ( c_Finite__Set_Ofinite(tc_fun(X12,X18),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X12,X18),tc_HOL_Obool)))
     => ( c_Finite__Set_Ocard(X18,c_Orderings_Otop__class_Otop(tc_fun(X18,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/sandbox/benchmark/theBenchmark.p',fact_finite__fun__UNIVD1) ).

fof(fact_order__less__trans,axiom,
    ! [X35,X30,X31,X12] :
      ( class_Orderings_Opreorder(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X31),X30))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X30),X35))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X31),X35)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__trans) ).

fof(fact_xt1_I10_J,axiom,
    ! [X35,X31,X30,X12] :
      ( class_Orderings_Oorder(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X30),X31))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X35),X30))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X35),X31)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I10_J) ).

fof(fact_image__Suc__atLeastLessThan,axiom,
    ! [X77,X54] : c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X54,X77)) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X54),hAPP(c_Nat_OSuc,X77)),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__eq__0__iff) ).

fof(fact_UNIV__Plus__UNIV,axiom,
    ! [X18,X12] : c_Sum__Type_OPlus(X12,X18,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X12,X18),tc_HOL_Obool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__Plus__UNIV) ).

fof(fact_termination__basic__simps_I1_J,axiom,
    ! [X35,X30,X31] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31),X30))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X35))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).

fof(fact_trans__less__add1,axiom,
    ! [X23,X19,X20] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),X19))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X23))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add1) ).

fof(fact_termination__basic__simps_I2_J,axiom,
    ! [X30,X35,X31] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31),X35))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X35))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).

fof(fact_trans__less__add2,axiom,
    ! [X23,X19,X20] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),X19))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23),X19))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add2) ).

fof(fact_less__Suc__eq__0__disj,axiom,
    ! [X10,X21] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),hAPP(c_Nat_OSuc,X10)))
    <=> ( X21 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ? [X63] :
            ( X21 = hAPP(c_Nat_OSuc,X63)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X63),X10)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq__0__disj) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
    ! [X40,X41,X11,X12] :
      ( class_Rings_Ocomm__semiring__1(X12)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X11),X41)),X40) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X11),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X41),X40)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).

fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
    ! [X40,X41,X11,X12] :
      ( class_Groups_Oab__semigroup__add(X12)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X11),X41)),X40) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X11),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X41),X40)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
    ! [X39,X40,X11,X12] :
      ( class_Rings_Ocomm__semiring__1(X12)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X11),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X40),X39)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X11),X40)),X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).

fof(fact_insert__code,axiom,
    ! [X9,X15,X8,X12] :
      ( hBOOL(hAPP(c_Set_Oinsert(X12,X8,X15),X9))
    <=> ( X8 = X9
        | hBOOL(hAPP(X15,X9)) ) ),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_zero__less__two) ).

fof(fact_Suc__le__mono,axiom,
    ! [X21,X10] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X10)),hAPP(c_Nat_OSuc,X21)))
    <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10),X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__mono) ).

fof(fact_order__le__less__trans,axiom,
    ! [X35,X30,X31,X12] :
      ( class_Orderings_Opreorder(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X31),X30))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X30),X35))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X31),X35)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__less__trans) ).

fof(fact_order__less__le__trans,axiom,
    ! [X35,X30,X31,X12] :
      ( class_Orderings_Opreorder(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X31),X30))
       => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X30),X35))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X31),X35)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__le__trans) ).

fof(fact_xt1_I8_J,axiom,
    ! [X35,X31,X30,X12] :
      ( class_Orderings_Oorder(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X30),X31))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X35),X30))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X35),X31)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I8_J) ).

fof(fact_xt1_I7_J,axiom,
    ! [X35,X31,X30,X12] :
      ( class_Orderings_Oorder(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X30),X31))
       => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X35),X30))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X35),X31)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I7_J) ).

fof(fact_finite__Plus__UNIV__iff,axiom,
    ! [X18,X12] :
      ( c_Finite__Set_Ofinite(tc_sum(X12,X18),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X12,X18),tc_HOL_Obool)))
    <=> ( c_Finite__Set_Ofinite(X12,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))
        & c_Finite__Set_Ofinite(X18,c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Plus__UNIV__iff) ).

fof(fact_finite__Prod__UNIV,axiom,
    ! [X18,X12] :
      ( c_Finite__Set_Ofinite(X12,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))
     => ( c_Finite__Set_Ofinite(X18,c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool)))
       => c_Finite__Set_Ofinite(tc_prod(X12,X18),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X12,X18),tc_HOL_Obool))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Prod__UNIV) ).

fof(fact_less__add__eq__less,axiom,
    ! [X24,X23,X26,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),X26))
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23),X26) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),X24)
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23),X24)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__eq__less) ).

fof(fact_subset__insertI,axiom,
    ! [X29,X14,X12] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X14),c_Set_Oinsert(X12,X29,X14))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insertI) ).

fof(fact_Suc__lessD,axiom,
    ! [X24,X23] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X23)),X24))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23),X24)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__lessD) ).

fof(fact_Suc__mono,axiom,
    ! [X24,X23] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23),X24))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X23)),hAPP(c_Nat_OSuc,X24))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mono) ).

fof(fact_termination__basic__simps_I3_J,axiom,
    ! [X35,X30,X31] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),X30))
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X35))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I3_J) ).

fof(fact_trans__le__add1,axiom,
    ! [X23,X19,X20] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20),X19))
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X23))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__le__add1) ).

fof(fact_termination__basic__simps_I4_J,axiom,
    ! [X30,X35,X31] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),X35))
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X35))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I4_J) ).

fof(fact_trans__le__add2,axiom,
    ! [X23,X19,X20] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20),X19))
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23),X19))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__le__add2) ).

fof(fact_finite__fun__UNIVD2,axiom,
    ! [X18,X12] :
      ( c_Finite__Set_Ofinite(tc_fun(X12,X18),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X12,X18),tc_HOL_Obool)))
     => c_Finite__Set_Ofinite(X18,c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__fun__UNIVD2) ).

fof(fact_nat__add__assoc,axiom,
    ! [X25,X24,X23] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23),X24)),X25) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X25)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__assoc) ).

fof(fact_less__eq__Suc__le,axiom,
    ! [X21,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10),X21))
    <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X10)),X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__Suc__le) ).

fof(fact_Suc__le__eq,axiom,
    ! [X10,X21] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X21)),X10))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X10)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__eq) ).

fof(fact_Suc__le__lessD,axiom,
    ! [X24,X23] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X23)),X24))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23),X24)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__lessD) ).

fof(fact_predicate1D,axiom,
    ! [X9,X50,X32,X12] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X32),X50))
     => ( hBOOL(hAPP(X32,X9))
       => hBOOL(hAPP(X50,X9)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_predicate1D) ).

fof(fact_rev__predicate1D,axiom,
    ! [X50,X12,X9,X32] :
      ( hBOOL(hAPP(X32,X9))
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X32),X50))
       => hBOOL(hAPP(X50,X9)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__predicate1D) ).

fof(fact_order__trans,axiom,
    ! [X35,X30,X31,X12] :
      ( class_Orderings_Opreorder(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X31),X30))
       => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X30),X35))
         => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X31),X35)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__trans) ).

fof(fact_xt1_I6_J,axiom,
    ! [X35,X31,X30,X12] :
      ( class_Orderings_Oorder(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X30),X31))
       => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X35),X30))
         => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X35),X31)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I6_J) ).

fof(fact_Suc__lessI,axiom,
    ! [X24,X23] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23),X24))
     => ( hAPP(c_Nat_OSuc,X23) != X24
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X23)),X24)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__lessI) ).

fof(fact_less__add__one,axiom,
    ! [X11,X12] :
      ( class_Rings_Olinordered__semidom(X12)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X11),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X11),c_Groups_Oone__class_Oone(X12)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__one) ).

fof(fact_le__less__Suc__eq,axiom,
    ! [X10,X21] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21),X10))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10),hAPP(c_Nat_OSuc,X21)))
      <=> X10 = X21 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__less__Suc__eq) ).

fof(fact_Suc__leD,axiom,
    ! [X24,X23] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X23)),X24))
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X23),X24)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__leD) ).

fof(fact_finite__nat__set__iff__bounded,axiom,
    ! [X51] :
      ( c_Finite__Set_Ofinite(tc_Nat_Onat,X51)
    <=> ? [X5] :
        ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),X51))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X5)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded) ).

fof(fact_insert__commute,axiom,
    ! [X15,X8,X9,X12] : c_Set_Oinsert(X12,X9,c_Set_Oinsert(X12,X8,X15)) = c_Set_Oinsert(X12,X8,c_Set_Oinsert(X12,X9,X15)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__commute) ).

fof(fact_insertI1,axiom,
    ! [X14,X29,X12] : hBOOL(hAPP(hAPP(c_member(X12),X29),c_Set_Oinsert(X12,X29,X14))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertI1) ).

fof(fact_less__Suc__eq,axiom,
    ! [X10,X21] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),hAPP(c_Nat_OSuc,X10)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X10))
        | X21 = X10 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq) ).

fof(fact_Suc__leI,axiom,
    ! [X24,X23] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23),X24))
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X23)),X24)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__leI) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
    ! [X39,X40,X11,X12] :
      ( class_Rings_Ocomm__semiring__1(X12)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X11),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X40),X39)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X40),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X11),X39)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).

fof(fact_le__trans,axiom,
    ! [X25,X19,X20] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20),X19))
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19),X25))
       => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20),X25)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__trans) ).

fof(fact_finite__subset,axiom,
    ! [X14,X15,X12] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X15),X14))
     => ( c_Finite__Set_Ofinite(X12,X14)
       => c_Finite__Set_Ofinite(X12,X15) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__subset) ).

fof(fact_rev__finite__subset,axiom,
    ! [X15,X14,X12] :
      ( c_Finite__Set_Ofinite(X12,X14)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X15),X14))
       => c_Finite__Set_Ofinite(X12,X15) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__finite__subset) ).

fof(fact_less__iff__Suc__add,axiom,
    ! [X10,X21] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X10))
    <=> ? [X27] : X10 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X27)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).

fof(fact_less__Suc__eq__le,axiom,
    ! [X10,X21] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),hAPP(c_Nat_OSuc,X10)))
    <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21),X10)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).

fof(fact_finite__nat__set__iff__bounded__le,axiom,
    ! [X51] :
      ( c_Finite__Set_Ofinite(tc_Nat_Onat,X51)
    <=> ? [X5] :
        ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),X51))
         => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X5)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded__le) ).

fof(fact_less__SucI,axiom,
    ! [X24,X23] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23),X24))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23),hAPP(c_Nat_OSuc,X24))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__SucI) ).

fof(fact_Ints__double__eq__0__iff,axiom,
    ! [X29,X12] :
      ( class_Int_Oring__char__0(X12)
     => ( hBOOL(hAPP(hAPP(c_member(X12),X29),c_Int_Oring__1__class_OInts(X12)))
       => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),X29) = c_Groups_Ozero__class_Ozero(X12)
        <=> X29 = c_Groups_Ozero__class_Ozero(X12) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__double__eq__0__iff) ).

fof(fact_nat__case__Suc,axiom,
    ! [X62,X69,X70,X12] : c_Nat_Onat_Onat__case(X12,X70,X69,hAPP(c_Nat_OSuc,X62)) = hAPP(X69,X62),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__case__Suc) ).

fof(fact_le__Suc__eq,axiom,
    ! [X10,X21] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21),hAPP(c_Nat_OSuc,X10)))
    <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21),X10))
        | X21 = hAPP(c_Nat_OSuc,X10) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__Suc__eq) ).

fof(fact_subset__UNIV,axiom,
    ! [X15,X12] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X15),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__UNIV) ).

fof(fact_nat__less__cases,axiom,
    ! [X32,X10,X21] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X10))
       => hBOOL(hAPP(hAPP(X32,X10),X21)) )
     => ( ( X21 = X10
         => hBOOL(hAPP(hAPP(X32,X10),X21)) )
       => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10),X21))
           => hBOOL(hAPP(hAPP(X32,X10),X21)) )
         => hBOOL(hAPP(hAPP(X32,X10),X21)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__cases) ).

fof(fact_nat__add__left__commute,axiom,
    ! [X35,X30,X31] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X35)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),X35)),
    file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_order__antisym__conv) ).

fof(fact_order__antisym,axiom,
    ! [X30,X31,X12] :
      ( class_Orderings_Oorder(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X31),X30))
       => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X30),X31))
         => X31 = X30 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__antisym) ).

fof(fact_xt1_I5_J,axiom,
    ! [X31,X30,X12] :
      ( class_Orderings_Oorder(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X30),X31))
       => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X31),X30))
         => X31 = X30 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I5_J) ).

fof(fact_card__ge__0__finite,axiom,
    ! [X15,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,X15)))
     => c_Finite__Set_Ofinite(X12,X15) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__ge__0__finite) ).

fof(fact_le__imp__less__Suc,axiom,
    ! [X24,X23] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X23),X24))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23),hAPP(c_Nat_OSuc,X24))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__less__Suc) ).

fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
    ! [X15,X12] :
      ( c_Finite__Set_Ofinite(X12,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))
     => ( c_Finite__Set_Ocard(X12,X15) = c_Finite__Set_Ocard(X12,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))
       => X15 = c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_order__less__le) ).

fof(fact_order__less__imp__le,axiom,
    ! [X30,X31,X12] :
      ( class_Orderings_Opreorder(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X31),X30))
       => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X31),X30)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__le) ).

fof(fact_le__add1,axiom,
    ! [X23,X24] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X23))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add1) ).

fof(fact_le__add2,axiom,
    ! [X23,X24] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23),X24))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add2) ).

fof(fact_image__ident,axiom,
    ! [X68,X12] : c_Set_Oimage(X12,X12,c_COMBI(X12),X68) = X68,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__ident) ).

fof(fact_inj__on__id2,axiom,
    ! [X15,X12] : c_Fun_Oinj__on(X12,X12,c_COMBI(X12),X15),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__id2) ).

fof(fact_nat__case__0,axiom,
    ! [X69,X70,X12] : c_Nat_Onat_Onat__case(X12,X70,X69,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X70,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__case__0) ).

fof(fact_xt1_I11_J,axiom,
    ! [X11,X41,X12] :
      ( class_Orderings_Oorder(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X41),X11))
       => ( X11 != X41
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X41),X11)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I11_J) ).

fof(fact_order__le__neq__trans,axiom,
    ! [X41,X11,X12] :
      ( class_Orderings_Oorder(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X11),X41))
       => ( X11 != X41
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X11),X41)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__neq__trans) ).

fof(fact_order__le__imp__less__or__eq,axiom,
    ! [X30,X31,X12] :
      ( class_Orderings_Oorder(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X31),X30))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X31),X30))
          | X31 = X30 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__imp__less__or__eq) ).

fof(fact_order__neq__le__trans,axiom,
    ! [X41,X11,X12] :
      ( class_Orderings_Oorder(X12)
     => ( X11 != X41
       => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X11),X41))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X11),X41)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).

fof(fact_xt1_I12_J,axiom,
    ! [X41,X11,X12] :
      ( class_Orderings_Oorder(X12)
     => ( X11 != X41
       => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X41),X11))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X41),X11)) ) ) ),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_less__Suc0) ).

fof(fact_inj__Suc,axiom,
    ! [X51] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X51),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__Suc) ).

fof(fact_le__antisym,axiom,
    ! [X24,X23] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X23),X24))
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24),X23))
       => X23 = X24 ) ),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_eq__mem) ).

fof(fact_le__SucI,axiom,
    ! [X24,X23] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X23),X24))
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X23),hAPP(c_Nat_OSuc,X24))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SucI) ).

fof(fact_termination__basic__simps_I5_J,axiom,
    ! [X30,X31] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31),X30))
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),X30)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).

fof(fact_nat__less__le,axiom,
    ! [X10,X21] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X10))
    <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21),X10))
        & X21 != X10 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__le) ).

fof(fact_le__eq__less__or__eq,axiom,
    ! [X10,X21] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21),X10))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X10))
        | X21 = X10 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).

fof(fact_less__imp__le__nat,axiom,
    ! [X24,X23] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23),X24))
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X23),X24)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).

fof(fact_less__or__eq__imp__le,axiom,
    ! [X24,X23] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23),X24))
        | X23 = X24 )
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X23),X24)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).

fof(fact_insert__absorb,axiom,
    ! [X15,X29,X12] :
      ( hBOOL(hAPP(hAPP(c_member(X12),X29),X15))
     => c_Set_Oinsert(X12,X29,X15) = X15 ),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).

fof(fact_linorder__less__linear,axiom,
    ! [X30,X31,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X31),X30))
        | X31 = X30
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X30),X31)) ) ),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_finite__option__UNIV) ).

fof(fact_le__neq__implies__less,axiom,
    ! [X24,X23] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X23),X24))
     => ( X23 != X24
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23),X24)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).

fof(fact_insert__absorb2,axiom,
    ! [X15,X9,X12] : c_Set_Oinsert(X12,X9,c_Set_Oinsert(X12,X9,X15)) = c_Set_Oinsert(X12,X9,X15),
    file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_UNIV__I) ).

fof(fact_finite__insert,axiom,
    ! [X15,X29,X12] :
      ( c_Finite__Set_Ofinite(X12,c_Set_Oinsert(X12,X29,X15))
    <=> c_Finite__Set_Ofinite(X12,X15) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__insert) ).

fof(fact_mem__def,axiom,
    ! [X15,X9,X12] :
      ( hBOOL(hAPP(hAPP(c_member(X12),X9),X15))
    <=> hBOOL(hAPP(X15,X9)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__def) ).

fof(fact_linorder__le__less__linear,axiom,
    ! [X30,X31,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X31),X30))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X30),X31)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).

fof(fact_add__Suc,axiom,
    ! [X24,X23] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X23)),X24) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23),X24)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc) ).

fof(fact_le__iff__add,axiom,
    ! [X10,X21] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21),X10))
    <=> ? [X27] : X10 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X27) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__add) ).

fof(fact_nat__neq__iff,axiom,
    ! [X10,X21] :
      ( X21 != X10
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X10))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10),X21)) ) ),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).

fof(fact_order__less__imp__not__eq2,axiom,
    ! [X30,X31,X12] :
      ( class_Orderings_Oorder(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X31),X30))
       => X30 != X31 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).

fof(fact_order__less__imp__not__eq,axiom,
    ! [X30,X31,X12] :
      ( class_Orderings_Oorder(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X31),X30))
       => X31 != X30 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).

fof(fact_less__imp__neq,axiom,
    ! [X30,X31,X12] :
      ( class_Orderings_Oorder(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X31),X30))
       => X31 != X30 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__neq) ).

fof(fact_equalityD1,axiom,
    ! [X12,X14,X15] :
      ( X15 = X14
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X15),X14)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityD1) ).

fof(fact_equalityD2,axiom,
    ! [X12,X14,X15] :
      ( X15 = X14
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X14),X15)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityD2) ).

fof(fact_subset__refl,axiom,
    ! [X15,X12] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X15),X15)),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_neq0__conv) ).

fof(fact_add__right__imp__eq,axiom,
    ! [X40,X11,X41,X12] :
      ( class_Groups_Ocancel__semigroup__add(X12)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X41),X11) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X40),X11)
       => X41 = X40 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__imp__eq) ).

fof(fact_add__right__cancel,axiom,
    ! [X13,X29,X28,X12] :
      ( class_Groups_Ocancel__semigroup__add(X12)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X28),X29) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X13),X29)
      <=> X28 = X13 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__cancel) ).

fof(fact_add__imp__eq,axiom,
    ! [X40,X41,X11,X12] :
      ( class_Groups_Ocancel__ab__semigroup__add(X12)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X11),X41) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X11),X40)
       => X41 = X40 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__imp__eq) ).

fof(fact_add__left__imp__eq,axiom,
    ! [X40,X41,X11,X12] :
      ( class_Groups_Ocancel__semigroup__add(X12)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X11),X41) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X11),X40)
       => X41 = X40 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).

fof(fact_add__left__cancel,axiom,
    ! [X13,X28,X29,X12] :
      ( class_Groups_Ocancel__semigroup__add(X12)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),X28) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),X13)
      <=> X28 = X13 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__cancel) ).

fof(fact_linorder__linear,axiom,
    ! [X30,X31,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X31),X30))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X30),X31)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__linear) ).

fof(fact_add__Suc__right,axiom,
    ! [X24,X23] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23),hAPP(c_Nat_OSuc,X24)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23),X24)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__right) ).

fof(fact_add__Suc__shift,axiom,
    ! [X24,X23] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X23)),X24) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23),hAPP(c_Nat_OSuc,X24)),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_nat_Osize_I4_J) ).

fof(fact_gr__implies__not0,axiom,
    ! [X24,X23] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23),X24))
     => X24 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr__implies__not0) ).

fof(fact_nat__le__linear,axiom,
    ! [X24,X23] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X23),X24))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24),X23)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__linear) ).

fof(fact_zero__less__Suc,axiom,
    ! [X24] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X24))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__Suc) ).

fof(fact_less__not__refl2,axiom,
    ! [X23,X24] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X23))
     => X23 != X24 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl2) ).

fof(fact_less__not__refl3,axiom,
    ! [X33,X34] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34),X33))
     => X34 != X33 ),
    file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_Ints__1) ).

fof(fact_nat__add__right__cancel,axiom,
    ! [X10,X22,X21] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X22) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10),X22)
    <=> X21 = X10 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).

fof(fact_nat__add__left__cancel,axiom,
    ! [X10,X21,X22] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22),X21) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22),X10)
    <=> X21 = X10 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).

fof(fact_finite_OinsertI,axiom,
    ! [X29,X15,X12] :
      ( c_Finite__Set_Ofinite(X12,X15)
     => c_Finite__Set_Ofinite(X12,c_Set_Oinsert(X12,X29,X15)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite_OinsertI) ).

fof(fact_lessI,axiom,
    ! [X24] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),hAPP(c_Nat_OSuc,X24))),
    file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_le__0__eq) ).

fof(fact_add__is__1,axiom,
    ! [X10,X21] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X10) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    <=> ( ( X21 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & X10 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( X21 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & X10 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__is__1) ).

fof(fact_one__is__add,axiom,
    ! [X10,X21] :
      ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X10)
    <=> ( ( X21 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & X10 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( X21 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & X10 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
    file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_nat_Osize_I2_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
    ! [X40,X11,X12] :
      ( class_Rings_Ocomm__semiring__1(X12)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X11),X40) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X40),X11) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).

fof(fact_gr0I,axiom,
    ! [X24] :
      ( X24 != 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)),X24)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0I) ).

fof(fact_top__greatest,axiom,
    ! [X31,X12] :
      ( class_Orderings_Otop(X12)
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X31),c_Orderings_Otop__class_Otop(X12))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_top__greatest) ).

fof(fact_double__eq__0__iff,axiom,
    ! [X29,X12] :
      ( class_Groups_Olinordered__ab__group__add(X12)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),X29) = c_Groups_Ozero__class_Ozero(X12)
      <=> X29 = c_Groups_Ozero__class_Ozero(X12) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__eq__0__iff) ).

fof(fact_double__zero__sym,axiom,
    ! [X29,X12] :
      ( class_Groups_Olinordered__ab__group__add(X12)
     => ( c_Groups_Ozero__class_Ozero(X12) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X29),X29)
      <=> X29 = c_Groups_Ozero__class_Ozero(X12) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__zero__sym) ).

fof(fact_add__0__iff,axiom,
    ! [X29,X28,X12] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X12)
     => ( X28 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X28),X29)
      <=> X29 = c_Groups_Ozero__class_Ozero(X12) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__iff) ).

fof(fact_order__eq__refl,axiom,
    ! [X30,X31,X12] :
      ( class_Orderings_Opreorder(X12)
     => ( X31 = X30
       => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X31),X30)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__eq__refl) ).

fof(help_c__COMBK__1,axiom,
    ! [X82,X81,X18,X12] : hAPP(hAPP(c_COMBK(X12,X18),X81),X82) = X81,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBK__1) ).

fof(fact_nat__add__commute,axiom,
    ! [X24,X23] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23),X24) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X23),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__commute) ).

fof(fact_order__refl,axiom,
    ! [X31,X12] :
      ( class_Orderings_Opreorder(X12)
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X31),X31)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__refl) ).

fof(fact_less__eq__nat_Osimps_I1_J,axiom,
    ! [X24] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X24)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).

fof(fact_le0,axiom,
    ! [X24] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X24)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le0) ).

fof(fact_top__apply,axiom,
    ! [X9,X18,X12] :
      ( class_Orderings_Otop(X12)
     => hAPP(c_Orderings_Otop__class_Otop(tc_fun(X18,X12)),X9) = c_Orderings_Otop__class_Otop(X12) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_top__apply) ).

fof(fact_add__is__0,axiom,
    ! [X10,X21] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X10) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ( X21 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & X10 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__is__0) ).

fof(fact_eq__imp__le,axiom,
    ! [X24,X23] :
      ( X23 = X24
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X23),X24)) ),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',help_c__fequal__2) ).

fof(fact_add__eq__self__zero,axiom,
    ! [X24,X23] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23),X24) = X23
     => X24 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).

fof(fact_le__refl,axiom,
    ! [X24] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24),X24)),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
    ! [X11,X12] :
      ( class_Rings_Ocomm__semiring__1(X12)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),c_Groups_Ozero__class_Ozero(X12)),X11) = X11 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).

fof(fact_add__0,axiom,
    ! [X11,X12] :
      ( class_Groups_Ocomm__monoid__add(X12)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),c_Groups_Ozero__class_Ozero(X12)),X11) = X11 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0) ).

fof(fact_add__0__left,axiom,
    ! [X11,X12] :
      ( class_Groups_Omonoid__add(X12)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),c_Groups_Ozero__class_Ozero(X12)),X11) = X11 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__left) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
    ! [X11,X12] :
      ( class_Rings_Ocomm__semiring__1(X12)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X11),c_Groups_Ozero__class_Ozero(X12)) = X11 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).

fof(fact_add_Ocomm__neutral,axiom,
    ! [X11,X12] :
      ( class_Groups_Ocomm__monoid__add(X12)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X11),c_Groups_Ozero__class_Ozero(X12)) = X11 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).

fof(fact_add__0__right,axiom,
    ! [X11,X12] :
      ( class_Groups_Omonoid__add(X12)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),X11),c_Groups_Ozero__class_Ozero(X12)) = X11 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__right) ).

fof(fact_Suc__eq__plus1__left,axiom,
    ! [X24] : hAPP(c_Nat_OSuc,X24) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X24),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).

fof(fact_Suc__eq__plus1,axiom,
    ! [X24] : hAPP(c_Nat_OSuc,X24) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).

fof(fact_plus__nat_Oadd__0,axiom,
    ! [X24] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X24) = X24,
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_less__eq__Suc__le__raw) ).

fof(fact_Nat_Oadd__0__right,axiom,
    ! [X23] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X23,
    file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',arity_prod__Finite__Set_Ofinite) ).

fof(fact_Suc__inject,axiom,
    ! [X30,X31] :
      ( hAPP(c_Nat_OSuc,X31) = hAPP(c_Nat_OSuc,X30)
     => X31 = X30 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__inject) ).

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

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

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

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

fof(fact_Suc__not__Zero,axiom,
    ! [X23] : hAPP(c_Nat_OSuc,X23) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__not__Zero) ).

fof(fact_nat_Osimps_I3_J,axiom,
    ! [X59] : hAPP(c_Nat_OSuc,X59) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osimps_I3_J) ).

fof(fact_Suc__neq__Zero,axiom,
    ! [X23] : hAPP(c_Nat_OSuc,X23) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__neq__Zero) ).

fof(fact_Zero__not__Suc,axiom,
    ! [X23] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X23),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).

fof(fact_nat_Osimps_I2_J,axiom,
    ! [X60] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X60),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osimps_I2_J) ).

fof(fact_Zero__neq__Suc,axiom,
    ! [X23] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X23),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).

fof(fact_finite__code,axiom,
    ! [X15,X12] :
      ( class_Finite__Set_Ofinite(X12)
     => c_Finite__Set_Ofinite(X12,X15) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__code) ).

fof(fact_finite,axiom,
    ! [X15,X12] :
      ( class_Finite__Set_Ofinite(X12)
     => c_Finite__Set_Ofinite(X12,X15) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite) ).

fof(fact_Suc__n__not__n,axiom,
    ! [X24] : hAPP(c_Nat_OSuc,X24) != X24,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).

fof(fact_n__not__Suc__n,axiom,
    ! [X24] : X24 != hAPP(c_Nat_OSuc,X24),
    file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',arity_Option__Ooption__Finite__Set_Ofinite) ).

fof(fact_nat__size,axiom,
    ! [X24] : c_Nat_Osize__class_Osize(tc_Nat_Onat,X24) = X24,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__size) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

fof(fact__096c_A_126_061_Ad_096,axiom,
    v_c____ != v_d____,
    file('/export/starexec/sandbox/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/sandbox/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_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____)) ) ) )
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____)))) ) ) ),
    introduced(definition) ).

fof(i_0_520,plain,
    ( v_c____ != v_e____
   => ( v_a____ != v_b____
     => ( 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____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),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_Ac_A_126_061_Ae_059_Aa_A_126_061_Ab_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_A_L_A1_Athen_ALab_Aelse_ALba_J_A_058_AProf_059_AALL_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_A_124_093_061_061_062_A_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_A_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]),c_0_519]) ).

fof(i_0_521,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_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(assume_negation,[status(cth)],[conj_0]) ).

fof(i_0_522,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_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____)) ) ) )
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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_equiv,[status(thm)],[i_0_519]) ).

fof(i_0_523,plain,
    ~ ! [X42] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),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),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),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),X42),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_524,plain,
    ! [X9,X15,X46,X1,X6,X2,X18,X12] :
      ( c_Finite__Set_Ofolding__image__simple(X12,X18,X2,X6,X1,X46)
     => ( c_Finite__Set_Ofinite(X18,X15)
       => ( ~ hBOOL(hAPP(hAPP(c_member(X18),X9),X15))
         => hAPP(X46,c_Set_Oinsert(X18,X9,X15)) = hAPP(hAPP(X2,hAPP(X1,X9)),hAPP(X46,X15)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_folding__image__simple_Oinsert]) ).

fof(i_0_525,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_526,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_527,plain,
    ! [X15,X2,X18,X12] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X12,c_Set_Oimage(X18,X12,X2,X15))),c_Finite__Set_Ocard(X18,X15)))
     => ~ c_Fun_Oinj__on(X18,X12,X2,X15) ),
    inference(fof_simplification,[status(thm)],[fact_pigeonhole]) ).

fof(i_0_528,plain,
    ! [X15,X12] :
      ( ( c_Finite__Set_Ofinite(X12,X15)
       => c_Finite__Set_Ocard(X12,X15) = 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),X15) )
      & ( ~ c_Finite__Set_Ofinite(X12,X15)
       => c_Finite__Set_Ocard(X12,X15) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_simplification,[status(thm)],[fact_card__def]) ).

fof(i_0_529,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_530,plain,
    ! [X28,X29,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),X29),X28)),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),X28),X29)),X7)) ) ),
    inference(fof_simplification,[status(thm)],[fact_Lin__irrefl]) ).

fof(i_0_531,plain,
    ! [X9,X14,X15,X2,X18,X12] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(X12,X18)),X2),c_FuncSet_OPi(X12,X18,X15,X14)))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X18),hAPP(X2,X9)),hAPP(X14,X9)))
       => ~ hBOOL(hAPP(hAPP(c_member(X12),X9),X15)) ) ),
    inference(fof_simplification,[status(thm)],[fact_PiE]) ).

fof(i_0_532,plain,
    ! [X14,X15,X9,X12] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X12),X9),X15))
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X15),c_Set_Oinsert(X12,X9,X14)))
      <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X15),X14)) ) ),
    inference(fof_simplification,[status(thm)],[fact_subset__insert]) ).

fof(i_0_533,plain,
    ~ ! [X45] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),X45))
       => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X45),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_534,plain,
    ~ ! [X44] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____)),X44))
       => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X44),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_535,plain,
    ! [X1,X2,X12,X18] :
      ( class_Orderings_Oord(X18)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12,X18)),X2),X1))
      <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,X18),X2),X1))
          & ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,X18),X1),X2)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_less__fun__def]) ).

fof(i_0_536,plain,
    ! [X24,X25,X23] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23),X25)),X24))
     => ~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X23),X24))
         => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X25),X24)) ) ),
    inference(fof_simplification,[status(thm)],[fact_add__leE]) ).

fof(i_0_537,plain,
    ! [X19,X20] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),X19)),X20)),
    inference(fof_simplification,[status(thm)],[fact_not__add__less1]) ).

fof(i_0_538,plain,
    ! [X20,X19] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X20)),X20)),
    inference(fof_simplification,[status(thm)],[fact_not__add__less2]) ).

fof(i_0_539,plain,
    ! [X10,X32] :
      ( ~ hBOOL(hAPP(X32,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
     => ( hBOOL(hAPP(X32,X10))
       => ? [X27] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X27),X10))
            & ! [X4] :
                ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),X27))
               => ~ hBOOL(hAPP(X32,X4)) )
            & hBOOL(hAPP(X32,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_ex__least__nat__less]) ).

fof(i_0_540,plain,
    ! [X28,X14,X29,X12] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X12),X29),X14))
       => X29 = X28 )
     => hBOOL(hAPP(hAPP(c_member(X12),X29),c_Set_Oinsert(X12,X28,X14))) ),
    inference(fof_simplification,[status(thm)],[fact_insertCI]) ).

fof(i_0_541,plain,
    ! [X14,X15,X9,X12] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X12),X9),X15))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X12),X9),X14))
       => ( c_Set_Oinsert(X12,X9,X15) = c_Set_Oinsert(X12,X9,X14)
        <=> X15 = X14 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_insert__ident]) ).

fof(i_0_542,plain,
    ! [X10,X21] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21),X10))
    <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X10)),X21)) ),
    inference(fof_simplification,[status(thm)],[fact_not__less__eq__eq]) ).

fof(i_0_543,plain,
    ! [X10,X21] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X10))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10),hAPP(c_Nat_OSuc,X21))) ),
    inference(fof_simplification,[status(thm)],[fact_not__less__eq]) ).

fof(i_0_544,plain,
    ! [X11,X41,X12] :
      ( class_Orderings_Oorder(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X41),X11))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X11),X41)) ) ),
    inference(fof_simplification,[status(thm)],[fact_xt1_I9_J]) ).

fof(i_0_545,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_546,plain,
    ! [X30,X31,X12] :
      ( class_Orderings_Opreorder(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X31),X30))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X30),X31)) ) ),
    inference(fof_simplification,[status(thm)],[fact_order__less__asym]) ).

fof(i_0_547,plain,
    ! [X41,X11,X12] :
      ( class_Orderings_Opreorder(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X11),X41))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X41),X11)) ) ),
    inference(fof_simplification,[status(thm)],[fact_order__less__asym_H]) ).

fof(i_0_548,plain,
    ! [X30,X31,X12] :
      ( class_Orderings_Opreorder(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X31),X30))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X30),X31)) ) ),
    inference(fof_simplification,[status(thm)],[fact_order__less__imp__not__less]) ).

fof(i_0_549,plain,
    ! [X30,X31,X12] :
      ( class_Orderings_Opreorder(X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X31),X30))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X30),X31)) ) ),
    inference(fof_simplification,[status(thm)],[fact_order__less__not__sym]) ).

fof(i_0_550,plain,
    ! [X9,X15,X12] :
      ( c_Finite__Set_Ofinite(X12,X15)
     => ( ~ hBOOL(hAPP(hAPP(c_member(X12),X9),X15))
       => c_Finite__Set_Ocard(X12,c_Set_Oinsert(X12,X9,X15)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Finite__Set_Ocard(X12,X15)) ) ),
    inference(fof_simplification,[status(thm)],[fact_card_Oinsert]) ).

fof(i_0_551,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_552,plain,
    ! [X9,X15,X12] :
      ( c_Finite__Set_Ofinite(X12,X15)
     => ( ( hBOOL(hAPP(hAPP(c_member(X12),X9),X15))
         => c_Finite__Set_Ocard(X12,c_Set_Oinsert(X12,X9,X15)) = c_Finite__Set_Ocard(X12,X15) )
        & ( ~ hBOOL(hAPP(hAPP(c_member(X12),X9),X15))
         => c_Finite__Set_Ocard(X12,c_Set_Oinsert(X12,X9,X15)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X12,X15)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_card__insert__if]) ).

fof(i_0_553,plain,
    ! [X21,X10] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10),X21))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10),hAPP(c_Nat_OSuc,X21)))
      <=> X10 = X21 ) ),
    inference(fof_simplification,[status(thm)],[fact_not__less__less__Suc__eq]) ).

fof(i_0_554,plain,
    ! [X23,X24] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X23))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),hAPP(c_Nat_OSuc,X23)))
       => X23 = X24 ) ),
    inference(fof_simplification,[status(thm)],[fact_less__antisym]) ).

fof(i_0_555,plain,
    ! [X24,X23] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23),hAPP(c_Nat_OSuc,X24)))
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23),X24))
       => X23 = X24 ) ),
    inference(fof_simplification,[status(thm)],[fact_less__SucE]) ).

fof(i_0_556,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_557,plain,
    ! [X31,X30,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X30),X31))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X31),X30)) ) ),
    inference(fof_simplification,[status(thm)],[fact_leD]) ).

fof(i_0_558,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_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),X8),X9)) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__not__le]) ).

fof(i_0_560,plain,
    ! [X9,X15,X12] :
      ( c_Finite__Set_Ofinite(X12,X15)
     => ( ~ hBOOL(hAPP(hAPP(c_member(X12),X9),X15))
       => c_Finite__Set_Ocard(X12,c_Set_Oinsert(X12,X9,X15)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X12,X15)) ) ),
    inference(fof_simplification,[status(thm)],[fact_card__insert__disjoint]) ).

fof(i_0_561,plain,
    ! [X24,X23] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X23),hAPP(c_Nat_OSuc,X24)))
     => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X23),X24))
       => X23 = hAPP(c_Nat_OSuc,X24) ) ),
    inference(fof_simplification,[status(thm)],[fact_le__SucE]) ).

fof(i_0_562,plain,
    ! [X24] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X24)),X24)),
    inference(fof_simplification,[status(thm)],[fact_Suc__n__not__le__n]) ).

fof(i_0_563,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_564,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_565,plain,
    ! [X30,X31,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X31),X30))
       => ( X31 != X30
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X30),X31)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__cases]) ).

fof(i_0_566,plain,
    ! [X30,X31,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( X31 != X30
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X31),X30))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X30),X31)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__neqE]) ).

fof(i_0_567,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_568,plain,
    ! [X30,X31,X12] :
      ( class_Rings_Olinordered__idom(X12)
     => ( X31 != X30
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X31),X30))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X30),X31)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__neqE__linordered__idom]) ).

fof(i_0_569,plain,
    ! [X31,X30,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X30),X31))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X31),X30)) ) ),
    inference(fof_simplification,[status(thm)],[fact_not__leE]) ).

fof(i_0_570,plain,
    ! [X30,X31,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X31),X30))
       => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X30),X31)) ) ),
    inference(fof_simplification,[status(thm)],[fact_leI]) ).

fof(i_0_571,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_572,plain,
    ! [X30,X31] :
      ( X31 != X30
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31),X30))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30),X31)) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__neqE__nat]) ).

fof(i_0_573,plain,
    ! [X12,X14,X15] :
      ( X15 = X14
     => ~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X15),X14))
         => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool),X14),X15)) ) ),
    inference(fof_simplification,[status(thm)],[fact_equalityE]) ).

fof(i_0_574,plain,
    ! [X31,X12] :
      ( class_Orderings_Opreorder(X12)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),X31),X31)) ),
    inference(fof_simplification,[status(thm)],[fact_order__less__irrefl]) ).

fof(i_0_575,plain,
    ! [X30,X31,X12] :
      ( class_Orderings_Olinorder(X12)
     => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X31),X30))
       => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X12,X30),X31)) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__le__cases]) ).

fof(i_0_576,plain,
    ! [X24] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_simplification,[status(thm)],[fact_less__nat__zero__code]) ).

fof(i_0_577,plain,
    ! [X24] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_simplification,[status(thm)],[fact_not__less0]) ).

fof(i_0_578,plain,
    ! [X24] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_simplification,[status(thm)],[fact_less__zeroE]) ).

fof(i_0_579,plain,
    ! [X24] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X24)),
    inference(fof_simplification,[status(thm)],[fact_less__not__refl]) ).

fof(i_0_580,plain,
    ! [X24] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X24)),
    inference(fof_simplification,[status(thm)],[fact_less__irrefl__nat]) ).

fof(i_0_581,plain,
    ! [X8,X9] :
      ( ~ hBOOL(hAPP(hAPP(c_fequal,X9),X8))
      | X9 = X8 ),
    inference(fof_simplification,[status(thm)],[help_c__fequal__1]) ).

fof(i_0_582,plain,
    ! [X15,X12] :
      ( ~ c_Finite__Set_Ofinite(X12,X15)
     => c_Finite__Set_Ocard(X12,X15) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(fof_simplification,[status(thm)],[fact_card__infinite]) ).

fof(i_0_583,plain,
    ( v_c____ = v_e____
    | v_a____ = v_b____
    | ~ 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____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)),c_Arrow__Order__Mirabelle_OProf))
    | epred1_0 ),
    inference(fof_nnf,[status(thm)],[i_0_520]) ).

fof(i_0_584,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_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_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(fof_nnf,[status(thm)],[i_0_521]) ).

fof(i_0_585,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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_0)),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____,esk45_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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____))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_0)),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____,esk45_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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____)),v_Lba____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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____))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,esk45_0)),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____,esk45_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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____))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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____)),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____))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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____))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
      | hAPP(v_h____,esk45_0) != v_n____
      | hAPP(v_h____,esk45_0) = v_n____
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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____))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
      | hAPP(v_h____,esk45_0) != v_n____
      | hAPP(v_h____,esk45_0) = v_n____
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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____)),v_Lba____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
      | hAPP(v_h____,esk45_0) != v_n____
      | hAPP(v_h____,esk45_0) = v_n____
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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____))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,esk45_0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
      | hAPP(v_h____,esk45_0) != v_n____
      | hAPP(v_h____,esk45_0) = v_n____
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_0) != v_n____
      | hAPP(v_h____,esk45_0) = v_n____
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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____))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_0) != v_n____
      | hAPP(v_h____,esk45_0) = v_n____
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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____)),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____,esk45_0) != v_n____
      | hAPP(v_h____,esk45_0) = v_n____
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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____))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,esk45_0) != v_n____
      | hAPP(v_h____,esk45_0) = v_n____
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_0)),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____,esk45_0)),v_e____)))
      | hAPP(v_h____,esk45_0) = v_n____
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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____))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_0)),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____,esk45_0)),v_e____)))
      | hAPP(v_h____,esk45_0) = v_n____
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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____)),v_Lba____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_0)),v_e____)))
      | hAPP(v_h____,esk45_0) = v_n____
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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____))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,esk45_0)),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____,esk45_0)),v_e____)))
      | hAPP(v_h____,esk45_0) = v_n____
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_0)),v_e____)))
      | hAPP(v_h____,esk45_0) = v_n____
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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____))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_0)),v_e____)))
      | hAPP(v_h____,esk45_0) = v_n____
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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____)),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____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,esk45_0)),v_e____)))
      | hAPP(v_h____,esk45_0) = v_n____
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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____))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,esk45_0)),v_e____)))
      | hAPP(v_h____,esk45_0) = v_n____
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
      | hAPP(v_h____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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____))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
      | hAPP(v_h____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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____)),v_Lba____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
      | hAPP(v_h____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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____))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,esk45_0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
      | hAPP(v_h____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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____))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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____)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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____))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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____))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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____)),v_Lba____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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____))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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____))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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____)),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____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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____))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_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_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____))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_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_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____)),v_Lba____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_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_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____))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_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_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____))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_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_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____)),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____))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_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_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____))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
      | hAPP(v_h____,esk45_0) != v_n____
      | hAPP(v_h____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_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_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____))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
      | hAPP(v_h____,esk45_0) != v_n____
      | hAPP(v_h____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_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_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____)),v_Lba____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
      | hAPP(v_h____,esk45_0) != v_n____
      | hAPP(v_h____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_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_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____))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,esk45_0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
      | hAPP(v_h____,esk45_0) != v_n____
      | hAPP(v_h____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_0) != v_n____
      | hAPP(v_h____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_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_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____))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_0) != v_n____
      | hAPP(v_h____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_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_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____)),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____,esk45_0) != v_n____
      | hAPP(v_h____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_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_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____))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,esk45_0) != v_n____
      | hAPP(v_h____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_0)),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____,esk45_0)),v_e____)))
      | hAPP(v_h____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_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_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____))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_0)),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____,esk45_0)),v_e____)))
      | hAPP(v_h____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_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_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____)),v_Lba____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_0)),v_e____)))
      | hAPP(v_h____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_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_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____))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,esk45_0)),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____,esk45_0)),v_e____)))
      | hAPP(v_h____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_0)),v_e____)))
      | hAPP(v_h____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_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_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____))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_0)),v_e____)))
      | hAPP(v_h____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_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_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____)),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____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,esk45_0)),v_e____)))
      | hAPP(v_h____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_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_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____))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,esk45_0)),v_e____)))
      | hAPP(v_h____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
      | hAPP(v_h____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_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_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____))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
      | hAPP(v_h____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_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_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____)),v_Lba____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
      | hAPP(v_h____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_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_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____))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,esk45_0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
      | hAPP(v_h____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_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_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____))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_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_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____)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_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_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____))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_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_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____))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_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_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____)),v_Lba____))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_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_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____))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_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_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____))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_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_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____)),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____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_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_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____))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_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_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____))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_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_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____))))))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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____))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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____))))))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk45_0)),v_e____)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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____))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk45_0)),v_e____)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk45_0)),v_e____)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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____))))))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk45_0)),v_e____)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_522])])])]) ).

fof(i_0_586,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_587,plain,
    ! [X2211] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk12_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,X2211),esk12_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____)),X2211))),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),esk12_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_523])])])]) ).

fof(i_0_588,plain,
    ! [X1830] :
      ( 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,X1830),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____)),X1830))),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)],[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_589,plain,
    ! [X1637] : 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____)),X1637))),v_Lab____)),v_Lba____)),c_Arrow__Order__Mirabelle_OProf)),
    inference(variable_rename,[status(thm)],[fact_PiProf]) ).

fof(i_0_590,plain,
    ! [X1627] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1627),v_n____))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_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____)),X1627))),v_Lab____)),v_Lba____)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_n_I2_J])]) ).

fof(i_0_591,plain,
    ! [X1874,X1875,X1876,X1877] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1877,tc_fun(X1876,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X1877,tc_fun(tc_prod(X1877,X1876),tc_HOL_Obool),tc_fun(X1876,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1876,tc_fun(tc_fun(tc_prod(X1877,X1876),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1877,X1876),tc_HOL_Obool),tc_fun(X1876,tc_HOL_Obool)),X1877,c_COMBC(X1876,tc_fun(tc_prod(X1877,X1876),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1876,tc_prod(X1877,X1876)),tc_fun(X1876,tc_fun(tc_fun(tc_prod(X1877,X1876),tc_HOL_Obool),tc_HOL_Obool)),X1877,c_COMBB(tc_prod(X1877,X1876),tc_fun(tc_fun(tc_prod(X1877,X1876),tc_HOL_Obool),tc_HOL_Obool),X1876,c_member(tc_prod(X1877,X1876)))),c_Product__Type_OPair(X1877,X1876)))),X1875)),hAPP(hAPP(c_COMBC(X1877,tc_fun(tc_prod(X1877,X1876),tc_HOL_Obool),tc_fun(X1876,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1876,tc_fun(tc_fun(tc_prod(X1877,X1876),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1877,X1876),tc_HOL_Obool),tc_fun(X1876,tc_HOL_Obool)),X1877,c_COMBC(X1876,tc_fun(tc_prod(X1877,X1876),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1876,tc_prod(X1877,X1876)),tc_fun(X1876,tc_fun(tc_fun(tc_prod(X1877,X1876),tc_HOL_Obool),tc_HOL_Obool)),X1877,c_COMBB(tc_prod(X1877,X1876),tc_fun(tc_fun(tc_prod(X1877,X1876),tc_HOL_Obool),tc_HOL_Obool),X1876,c_member(tc_prod(X1877,X1876)))),c_Product__Type_OPair(X1877,X1876)))),X1874)))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1877,X1876),tc_HOL_Obool),X1875),X1874)) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1877,X1876),tc_HOL_Obool),X1875),X1874))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1877,tc_fun(X1876,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X1877,tc_fun(tc_prod(X1877,X1876),tc_HOL_Obool),tc_fun(X1876,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1876,tc_fun(tc_fun(tc_prod(X1877,X1876),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1877,X1876),tc_HOL_Obool),tc_fun(X1876,tc_HOL_Obool)),X1877,c_COMBC(X1876,tc_fun(tc_prod(X1877,X1876),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1876,tc_prod(X1877,X1876)),tc_fun(X1876,tc_fun(tc_fun(tc_prod(X1877,X1876),tc_HOL_Obool),tc_HOL_Obool)),X1877,c_COMBB(tc_prod(X1877,X1876),tc_fun(tc_fun(tc_prod(X1877,X1876),tc_HOL_Obool),tc_HOL_Obool),X1876,c_member(tc_prod(X1877,X1876)))),c_Product__Type_OPair(X1877,X1876)))),X1875)),hAPP(hAPP(c_COMBC(X1877,tc_fun(tc_prod(X1877,X1876),tc_HOL_Obool),tc_fun(X1876,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1876,tc_fun(tc_fun(tc_prod(X1877,X1876),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1877,X1876),tc_HOL_Obool),tc_fun(X1876,tc_HOL_Obool)),X1877,c_COMBC(X1876,tc_fun(tc_prod(X1877,X1876),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1876,tc_prod(X1877,X1876)),tc_fun(X1876,tc_fun(tc_fun(tc_prod(X1877,X1876),tc_HOL_Obool),tc_HOL_Obool)),X1877,c_COMBB(tc_prod(X1877,X1876),tc_fun(tc_fun(tc_prod(X1877,X1876),tc_HOL_Obool),tc_HOL_Obool),X1876,c_member(tc_prod(X1877,X1876)))),c_Product__Type_OPair(X1877,X1876)))),X1874))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__subset__eq2])]) ).

fof(i_0_592,plain,
    ! [X1810,X1811,X1812,X1813,X1814,X1815] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1815),X1814)),hAPP(v_F,X1811)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1813),X1812)),hAPP(v_F,X1810)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1815),X1814)),hAPP(X1811,esk7_6(X1810,X1811,X1812,X1813,X1814,X1815))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1813),X1812)),hAPP(X1810,esk7_6(X1810,X1811,X1812,X1813,X1814,X1815))))
        | ~ 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))),X1810),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))),X1811),c_Arrow__Order__Mirabelle_OProf))
        | X1814 = X1813
        | X1815 = X1812
        | X1813 = X1812
        | X1815 = X1814 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1813),X1812)),hAPP(v_F,X1810)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1815),X1814)),hAPP(v_F,X1811)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1815),X1814)),hAPP(X1811,esk7_6(X1810,X1811,X1812,X1813,X1814,X1815))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1813),X1812)),hAPP(X1810,esk7_6(X1810,X1811,X1812,X1813,X1814,X1815))))
        | ~ 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))),X1810),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))),X1811),c_Arrow__Order__Mirabelle_OProf))
        | X1814 = X1813
        | X1815 = X1812
        | X1813 = X1812
        | X1815 = X1814 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1815),X1814)),hAPP(v_F,X1811)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1813),X1812)),hAPP(v_F,X1810)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1815),X1814)),hAPP(X1811,esk7_6(X1810,X1811,X1812,X1813,X1814,X1815))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1813),X1812)),hAPP(X1810,esk7_6(X1810,X1811,X1812,X1813,X1814,X1815))))
        | ~ 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))),X1810),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))),X1811),c_Arrow__Order__Mirabelle_OProf))
        | X1814 = X1813
        | X1815 = X1812
        | X1813 = X1812
        | X1815 = X1814 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1813),X1812)),hAPP(v_F,X1810)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1815),X1814)),hAPP(v_F,X1811)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1815),X1814)),hAPP(X1811,esk7_6(X1810,X1811,X1812,X1813,X1814,X1815))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1813),X1812)),hAPP(X1810,esk7_6(X1810,X1811,X1812,X1813,X1814,X1815))))
        | ~ 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))),X1810),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))),X1811),c_Arrow__Order__Mirabelle_OProf))
        | X1814 = X1813
        | X1815 = X1812
        | X1813 = X1812
        | X1815 = X1814 ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__C2_C])])])]) ).

fof(i_0_593,plain,
    ! [X1803,X1804,X1805,X1806,X1807,X1808] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1808),X1807)),hAPP(X1804,esk6_6(X1803,X1804,X1805,X1806,X1807,X1808))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1806),X1805)),hAPP(X1803,esk6_6(X1803,X1804,X1805,X1806,X1807,X1808))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1808),X1807)),hAPP(v_F,X1804)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1806),X1805)),hAPP(v_F,X1803)))
        | ~ 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))),X1803),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))),X1804),c_Arrow__Order__Mirabelle_OProf))
        | X1807 = X1806
        | X1808 = X1805
        | X1806 = X1805
        | X1808 = X1807 )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1808),X1807)),hAPP(X1804,esk6_6(X1803,X1804,X1805,X1806,X1807,X1808))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1806),X1805)),hAPP(X1803,esk6_6(X1803,X1804,X1805,X1806,X1807,X1808))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1808),X1807)),hAPP(v_F,X1804)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1806),X1805)),hAPP(v_F,X1803)))
        | ~ 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))),X1803),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))),X1804),c_Arrow__Order__Mirabelle_OProf))
        | X1807 = X1806
        | X1808 = X1805
        | X1806 = X1805
        | X1808 = X1807 ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__C1_C])])])]) ).

fof(i_0_594,plain,
    ! [X1790,X1791,X1792,X1793,X1794,X1795] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1795),X1794)),hAPP(v_F,X1791)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1793),X1792)),hAPP(v_F,X1790)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1795),X1794)),hAPP(X1791,esk4_6(X1790,X1791,X1792,X1793,X1794,X1795))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1793),X1792)),hAPP(X1790,esk4_6(X1790,X1791,X1792,X1793,X1794,X1795))))
        | ~ 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))),X1790),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))),X1791),c_Arrow__Order__Mirabelle_OProf))
        | X1793 = X1792
        | X1795 = X1794 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1793),X1792)),hAPP(v_F,X1790)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1795),X1794)),hAPP(v_F,X1791)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1795),X1794)),hAPP(X1791,esk4_6(X1790,X1791,X1792,X1793,X1794,X1795))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1793),X1792)),hAPP(X1790,esk4_6(X1790,X1791,X1792,X1793,X1794,X1795))))
        | ~ 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))),X1790),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))),X1791),c_Arrow__Order__Mirabelle_OProf))
        | X1793 = X1792
        | X1795 = X1794 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1795),X1794)),hAPP(v_F,X1791)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1793),X1792)),hAPP(v_F,X1790)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1795),X1794)),hAPP(X1791,esk4_6(X1790,X1791,X1792,X1793,X1794,X1795))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1793),X1792)),hAPP(X1790,esk4_6(X1790,X1791,X1792,X1793,X1794,X1795))))
        | ~ 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))),X1790),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))),X1791),c_Arrow__Order__Mirabelle_OProf))
        | X1793 = X1792
        | X1795 = X1794 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1793),X1792)),hAPP(v_F,X1790)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1795),X1794)),hAPP(v_F,X1791)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1795),X1794)),hAPP(X1791,esk4_6(X1790,X1791,X1792,X1793,X1794,X1795))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1793),X1792)),hAPP(X1790,esk4_6(X1790,X1791,X1792,X1793,X1794,X1795))))
        | ~ 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))),X1790),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))),X1791),c_Arrow__Order__Mirabelle_OProf))
        | X1793 = X1792
        | X1795 = X1794 ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pairwise__neutrality])])])]) ).

fof(i_0_595,plain,
    ! [X1644,X1645,X1646,X1647] :
      ( ( hAPP(hAPP(c_COMBC(X1647,tc_fun(tc_prod(X1647,X1646),tc_HOL_Obool),tc_fun(X1646,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1646,tc_fun(tc_fun(tc_prod(X1647,X1646),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1647,X1646),tc_HOL_Obool),tc_fun(X1646,tc_HOL_Obool)),X1647,c_COMBC(X1646,tc_fun(tc_prod(X1647,X1646),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1646,tc_prod(X1647,X1646)),tc_fun(X1646,tc_fun(tc_fun(tc_prod(X1647,X1646),tc_HOL_Obool),tc_HOL_Obool)),X1647,c_COMBB(tc_prod(X1647,X1646),tc_fun(tc_fun(tc_prod(X1647,X1646),tc_HOL_Obool),tc_HOL_Obool),X1646,c_member(tc_prod(X1647,X1646)))),c_Product__Type_OPair(X1647,X1646)))),X1645) != hAPP(hAPP(c_COMBC(X1647,tc_fun(tc_prod(X1647,X1646),tc_HOL_Obool),tc_fun(X1646,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1646,tc_fun(tc_fun(tc_prod(X1647,X1646),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1647,X1646),tc_HOL_Obool),tc_fun(X1646,tc_HOL_Obool)),X1647,c_COMBC(X1646,tc_fun(tc_prod(X1647,X1646),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1646,tc_prod(X1647,X1646)),tc_fun(X1646,tc_fun(tc_fun(tc_prod(X1647,X1646),tc_HOL_Obool),tc_HOL_Obool)),X1647,c_COMBB(tc_prod(X1647,X1646),tc_fun(tc_fun(tc_prod(X1647,X1646),tc_HOL_Obool),tc_HOL_Obool),X1646,c_member(tc_prod(X1647,X1646)))),c_Product__Type_OPair(X1647,X1646)))),X1644)
        | X1645 = X1644 )
      & ( X1645 != X1644
        | hAPP(hAPP(c_COMBC(X1647,tc_fun(tc_prod(X1647,X1646),tc_HOL_Obool),tc_fun(X1646,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1646,tc_fun(tc_fun(tc_prod(X1647,X1646),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1647,X1646),tc_HOL_Obool),tc_fun(X1646,tc_HOL_Obool)),X1647,c_COMBC(X1646,tc_fun(tc_prod(X1647,X1646),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1646,tc_prod(X1647,X1646)),tc_fun(X1646,tc_fun(tc_fun(tc_prod(X1647,X1646),tc_HOL_Obool),tc_HOL_Obool)),X1647,c_COMBB(tc_prod(X1647,X1646),tc_fun(tc_fun(tc_prod(X1647,X1646),tc_HOL_Obool),tc_HOL_Obool),X1646,c_member(tc_prod(X1647,X1646)))),c_Product__Type_OPair(X1647,X1646)))),X1645) = hAPP(hAPP(c_COMBC(X1647,tc_fun(tc_prod(X1647,X1646),tc_HOL_Obool),tc_fun(X1646,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1646,tc_fun(tc_fun(tc_prod(X1647,X1646),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1647,X1646),tc_HOL_Obool),tc_fun(X1646,tc_HOL_Obool)),X1647,c_COMBC(X1646,tc_fun(tc_prod(X1647,X1646),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1646,tc_prod(X1647,X1646)),tc_fun(X1646,tc_fun(tc_fun(tc_prod(X1647,X1646),tc_HOL_Obool),tc_HOL_Obool)),X1647,c_COMBB(tc_prod(X1647,X1646),tc_fun(tc_fun(tc_prod(X1647,X1646),tc_HOL_Obool),tc_HOL_Obool),X1646,c_member(tc_prod(X1647,X1646)))),c_Product__Type_OPair(X1647,X1646)))),X1644) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__equals__eq2])]) ).

fof(i_0_596,plain,
    ! [X2403,X2404,X2405,X2406,X2407] :
      ( ( hBOOL(hAPP(hAPP(c_member(X2407),esk28_5(X2403,X2404,X2405,X2406,X2407)),X2406))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X2407,X2405),tc_HOL_Obool),c_FuncSet_OPi(X2407,X2405,X2406,X2404)),c_FuncSet_OPi(X2407,X2405,X2406,X2403))) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2405,tc_HOL_Obool),hAPP(X2404,esk28_5(X2403,X2404,X2405,X2406,X2407))),hAPP(X2403,esk28_5(X2403,X2404,X2405,X2406,X2407))))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X2407,X2405),tc_HOL_Obool),c_FuncSet_OPi(X2407,X2405,X2406,X2404)),c_FuncSet_OPi(X2407,X2405,X2406,X2403))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__mono])])])]) ).

fof(i_0_597,plain,
    ! [X2409,X2410,X2411,X2412,X2413] :
      ( ( hBOOL(hAPP(hAPP(c_member(X2413),esk29_5(X2409,X2410,X2411,X2412,X2413)),X2412))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X2413,X2411)),X2410),c_FuncSet_OPi(X2413,X2411,X2412,X2409))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X2411),hAPP(X2410,esk29_5(X2409,X2410,X2411,X2412,X2413))),hAPP(X2409,esk29_5(X2409,X2410,X2411,X2412,X2413))))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X2413,X2411)),X2410),c_FuncSet_OPi(X2413,X2411,X2412,X2409))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__I])])])]) ).

fof(i_0_598,plain,
    ! [X2230,X2231,X2232,X2233,X2234,X2236,X2241,X2242] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2233),X2234)),hAPP(X2230,X2231)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2233),X2234)),hAPP(X2230,X2232)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2233),X2234)),hAPP(X2231,esk17_5(X2230,X2231,X2232,X2233,X2234))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2233),X2234)),hAPP(X2232,esk17_5(X2230,X2231,X2232,X2233,X2234))))
        | ~ 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))),X2232),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))),X2231),c_Arrow__Order__Mirabelle_OProf))
        | ~ c_Arrow__Order__Mirabelle_OIIA(X2230) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2233),X2234)),hAPP(X2230,X2232)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2233),X2234)),hAPP(X2230,X2231)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2233),X2234)),hAPP(X2231,esk17_5(X2230,X2231,X2232,X2233,X2234))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2233),X2234)),hAPP(X2232,esk17_5(X2230,X2231,X2232,X2233,X2234))))
        | ~ 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))),X2232),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))),X2231),c_Arrow__Order__Mirabelle_OProf))
        | ~ c_Arrow__Order__Mirabelle_OIIA(X2230) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2233),X2234)),hAPP(X2230,X2231)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2233),X2234)),hAPP(X2230,X2232)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2233),X2234)),hAPP(X2231,esk17_5(X2230,X2231,X2232,X2233,X2234))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2233),X2234)),hAPP(X2232,esk17_5(X2230,X2231,X2232,X2233,X2234))))
        | ~ 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))),X2232),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))),X2231),c_Arrow__Order__Mirabelle_OProf))
        | ~ c_Arrow__Order__Mirabelle_OIIA(X2230) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2233),X2234)),hAPP(X2230,X2232)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2233),X2234)),hAPP(X2230,X2231)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2233),X2234)),hAPP(X2231,esk17_5(X2230,X2231,X2232,X2233,X2234))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2233),X2234)),hAPP(X2232,esk17_5(X2230,X2231,X2232,X2233,X2234))))
        | ~ 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))),X2232),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))),X2231),c_Arrow__Order__Mirabelle_OProf))
        | ~ c_Arrow__Order__Mirabelle_OIIA(X2230) )
      & ( 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))),esk18_1(X2236)),c_Arrow__Order__Mirabelle_OProf))
        | c_Arrow__Order__Mirabelle_OIIA(X2236) )
      & ( 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))),esk19_1(X2236)),c_Arrow__Order__Mirabelle_OProf))
        | c_Arrow__Order__Mirabelle_OIIA(X2236) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk20_1(X2236)),esk21_1(X2236))),hAPP(esk18_1(X2236),X2241)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk20_1(X2236)),esk21_1(X2236))),hAPP(esk19_1(X2236),X2241)))
        | c_Arrow__Order__Mirabelle_OIIA(X2236) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk20_1(X2236)),esk21_1(X2236))),hAPP(esk19_1(X2236),X2242)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk20_1(X2236)),esk21_1(X2236))),hAPP(esk18_1(X2236),X2242)))
        | c_Arrow__Order__Mirabelle_OIIA(X2236) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk20_1(X2236)),esk21_1(X2236))),hAPP(X2236,esk18_1(X2236))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk20_1(X2236)),esk21_1(X2236))),hAPP(X2236,esk19_1(X2236))))
        | c_Arrow__Order__Mirabelle_OIIA(X2236) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk20_1(X2236)),esk21_1(X2236))),hAPP(X2236,esk18_1(X2236))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk20_1(X2236)),esk21_1(X2236))),hAPP(X2236,esk19_1(X2236))))
        | c_Arrow__Order__Mirabelle_OIIA(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_IIA__def])])])])])]) ).

fof(i_0_599,plain,
    ! [X1797,X1798,X1799,X1800,X1801] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1801),X1800)),hAPP(v_F,X1798)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1800),X1799)),hAPP(v_F,X1797)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1801),X1800)),hAPP(X1798,esk5_5(X1797,X1798,X1799,X1800,X1801))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1800),X1799)),hAPP(X1797,esk5_5(X1797,X1798,X1799,X1800,X1801))))
        | ~ 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))),X1797),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))),X1798),c_Arrow__Order__Mirabelle_OProf))
        | X1801 = X1799
        | X1800 = X1799
        | X1801 = X1800 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1800),X1799)),hAPP(v_F,X1797)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1801),X1800)),hAPP(v_F,X1798)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1801),X1800)),hAPP(X1798,esk5_5(X1797,X1798,X1799,X1800,X1801))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1800),X1799)),hAPP(X1797,esk5_5(X1797,X1798,X1799,X1800,X1801))))
        | ~ 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))),X1797),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))),X1798),c_Arrow__Order__Mirabelle_OProf))
        | X1801 = X1799
        | X1800 = X1799
        | X1801 = X1800 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1801),X1800)),hAPP(v_F,X1798)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1800),X1799)),hAPP(v_F,X1797)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1801),X1800)),hAPP(X1798,esk5_5(X1797,X1798,X1799,X1800,X1801))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1800),X1799)),hAPP(X1797,esk5_5(X1797,X1798,X1799,X1800,X1801))))
        | ~ 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))),X1797),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))),X1798),c_Arrow__Order__Mirabelle_OProf))
        | X1801 = X1799
        | X1800 = X1799
        | X1801 = X1800 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1800),X1799)),hAPP(v_F,X1797)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1801),X1800)),hAPP(v_F,X1798)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1801),X1800)),hAPP(X1798,esk5_5(X1797,X1798,X1799,X1800,X1801))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1800),X1799)),hAPP(X1797,esk5_5(X1797,X1798,X1799,X1800,X1801))))
        | ~ 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))),X1797),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))),X1798),c_Arrow__Order__Mirabelle_OProf))
        | X1801 = X1799
        | X1800 = X1799
        | X1801 = X1800 ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__C4_C])])])]) ).

fof(i_0_600,plain,
    ! [X2338,X2339] :
      ( ( 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))),esk22_2(X2338,X2339)),c_Arrow__Order__Mirabelle_OProf))
        | c_Arrow__Order__Mirabelle_Odictator(X2339,X2338)
        | ~ 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))),X2339),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)))) )
      & ( esk23_2(X2338,X2339) != esk24_2(X2338,X2339)
        | c_Arrow__Order__Mirabelle_Odictator(X2339,X2338)
        | ~ 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))),X2339),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),esk23_2(X2338,X2339)),esk24_2(X2338,X2339))),hAPP(esk22_2(X2338,X2339),X2338)))
        | c_Arrow__Order__Mirabelle_Odictator(X2339,X2338)
        | ~ 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))),X2339),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),esk23_2(X2338,X2339)),esk24_2(X2338,X2339))),hAPP(X2339,esk22_2(X2338,X2339))))
        | c_Arrow__Order__Mirabelle_Odictator(X2339,X2338)
        | ~ 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))),X2339),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_601,plain,
    ! [X2692,X2693,X2694,X2695,X2696,X2697,X2698,X2699] :
      ( ( X2697 = X2695
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X2699,X2699)),hAPP(hAPP(c_Product__Type_OPair(X2699,X2699),X2697),X2695)),X2693))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2699,X2698),tc_prod(X2699,X2698))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2699,X2698),tc_prod(X2699,X2698)),hAPP(hAPP(c_Product__Type_OPair(X2699,X2698),X2697),X2696)),hAPP(hAPP(c_Product__Type_OPair(X2699,X2698),X2695),X2694))),c_Wellfounded_Olex__prod(X2699,X2698,X2693,X2692))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2698,X2698)),hAPP(hAPP(c_Product__Type_OPair(X2698,X2698),X2696),X2694)),X2692))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X2699,X2699)),hAPP(hAPP(c_Product__Type_OPair(X2699,X2699),X2697),X2695)),X2693))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2699,X2698),tc_prod(X2699,X2698))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2699,X2698),tc_prod(X2699,X2698)),hAPP(hAPP(c_Product__Type_OPair(X2699,X2698),X2697),X2696)),hAPP(hAPP(c_Product__Type_OPair(X2699,X2698),X2695),X2694))),c_Wellfounded_Olex__prod(X2699,X2698,X2693,X2692))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2699,X2699)),hAPP(hAPP(c_Product__Type_OPair(X2699,X2699),X2697),X2695)),X2693))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2699,X2698),tc_prod(X2699,X2698))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2699,X2698),tc_prod(X2699,X2698)),hAPP(hAPP(c_Product__Type_OPair(X2699,X2698),X2697),X2696)),hAPP(hAPP(c_Product__Type_OPair(X2699,X2698),X2695),X2694))),c_Wellfounded_Olex__prod(X2699,X2698,X2693,X2692))) )
      & ( X2697 != X2695
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2698,X2698)),hAPP(hAPP(c_Product__Type_OPair(X2698,X2698),X2696),X2694)),X2692))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2699,X2698),tc_prod(X2699,X2698))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2699,X2698),tc_prod(X2699,X2698)),hAPP(hAPP(c_Product__Type_OPair(X2699,X2698),X2697),X2696)),hAPP(hAPP(c_Product__Type_OPair(X2699,X2698),X2695),X2694))),c_Wellfounded_Olex__prod(X2699,X2698,X2693,X2692))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__lex__prod])])]) ).

fof(i_0_602,plain,
    ! [X1785,X1786,X1787,X1788] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1788),X1787)),hAPP(v_F,X1786)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1787),X1788)),hAPP(v_F,X1785)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1788),X1787)),hAPP(X1786,esk3_4(X1785,X1786,X1787,X1788))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1787),X1788)),hAPP(X1785,esk3_4(X1785,X1786,X1787,X1788))))
        | ~ 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))),X1785),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))),X1786),c_Arrow__Order__Mirabelle_OProf))
        | X1788 = X1787 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1787),X1788)),hAPP(v_F,X1785)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1788),X1787)),hAPP(v_F,X1786)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1788),X1787)),hAPP(X1786,esk3_4(X1785,X1786,X1787,X1788))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1787),X1788)),hAPP(X1785,esk3_4(X1785,X1786,X1787,X1788))))
        | ~ 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))),X1785),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))),X1786),c_Arrow__Order__Mirabelle_OProf))
        | X1788 = X1787 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1788),X1787)),hAPP(v_F,X1786)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1787),X1788)),hAPP(v_F,X1785)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1788),X1787)),hAPP(X1786,esk3_4(X1785,X1786,X1787,X1788))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1787),X1788)),hAPP(X1785,esk3_4(X1785,X1786,X1787,X1788))))
        | ~ 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))),X1785),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))),X1786),c_Arrow__Order__Mirabelle_OProf))
        | X1788 = X1787 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1787),X1788)),hAPP(v_F,X1785)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1788),X1787)),hAPP(v_F,X1786)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1788),X1787)),hAPP(X1786,esk3_4(X1785,X1786,X1787,X1788))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1787),X1788)),hAPP(X1785,esk3_4(X1785,X1786,X1787,X1788))))
        | ~ 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))),X1785),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))),X1786),c_Arrow__Order__Mirabelle_OProf))
        | X1788 = X1787 ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__C3_C])])])]) ).

fof(i_0_603,plain,
    ! [X2881,X2882,X2883,X2884,X2885,X2886,X2887] :
      ( ~ c_Finite__Set_Ofolding__image__simple(X2887,X2886,X2885,X2884,X2883,X2882)
      | ~ c_Finite__Set_Ofinite(X2886,X2881)
      | hAPP(X2882,X2881) = c_Finite__Set_Ofold__image(X2887,X2886,X2885,X2883,X2884,X2881) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oeq__fold__g])]) ).

fof(i_0_604,plain,
    ! [X2965,X2966,X2967,X2968,X2969,X2971,X2972,X2973,X2974,X2975,X2976] :
      ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2967,tc_HOL_Obool),esk35_5(X2965,X2966,X2967,X2968,X2969)),X2965))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2969,tc_HOL_Obool),X2968),c_Set_Oimage(X2967,X2969,X2966,X2965))) )
      & ( X2968 = c_Set_Oimage(X2967,X2969,X2966,esk35_5(X2965,X2966,X2967,X2968,X2969))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2969,tc_HOL_Obool),X2968),c_Set_Oimage(X2967,X2969,X2966,X2965))) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2973,tc_HOL_Obool),X2976),X2971))
        | X2974 != c_Set_Oimage(X2973,X2975,X2972,X2976)
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2975,tc_HOL_Obool),X2974),c_Set_Oimage(X2973,X2975,X2972,X2971))) ) ),
    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_605,plain,
    ! [X2586,X2587,X2588,X2589,X2590,X2591,X2592] :
      ( ~ hBOOL(hAPP(X2592,X2591))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2590,X2590)),hAPP(hAPP(c_Product__Type_OPair(X2590,X2590),X2589),X2588)),hAPP(X2587,X2591)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2586,X2590),tc_prod(X2586,X2590))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2586,X2590),tc_prod(X2586,X2590)),hAPP(hAPP(c_Product__Type_OPair(X2586,X2590),X2591),X2589)),hAPP(hAPP(c_Product__Type_OPair(X2586,X2590),X2591),X2588))),c_Recdef_Osame__fst(X2586,X2590,X2592,X2587))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_same__fstI])]) ).

fof(i_0_606,plain,
    ! [X1955,X1956,X1957,X1958,X1959] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1957,X1958),X1956),X1955))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1958,hAPP(X1956,X1959)),hAPP(X1955,X1959)))
        | ~ class_Orderings_Oord(X1958) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1958,hAPP(X1956,esk9_4(X1955,X1956,X1957,X1958))),hAPP(X1955,esk9_4(X1955,X1956,X1957,X1958))))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1957,X1958),X1956),X1955))
        | ~ class_Orderings_Oord(X1958) ) ),
    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_607,plain,
    ! [X2460,X2461,X2462,X2463,X2464,X2465,X2466,X2467] :
      ( ~ c_Finite__Set_Ofolding__image__simple__idem(X2467,X2466,X2465,X2464,X2463,X2462)
      | ~ c_Finite__Set_Ofinite(X2466,X2461)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2466,tc_HOL_Obool),X2460),X2461))
      | hAPP(hAPP(X2465,hAPP(X2462,X2460)),hAPP(X2462,X2461)) = hAPP(X2462,X2461) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Osubset__idem])]) ).

fof(i_0_608,plain,
    ! [X2578,X2579,X2580,X2581,X2582,X2583,X2584,X2585] :
      ( ~ c_Finite__Set_Ofolding__image__simple(X2585,X2584,X2583,X2582,X2581,X2580)
      | ~ c_Finite__Set_Ofinite(X2584,X2579)
      | hBOOL(hAPP(hAPP(c_member(X2584),X2578),X2579))
      | hAPP(X2580,c_Set_Oinsert(X2584,X2578,X2579)) = hAPP(hAPP(X2583,hAPP(X2581,X2578)),hAPP(X2580,X2579)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_524])]) ).

fof(i_0_609,plain,
    ! [X2468,X2469,X2470,X2471,X2472,X2473,X2474,X2475] :
      ( ~ c_Finite__Set_Ofolding__image__simple__idem(X2475,X2474,X2473,X2472,X2471,X2470)
      | ~ c_Finite__Set_Ofinite(X2474,X2469)
      | ~ hBOOL(hAPP(hAPP(c_member(X2474),X2468),X2469))
      | hAPP(hAPP(X2473,hAPP(X2471,X2468)),hAPP(X2470,X2469)) = hAPP(X2470,X2469) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oin__idem])]) ).

fof(i_0_610,plain,
    ! [X2487,X2488,X2489,X2490,X2491,X2492,X2493,X2494] :
      ( ~ c_Finite__Set_Ofolding__image__simple__idem(X2494,X2493,X2492,X2491,X2490,X2489)
      | ~ c_Finite__Set_Ofinite(X2493,X2488)
      | hAPP(X2489,c_Set_Oinsert(X2493,X2487,X2488)) = hAPP(hAPP(X2492,hAPP(X2490,X2487)),hAPP(X2489,X2488)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oinsert__idem])]) ).

fof(i_0_611,plain,
    ! [X2498,X2499,X2500,X2501,X2502,X2503,X2504] :
      ( ~ c_Finite__Set_Ofolding__image__simple__idem(X2504,X2503,X2502,X2501,X2500,X2499)
      | hAPP(hAPP(X2502,X2498),X2498) = X2498 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oidem])]) ).

fof(i_0_612,plain,
    ! [X3118,X3119,X3120,X3121,X3122,X3123] :
      ( ~ c_Fun_Oinj__on(X3123,X3122,X3121,X3120)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3122,tc_HOL_Obool),c_Set_Oimage(X3123,X3122,X3121,X3120)),X3119))
      | ~ c_Fun_Oinj__on(X3122,X3123,X3118,X3119)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3123,tc_HOL_Obool),c_Set_Oimage(X3122,X3123,X3118,X3119)),X3120))
      | ~ c_Finite__Set_Ofinite(X3123,X3120)
      | ~ c_Finite__Set_Ofinite(X3122,X3119)
      | c_Finite__Set_Ocard(X3123,X3120) = c_Finite__Set_Ocard(X3122,X3119) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__bij__eq])]) ).

fof(i_0_613,plain,
    ! [X2220,X2221,X2222,X2223,X2225,X2229] :
      ( ( ~ c_Arrow__Order__Mirabelle_Ounanimity(X2220)
        | ~ 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))),X2221),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),X2222),X2223)),hAPP(X2221,esk13_4(X2220,X2221,X2222,X2223))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2222),X2223)),hAPP(X2220,X2221))) )
      & ( 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_1(X2225)),c_Arrow__Order__Mirabelle_OProf))
        | c_Arrow__Order__Mirabelle_Ounanimity(X2225) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_1(X2225)),esk16_1(X2225))),hAPP(esk14_1(X2225),X2229)))
        | c_Arrow__Order__Mirabelle_Ounanimity(X2225) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_1(X2225)),esk16_1(X2225))),hAPP(X2225,esk14_1(X2225))))
        | c_Arrow__Order__Mirabelle_Ounanimity(X2225) ) ),
    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_614,plain,
    ! [X1626] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1626)),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____,X1626)),v_n____))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1626)),v_n____)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1626)),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____,X1626)),v_n____))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1626)),v_n____)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1626)),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____,X1626) != v_n____
        | hAPP(v_h____,X1626) = v_n____
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1626)),v_n____)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1626)),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____,X1626) != v_n____
        | hAPP(v_h____,X1626) = v_n____
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1626)),v_n____)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1626)),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____,X1626)),v_e____)))
        | hAPP(v_h____,X1626) = v_n____
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1626)),v_n____)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1626)),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____,X1626)),v_e____)))
        | hAPP(v_h____,X1626) = v_n____
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1626)),v_n____)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1626)),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____,X1626) != v_n____
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,X1626)),v_c____),v_e____)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1626)),v_n____)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1626)),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____,X1626) != v_n____
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,X1626)),v_c____),v_e____)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1626)),v_n____)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1626)),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____,X1626)),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____,X1626)),v_c____),v_e____)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1626)),v_n____)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1626)),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____,X1626)),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____,X1626)),v_c____),v_e____)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1626)),v_n____)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1626)),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____,X1626)),v_n____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,X1626)),v_e____))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1626)),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____,X1626)),v_n____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,X1626)),v_e____))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1626)),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____,X1626) != v_n____
        | hAPP(v_h____,X1626) = v_n____
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,X1626)),v_e____))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1626)),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____,X1626) != v_n____
        | hAPP(v_h____,X1626) = v_n____
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,X1626)),v_e____))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1626)),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____,X1626)),v_e____)))
        | hAPP(v_h____,X1626) = v_n____
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,X1626)),v_e____))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1626)),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____,X1626)),v_e____)))
        | hAPP(v_h____,X1626) = v_n____
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,X1626)),v_e____))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1626)),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____,X1626) != v_n____
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,X1626)),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____,X1626)),v_e____))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1626)),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____,X1626) != v_n____
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,X1626)),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____,X1626)),v_e____))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1626)),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____,X1626)),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____,X1626)),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____,X1626)),v_e____))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1626)),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____,X1626)),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____,X1626)),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____,X1626)),v_e____))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1626)),v_n____))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,X1626)),v_e____)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1626)),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____,X1626)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
      & ( hAPP(v_h____,X1626) != v_n____
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,X1626)),v_c____),v_e____)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1626)),v_n____))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1626)),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____,X1626)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
      & ( hAPP(v_h____,X1626) = v_n____
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,X1626)),v_e____)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1626)),v_n____))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1626)),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____,X1626)),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____,X1626)),v_n____))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,X1626)),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____,X1626)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
      & ( hAPP(v_h____,X1626) != v_n____
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,X1626)),v_c____),v_e____)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1626)),v_n____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,X1626)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
      & ( hAPP(v_h____,X1626) = v_n____
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,X1626)),v_e____)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1626)),v_n____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,X1626)),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____,X1626)),v_n____))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,X1626)),v_e____)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1626)),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____,X1626) != v_n____
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,X1626)),v_c____),v_e____)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1626)),v_n____))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1626)),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____,X1626) = v_n____
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,X1626)),v_e____)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1626)),v_n____))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1626)),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____,X1626)),v_n____))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,X1626)),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____,X1626) != v_n____
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,X1626)),v_c____),v_e____)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1626)),v_n____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,X1626) = v_n____
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,X1626)),v_e____)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1626)),v_n____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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_525])])]) ).

fof(i_0_615,plain,
    ! [X2415,X2416,X2417,X2418,X2419,X2420] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2420,X2419)),X2418),c_FuncSet_OPi(X2420,X2419,X2417,hAPP(c_COMBK(tc_fun(X2419,tc_HOL_Obool),X2420),X2416))))
      | ~ c_Fun_Oinj__on(X2420,X2419,X2418,X2417)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2419,X2420)),X2415),c_FuncSet_OPi(X2419,X2420,X2416,hAPP(c_COMBK(tc_fun(X2420,tc_HOL_Obool),X2419),X2417))))
      | ~ c_Fun_Oinj__on(X2419,X2420,X2415,X2416)
      | ~ c_Finite__Set_Ofinite(X2420,X2417)
      | ~ c_Finite__Set_Ofinite(X2419,X2416)
      | c_Finite__Set_Ocard(X2420,X2417) = c_Finite__Set_Ocard(X2419,X2416) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__bij])]) ).

fof(i_0_616,plain,
    ! [X1890,X1891,X1892] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1892,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1892,tc_fun(X1892,tc_HOL_Obool),tc_HOL_Obool),c_member(X1892)),X1891)),hAPP(hAPP(c_COMBC(X1892,tc_fun(X1892,tc_HOL_Obool),tc_HOL_Obool),c_member(X1892)),X1890)))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1892,tc_HOL_Obool),X1891),X1890)) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1892,tc_HOL_Obool),X1891),X1890))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1892,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1892,tc_fun(X1892,tc_HOL_Obool),tc_HOL_Obool),c_member(X1892)),X1891)),hAPP(hAPP(c_COMBC(X1892,tc_fun(X1892,tc_HOL_Obool),tc_HOL_Obool),c_member(X1892)),X1890))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__subset__eq])]) ).

fof(i_0_617,plain,
    ! [X1636] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1636)),v_n____))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,X1636)),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____,X1636))) )
      & ( hAPP(v_h____,X1636) != v_n____
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,X1636)),v_c____),v_e____)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1636)),v_n____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,X1636))) )
      & ( hAPP(v_h____,X1636) = v_n____
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,X1636)),v_e____)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1636)),v_n____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,X1636))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1636)),v_n____))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1636)),v_n____))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,X1636))) )
      & ( hAPP(v_h____,X1636) != v_n____
        | hAPP(v_h____,X1636) = v_n____
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1636)),v_n____))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,X1636))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,X1636)),v_e____)))
        | hAPP(v_h____,X1636) = v_n____
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1636)),v_n____))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,X1636))) )
      & ( hAPP(v_h____,X1636) != v_n____
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,X1636)),v_c____),v_e____)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1636)),v_n____))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,X1636))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,X1636)),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____,X1636)),v_c____),v_e____)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1636)),v_n____))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,X1636))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1636)),v_n____))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,X1636)),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____,X1636))) )
      & ( hAPP(v_h____,X1636) != v_n____
        | hAPP(v_h____,X1636) = v_n____
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,X1636)),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____,X1636))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,X1636)),v_e____)))
        | hAPP(v_h____,X1636) = v_n____
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,X1636)),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____,X1636))) )
      & ( hAPP(v_h____,X1636) != v_n____
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,X1636)),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____,X1636)),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____,X1636))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,X1636)),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____,X1636)),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____,X1636)),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____,X1636))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_526])])]) ).

fof(i_0_618,plain,
    ! [X2900,X2901,X2902,X2903] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X2903,c_Set_Oimage(X2902,X2903,X2901,X2900))),c_Finite__Set_Ocard(X2902,X2900)))
      | ~ c_Fun_Oinj__on(X2902,X2903,X2901,X2900) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_527])]) ).

fof(i_0_619,plain,
    ! [X3130,X3131,X3132,X3133,X3134] :
      ( ( ~ c_Fun_Oinj__on(X3133,X3131,X3134,X3132)
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3131,tc_HOL_Obool),c_Set_Oimage(X3133,X3131,X3134,X3132)),X3130))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X3133,X3132)),c_Finite__Set_Ocard(X3131,X3130)))
        | ~ c_Finite__Set_Ofinite(X3131,X3130)
        | ~ c_Finite__Set_Ofinite(X3133,X3132) )
      & ( c_Fun_Oinj__on(X3133,X3131,esk40_4(X3130,X3131,X3132,X3133),X3132)
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X3133,X3132)),c_Finite__Set_Ocard(X3131,X3130)))
        | ~ c_Finite__Set_Ofinite(X3131,X3130)
        | ~ c_Finite__Set_Ofinite(X3133,X3132) )
      & ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3131,tc_HOL_Obool),c_Set_Oimage(X3133,X3131,esk40_4(X3130,X3131,X3132,X3133),X3132)),X3130))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X3133,X3132)),c_Finite__Set_Ocard(X3131,X3130)))
        | ~ c_Finite__Set_Ofinite(X3131,X3130)
        | ~ c_Finite__Set_Ofinite(X3133,X3132) ) ),
    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_620,plain,
    ! [X2062,X2063,X2064,X2065,X2066] :
      ( ( 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),X2063),X2062)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2064),X2066),X2065)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2064),c_Arrow__Order__Mirabelle_OLin))
        | X2066 = X2065 )
      & ( X2063 != X2065
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2066),X2062)),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),X2062)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2064),X2066),X2065)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2064),c_Arrow__Order__Mirabelle_OLin))
        | X2066 = X2065 )
      & ( X2062 != X2065
        | X2063 = X2066
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X2066)),X2064))
        | X2063 = X2065
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X2062)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2064),X2066),X2065)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2064),c_Arrow__Order__Mirabelle_OLin))
        | X2066 = X2065 )
      & ( X2062 = X2065
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X2062)),X2064))
        | X2063 = X2065
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X2062)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2064),X2066),X2065)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2064),c_Arrow__Order__Mirabelle_OLin))
        | X2066 = X2065 )
      & ( X2063 != X2065
        | X2063 = X2065
        | 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),X2063),X2062)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2064),X2066),X2065)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2064),c_Arrow__Order__Mirabelle_OLin))
        | X2066 = X2065 )
      & ( X2062 != X2065
        | X2062 = X2065
        | X2063 = X2065
        | 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),X2063),X2062)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2064),X2066),X2065)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2064),c_Arrow__Order__Mirabelle_OLin))
        | X2066 = X2065 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X2062)),X2064))
        | X2062 = X2065
        | X2063 = X2065
        | 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),X2063),X2062)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2064),X2066),X2065)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2064),c_Arrow__Order__Mirabelle_OLin))
        | X2066 = X2065 )
      & ( X2062 != X2065
        | X2063 != X2066
        | X2063 = X2065
        | 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),X2063),X2062)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2064),X2066),X2065)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2064),c_Arrow__Order__Mirabelle_OLin))
        | X2066 = X2065 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X2062)),X2064))
        | X2063 != X2066
        | X2063 = X2065
        | 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),X2063),X2062)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2064),X2066),X2065)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2064),c_Arrow__Order__Mirabelle_OLin))
        | X2066 = X2065 )
      & ( X2062 != X2065
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X2066)),X2064))
        | X2063 = X2065
        | 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),X2063),X2062)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2064),X2066),X2065)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2064),c_Arrow__Order__Mirabelle_OLin))
        | X2066 = X2065 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X2062)),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),X2066)),X2064))
        | X2063 = X2065
        | 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),X2063),X2062)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2064),X2066),X2065)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2064),c_Arrow__Order__Mirabelle_OLin))
        | X2066 = X2065 )
      & ( X2063 != X2065
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2066),X2062)),X2064))
        | 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),X2063),X2062)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2064),X2066),X2065)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2064),c_Arrow__Order__Mirabelle_OLin))
        | X2066 = X2065 )
      & ( X2062 != X2065
        | X2062 = X2065
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2066),X2062)),X2064))
        | 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),X2063),X2062)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2064),X2066),X2065)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2064),c_Arrow__Order__Mirabelle_OLin))
        | X2066 = X2065 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X2062)),X2064))
        | X2062 = X2065
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2066),X2062)),X2064))
        | 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),X2063),X2062)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2064),X2066),X2065)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2064),c_Arrow__Order__Mirabelle_OLin))
        | X2066 = X2065 )
      & ( X2062 != X2065
        | X2063 != X2066
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2066),X2062)),X2064))
        | 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),X2063),X2062)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2064),X2066),X2065)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2064),c_Arrow__Order__Mirabelle_OLin))
        | X2066 = X2065 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X2062)),X2064))
        | X2063 != X2066
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2066),X2062)),X2064))
        | 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),X2063),X2062)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2064),X2066),X2065)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2064),c_Arrow__Order__Mirabelle_OLin))
        | X2066 = X2065 )
      & ( X2062 != X2065
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X2066)),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),X2066),X2062)),X2064))
        | 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),X2063),X2062)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2064),X2066),X2065)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2064),c_Arrow__Order__Mirabelle_OLin))
        | X2066 = X2065 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X2062)),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),X2066)),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),X2066),X2062)),X2064))
        | 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),X2063),X2062)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2064),X2066),X2065)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2064),c_Arrow__Order__Mirabelle_OLin))
        | X2066 = X2065 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__above])])]) ).

fof(i_0_621,plain,
    ! [X2212,X2213,X2214,X2215,X2216] :
      ( ( X2213 != X2212
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2213),X2212)),c_Arrow__Order__Mirabelle_Obelow(X2214,X2216,X2215)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2214),c_Arrow__Order__Mirabelle_OLin))
        | X2216 = X2215 )
      & ( X2212 != X2216
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2213),X2215)),X2214))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2213),X2212)),c_Arrow__Order__Mirabelle_Obelow(X2214,X2216,X2215)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2214),c_Arrow__Order__Mirabelle_OLin))
        | X2216 = X2215 )
      & ( X2213 != X2216
        | X2212 = X2215
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2215),X2212)),X2214))
        | X2212 = X2216
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2213),X2212)),c_Arrow__Order__Mirabelle_Obelow(X2214,X2216,X2215)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2214),c_Arrow__Order__Mirabelle_OLin))
        | X2216 = X2215 )
      & ( X2213 = X2216
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2213),X2212)),X2214))
        | X2212 = X2216
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2213),X2212)),c_Arrow__Order__Mirabelle_Obelow(X2214,X2216,X2215)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2214),c_Arrow__Order__Mirabelle_OLin))
        | X2216 = X2215 )
      & ( X2212 != X2216
        | X2212 = X2216
        | X2213 = X2212
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2213),X2212)),c_Arrow__Order__Mirabelle_Obelow(X2214,X2216,X2215)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2214),c_Arrow__Order__Mirabelle_OLin))
        | X2216 = X2215 )
      & ( X2213 != X2216
        | X2213 = X2216
        | X2212 = X2216
        | X2213 = X2212
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2213),X2212)),c_Arrow__Order__Mirabelle_Obelow(X2214,X2216,X2215)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2214),c_Arrow__Order__Mirabelle_OLin))
        | X2216 = X2215 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2213),X2212)),X2214))
        | X2213 = X2216
        | X2212 = X2216
        | X2213 = X2212
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2213),X2212)),c_Arrow__Order__Mirabelle_Obelow(X2214,X2216,X2215)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2214),c_Arrow__Order__Mirabelle_OLin))
        | X2216 = X2215 )
      & ( X2213 != X2216
        | X2212 != X2215
        | X2212 = X2216
        | X2213 = X2212
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2213),X2212)),c_Arrow__Order__Mirabelle_Obelow(X2214,X2216,X2215)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2214),c_Arrow__Order__Mirabelle_OLin))
        | X2216 = X2215 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2213),X2212)),X2214))
        | X2212 != X2215
        | X2212 = X2216
        | X2213 = X2212
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2213),X2212)),c_Arrow__Order__Mirabelle_Obelow(X2214,X2216,X2215)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2214),c_Arrow__Order__Mirabelle_OLin))
        | X2216 = X2215 )
      & ( X2213 != X2216
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2215),X2212)),X2214))
        | X2212 = X2216
        | X2213 = X2212
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2213),X2212)),c_Arrow__Order__Mirabelle_Obelow(X2214,X2216,X2215)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2214),c_Arrow__Order__Mirabelle_OLin))
        | X2216 = X2215 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2213),X2212)),X2214))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2215),X2212)),X2214))
        | X2212 = X2216
        | X2213 = X2212
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2213),X2212)),c_Arrow__Order__Mirabelle_Obelow(X2214,X2216,X2215)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2214),c_Arrow__Order__Mirabelle_OLin))
        | X2216 = X2215 )
      & ( X2212 != X2216
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2213),X2215)),X2214))
        | X2213 = X2212
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2213),X2212)),c_Arrow__Order__Mirabelle_Obelow(X2214,X2216,X2215)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2214),c_Arrow__Order__Mirabelle_OLin))
        | X2216 = X2215 )
      & ( X2213 != X2216
        | X2213 = X2216
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2213),X2215)),X2214))
        | X2213 = X2212
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2213),X2212)),c_Arrow__Order__Mirabelle_Obelow(X2214,X2216,X2215)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2214),c_Arrow__Order__Mirabelle_OLin))
        | X2216 = X2215 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2213),X2212)),X2214))
        | X2213 = X2216
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2213),X2215)),X2214))
        | X2213 = X2212
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2213),X2212)),c_Arrow__Order__Mirabelle_Obelow(X2214,X2216,X2215)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2214),c_Arrow__Order__Mirabelle_OLin))
        | X2216 = X2215 )
      & ( X2213 != X2216
        | X2212 != X2215
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2213),X2215)),X2214))
        | X2213 = X2212
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2213),X2212)),c_Arrow__Order__Mirabelle_Obelow(X2214,X2216,X2215)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2214),c_Arrow__Order__Mirabelle_OLin))
        | X2216 = X2215 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2213),X2212)),X2214))
        | X2212 != X2215
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2213),X2215)),X2214))
        | X2213 = X2212
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2213),X2212)),c_Arrow__Order__Mirabelle_Obelow(X2214,X2216,X2215)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2214),c_Arrow__Order__Mirabelle_OLin))
        | X2216 = X2215 )
      & ( X2213 != X2216
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2215),X2212)),X2214))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2213),X2215)),X2214))
        | X2213 = X2212
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2213),X2212)),c_Arrow__Order__Mirabelle_Obelow(X2214,X2216,X2215)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2214),c_Arrow__Order__Mirabelle_OLin))
        | X2216 = X2215 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2213),X2212)),X2214))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2215),X2212)),X2214))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2213),X2215)),X2214))
        | X2213 = X2212
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2213),X2212)),c_Arrow__Order__Mirabelle_Obelow(X2214,X2216,X2215)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2214),c_Arrow__Order__Mirabelle_OLin))
        | X2216 = X2215 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__below])])]) ).

fof(i_0_622,plain,
    ! [X2879,X2880] :
      ( ( ~ c_Finite__Set_Ofinite(X2880,X2879)
        | c_Finite__Set_Ocard(X2880,X2879) = c_Finite__Set_Ofold__image(tc_Nat_Onat,X2880,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X2880),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2879) )
      & ( c_Finite__Set_Ofinite(X2880,X2879)
        | c_Finite__Set_Ocard(X2880,X2879) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_528])]) ).

fof(i_0_623,plain,
    ! [X2877,X2878] :
      ( ~ c_Finite__Set_Ofinite(X2878,X2877)
      | c_Finite__Set_Ocard(X2878,X2877) = c_Finite__Set_Ofold__image(tc_Nat_Onat,X2878,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X2878),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2877) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card_Oeq__fold__g])]) ).

fof(i_0_624,plain,
    ! [X3065,X3066,X3067,X3068,X3069] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X3069),X3068),c_Set_Oimage(X3067,X3069,X3066,X3065)))
      | hBOOL(hAPP(hAPP(c_member(X3067),hAPP(c_Hilbert__Choice_Oinv__into(X3067,X3069,X3065,X3066),X3068)),X3065)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__into])]) ).

fof(i_0_625,plain,
    ! [X3008,X3009,X3010,X3011,X3012] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3011,tc_HOL_Obool),c_Set_Oimage(X3012,X3011,X3010,X3009)),c_Set_Oimage(X3012,X3011,X3010,X3008)))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3012,tc_HOL_Obool),X3009),X3008))
        | ~ c_Fun_Oinj__on(X3012,X3011,X3010,c_Orderings_Otop__class_Otop(tc_fun(X3012,tc_HOL_Obool))) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3012,tc_HOL_Obool),X3009),X3008))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3011,tc_HOL_Obool),c_Set_Oimage(X3012,X3011,X3010,X3009)),c_Set_Oimage(X3012,X3011,X3010,X3008)))
        | ~ c_Fun_Oinj__on(X3012,X3011,X3010,c_Orderings_Otop__class_Otop(tc_fun(X3012,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_626,plain,
    ! [X2870,X2871,X2872] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2872,tc_HOL_Obool)),X2871),X2870))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X2872,tc_HOL_Obool),tc_fun(X2872,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X2872,tc_HOL_Obool),tc_fun(X2872,tc_HOL_Obool)),X2871),X2870)),c_Wellfounded_Ofinite__psubset(X2872))) )
      & ( c_Finite__Set_Ofinite(X2872,X2870)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X2872,tc_HOL_Obool),tc_fun(X2872,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X2872,tc_HOL_Obool),tc_fun(X2872,tc_HOL_Obool)),X2871),X2870)),c_Wellfounded_Ofinite__psubset(X2872))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2872,tc_HOL_Obool)),X2871),X2870))
        | ~ c_Finite__Set_Ofinite(X2872,X2870)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X2872,tc_HOL_Obool),tc_fun(X2872,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X2872,tc_HOL_Obool),tc_fun(X2872,tc_HOL_Obool)),X2871),X2870)),c_Wellfounded_Ofinite__psubset(X2872))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__finite__psubset])])]) ).

fof(i_0_627,plain,
    ! [X3113,X3114,X3115,X3116,X3117] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3117,X3116)),X3115),c_FuncSet_OPi(X3117,X3116,X3114,hAPP(c_COMBK(tc_fun(X3116,tc_HOL_Obool),X3117),X3113))))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3116,tc_HOL_Obool),c_Set_Oimage(X3117,X3116,X3115,X3114)),X3113)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_funcset__image])]) ).

fof(i_0_628,plain,
    ! [X3059,X3060,X3061,X3062,X3063,X3064] :
      ( hAPP(c_Hilbert__Choice_Oinv__into(X3064,X3063,X3062,X3061),X3060) != hAPP(c_Hilbert__Choice_Oinv__into(X3064,X3063,X3062,X3061),X3059)
      | ~ hBOOL(hAPP(hAPP(c_member(X3063),X3060),c_Set_Oimage(X3064,X3063,X3061,X3062)))
      | ~ hBOOL(hAPP(hAPP(c_member(X3063),X3059),c_Set_Oimage(X3064,X3063,X3061,X3062)))
      | X3060 = X3059 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__injective])]) ).

fof(i_0_629,plain,
    ! [X2827,X2828] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2828),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2828),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2828),c_Groups_Oone__class_Oone(X2828)),X2827)),X2827)),c_Groups_Ozero__class_Ozero(X2828)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2828),X2827),c_Groups_Ozero__class_Ozero(X2828)))
        | ~ hBOOL(hAPP(hAPP(c_member(X2828),X2827),c_Int_Oring__1__class_OInts(X2828)))
        | ~ class_Rings_Olinordered__idom(X2828) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2828),X2827),c_Groups_Ozero__class_Ozero(X2828)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2828),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2828),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2828),c_Groups_Oone__class_Oone(X2828)),X2827)),X2827)),c_Groups_Ozero__class_Ozero(X2828)))
        | ~ hBOOL(hAPP(hAPP(c_member(X2828),X2827),c_Int_Oring__1__class_OInts(X2828)))
        | ~ class_Rings_Olinordered__idom(X2828) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__odd__less__0])])]) ).

fof(i_0_630,plain,
    ! [X3028,X3029,X3030,X3031,X3033,X3034] :
      ( ( X3028 = hAPP(X3029,esk36_4(X3028,X3029,X3030,X3031))
        | ~ hBOOL(hAPP(hAPP(c_member(X3030),X3028),c_Set_Oimage(X3031,X3030,X3029,c_Orderings_Otop__class_Otop(tc_fun(X3031,tc_HOL_Obool)))))
        | ~ c_Fun_Oinj__on(X3031,X3030,X3029,c_Orderings_Otop__class_Otop(tc_fun(X3031,tc_HOL_Obool))) )
      & ( X3028 != hAPP(X3029,X3033)
        | X3033 = esk36_4(X3028,X3029,X3030,X3031)
        | ~ hBOOL(hAPP(hAPP(c_member(X3030),X3028),c_Set_Oimage(X3031,X3030,X3029,c_Orderings_Otop__class_Otop(tc_fun(X3031,tc_HOL_Obool)))))
        | ~ c_Fun_Oinj__on(X3031,X3030,X3029,c_Orderings_Otop__class_Otop(tc_fun(X3031,tc_HOL_Obool))) )
      & ( X3028 = hAPP(X3029,esk37_5(X3028,X3029,X3030,X3031,X3034))
        | X3028 != hAPP(X3029,X3034)
        | hBOOL(hAPP(hAPP(c_member(X3030),X3028),c_Set_Oimage(X3031,X3030,X3029,c_Orderings_Otop__class_Otop(tc_fun(X3031,tc_HOL_Obool)))))
        | ~ c_Fun_Oinj__on(X3031,X3030,X3029,c_Orderings_Otop__class_Otop(tc_fun(X3031,tc_HOL_Obool))) )
      & ( esk37_5(X3028,X3029,X3030,X3031,X3034) != X3034
        | X3028 != hAPP(X3029,X3034)
        | hBOOL(hAPP(hAPP(c_member(X3030),X3028),c_Set_Oimage(X3031,X3030,X3029,c_Orderings_Otop__class_Otop(tc_fun(X3031,tc_HOL_Obool)))))
        | ~ c_Fun_Oinj__on(X3031,X3030,X3029,c_Orderings_Otop__class_Otop(tc_fun(X3031,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_631,plain,
    ! [X3004,X3005,X3006,X3007] :
      ( ~ c_Finite__Set_Ofinite(X3007,X3006)
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X3005,c_Set_Oimage(X3007,X3005,X3004,X3006))),c_Finite__Set_Ocard(X3007,X3006))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__image__le])]) ).

fof(i_0_632,plain,
    ! [X2944,X2945,X2946,X2947,X2948] :
      ( ~ c_Fun_Oinj__on(X2948,X2947,X2946,X2945)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2948,tc_HOL_Obool)),X2944),X2945))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2947,tc_HOL_Obool)),c_Set_Oimage(X2948,X2947,X2946,X2944)),c_Set_Oimage(X2948,X2947,X2946,X2945))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__strict__subset])]) ).

fof(i_0_633,plain,
    ! [X3020,X3021,X3022] :
      ( ~ c_Finite__Set_Ofinite(X3022,X3021)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3022,tc_HOL_Obool),c_Set_Oimage(X3022,X3022,X3020,X3021)),X3021))
      | ~ c_Fun_Oinj__on(X3022,X3022,X3020,X3021)
      | c_Set_Oimage(X3022,X3022,X3020,X3021) = X3021 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_endo__inj__surj])]) ).

fof(i_0_634,plain,
    ! [X3124,X3125,X3126,X3127,X3128] :
      ( ~ c_Fun_Oinj__on(X3128,X3127,X3126,X3125)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3127,tc_HOL_Obool),c_Set_Oimage(X3128,X3127,X3126,X3125)),X3124))
      | ~ c_Finite__Set_Ofinite(X3127,X3124)
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X3128,X3125)),c_Finite__Set_Ocard(X3127,X3124))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__inj__on__le])]) ).

fof(i_0_635,plain,
    ! [X3047,X3048,X3049,X3050,X3051,X3053,X3054,X3055,X3056,X3057,X3058] :
      ( ( hBOOL(hAPP(hAPP(c_member(X3049),esk38_4(X3047,X3048,X3049,X3050)),X3047))
        | ~ hBOOL(hAPP(hAPP(c_member(X3051),X3050),c_Set_Oimage(X3049,X3051,X3048,X3047))) )
      & ( X3050 = hAPP(X3048,esk38_4(X3047,X3048,X3049,X3050))
        | ~ hBOOL(hAPP(hAPP(c_member(X3051),X3050),c_Set_Oimage(X3049,X3051,X3048,X3047))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X3055),X3057),X3053))
        | X3056 != hAPP(X3054,X3057)
        | hBOOL(hAPP(hAPP(c_member(X3058),X3056),c_Set_Oimage(X3055,X3058,X3054,X3053))) ) ),
    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_636,plain,
    ! [X1961,X1962,X1963] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1962),X1961)),X1963))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1961),X1962)),X1963))
        | X1962 = X1961
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1963),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),X1961),X1962)),X1963))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1962),X1961)),X1963))
        | X1962 = X1961
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1963),c_Arrow__Order__Mirabelle_OLin)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_529])])]) ).

fof(i_0_637,plain,
    ! [X1964,X1965,X1966] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1966),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),X1965),X1964)),X1966))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1964),X1965)),X1966)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_530])]) ).

fof(i_0_638,plain,
    ! [X2398,X2399,X2400,X2401,X2402] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2402,X2401)),X2400),c_FuncSet_OPi(X2402,X2401,X2399,hAPP(c_COMBK(tc_fun(X2401,tc_HOL_Obool),X2402),X2398))))
      | ~ c_Fun_Oinj__on(X2402,X2401,X2400,X2399)
      | ~ c_Finite__Set_Ofinite(X2401,X2398)
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2402,X2399)),c_Finite__Set_Ocard(X2401,X2398))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__inj])]) ).

fof(i_0_639,plain,
    ! [X2313,X2314,X2315,X2316,X2317] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2317,tc_HOL_Obool),X2316),X2315))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X2317,X2314),tc_HOL_Obool),c_FuncSet_OPi(X2317,X2314,X2315,X2313)),c_FuncSet_OPi(X2317,X2314,X2316,X2313))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__anti__mono])]) ).

fof(i_0_640,plain,
    ! [X2991,X2992,X2993,X2994,X2995] :
      ( ~ c_Finite__Set_Ofinite(X2995,c_Set_Oimage(X2994,X2995,X2993,c_Orderings_Otop__class_Otop(tc_fun(X2994,tc_HOL_Obool))))
      | c_Finite__Set_Ofinite(X2992,c_Set_Oimage(X2994,X2992,hAPP(c_COMBB(X2995,X2992,X2994,X2991),X2993),c_Orderings_Otop__class_Otop(tc_fun(X2994,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__range__imageI])]) ).

fof(i_0_641,plain,
    ! [X2061] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2061),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),X2061)),c_Arrow__Order__Mirabelle_OProf)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_const__Lin__Prof])]) ).

fof(i_0_642,plain,
    ! [X2290,X2291,X2292,X2293,X2294,X2295] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2295,X2294)),X2293),c_FuncSet_OPi(X2295,X2294,X2292,hAPP(c_COMBK(tc_fun(X2294,tc_HOL_Obool),X2295),X2291))))
      | ~ hBOOL(hAPP(hAPP(c_member(X2295),X2290),X2292))
      | hBOOL(hAPP(hAPP(c_member(X2294),hAPP(X2293,X2290)),X2291)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_funcset__mem])]) ).

fof(i_0_643,plain,
    ! [X2977,X2978,X2979,X2980,X2981] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2981,tc_HOL_Obool),X2980),X2979))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2978,tc_HOL_Obool),c_Set_Oimage(X2981,X2978,X2977,X2980)),c_Set_Oimage(X2981,X2978,X2977,X2979))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__mono])]) ).

fof(i_0_644,plain,
    ! [X2816,X2817,X2818,X2819,X2820] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X2820,X2819)),hAPP(X2820,X2818)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2817,X2817)),hAPP(hAPP(c_Product__Type_OPair(X2817,X2817),X2819),X2818)),X2816))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X2817,X2817)),hAPP(hAPP(c_Product__Type_OPair(X2817,X2817),X2819),X2818)),c_Wellfounded_Omlex__prod(X2817,X2820,X2816))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mlex__leq])]) ).

fof(i_0_645,plain,
    ! [X2205,X2206,X2207,X2208,X2209] :
      ( ( ~ c_FunDef_Oin__rel(X2209,X2208,X2207,X2206,X2205)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X2209,X2208)),hAPP(hAPP(c_Product__Type_OPair(X2209,X2208),X2206),X2205)),X2207)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2209,X2208)),hAPP(hAPP(c_Product__Type_OPair(X2209,X2208),X2206),X2205)),X2207))
        | c_FunDef_Oin__rel(X2209,X2208,X2207,X2206,X2205) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__rel__def])]) ).

fof(i_0_646,plain,
    ! [X3070,X3071,X3072,X3073,X3074] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X3074),X3073),c_Set_Oimage(X3072,X3074,X3071,X3070)))
      | hAPP(X3071,hAPP(c_Hilbert__Choice_Oinv__into(X3072,X3074,X3070,X3071),X3073)) = X3073 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_f__inv__into__f])]) ).

fof(i_0_647,plain,
    ! [X2936,X2937,X2938,X2939,X2940,X2941,X2942] :
      ( ( c_Set_Oimage(X2938,X2937,X2936,c_Orderings_Otop__class_Otop(tc_fun(X2938,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X2937,tc_HOL_Obool))
        | hAPP(X2936,hAPP(c_Hilbert__Choice_Oinv__into(X2938,X2937,c_Orderings_Otop__class_Otop(tc_fun(X2938,tc_HOL_Obool)),X2936),X2939)) = X2939 )
      & ( hAPP(X2940,hAPP(c_Hilbert__Choice_Oinv__into(X2942,X2941,c_Orderings_Otop__class_Otop(tc_fun(X2942,tc_HOL_Obool)),X2940),esk34_3(X2940,X2941,X2942))) != esk34_3(X2940,X2941,X2942)
        | c_Set_Oimage(X2942,X2941,X2940,c_Orderings_Otop__class_Otop(tc_fun(X2942,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X2941,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_648,plain,
    ! [X3094,X3095,X3096,X3097,X3098] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3098,tc_HOL_Obool),X3097),c_Set_Oimage(X3096,X3098,X3095,X3094)))
      | c_Fun_Oinj__on(X3098,X3096,c_Hilbert__Choice_Oinv__into(X3096,X3098,X3094,X3095),X3097) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__inv__into])]) ).

fof(i_0_649,plain,
    ! [X1628,X1629,X1630,X1631] :
      ( ( X1630 != X1628
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1631),X1630)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1629),X1628))) )
      & ( X1631 != X1628
        | X1631 != X1630
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1631),X1630)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1629),X1628))) )
      & ( X1631 = X1628
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1631),X1630)),X1629))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1631),X1630)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1629),X1628))) )
      & ( X1631 != X1628
        | X1631 = X1628
        | X1630 = X1628
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1631),X1630)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1629),X1628))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1631),X1630)),X1629))
        | X1631 = X1628
        | X1630 = X1628
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1631),X1630)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1629),X1628))) )
      & ( X1631 != X1628
        | X1631 = X1630
        | X1630 = X1628
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1631),X1630)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1629),X1628))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1631),X1630)),X1629))
        | X1631 = X1630
        | X1630 = X1628
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1631),X1630)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1629),X1628))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__mkbot])])]) ).

fof(i_0_650,plain,
    ! [X1632,X1633,X1634,X1635] :
      ( ( X1635 != X1632
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1635),X1634)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1633),X1632))) )
      & ( X1634 != X1632
        | X1635 != X1634
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1635),X1634)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1633),X1632))) )
      & ( X1634 = X1632
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1635),X1634)),X1633))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1635),X1634)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1633),X1632))) )
      & ( X1634 != X1632
        | X1634 = X1632
        | X1635 = X1632
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1635),X1634)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1633),X1632))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1635),X1634)),X1633))
        | X1634 = X1632
        | X1635 = X1632
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1635),X1634)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1633),X1632))) )
      & ( X1634 != X1632
        | X1635 = X1634
        | X1635 = X1632
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1635),X1634)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1633),X1632))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1635),X1634)),X1633))
        | X1635 = X1634
        | X1635 = X1632
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1635),X1634)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1633),X1632))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__mktop])])]) ).

fof(i_0_651,plain,
    ! [X3210,X3211,X3212,X3213,X3214,X3215] : hAPP(c_COMBS(X3215,X3214,X3213,X3212,X3211),X3210) = hAPP(hAPP(X3212,X3210),hAPP(X3211,X3210)),
    inference(variable_rename,[status(thm)],[help_c__COMBS__1]) ).

fof(i_0_652,plain,
    ! [X2323,X2324,X2325,X2326,X2327,X2328] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2328,X2327)),X2326),c_FuncSet_OPi(X2328,X2327,X2325,X2324)))
      | ~ hBOOL(hAPP(hAPP(c_member(X2328),X2323),X2325))
      | hBOOL(hAPP(hAPP(c_member(X2327),hAPP(X2326,X2323)),hAPP(X2324,X2323))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__mem])]) ).

fof(i_0_653,plain,
    ! [X2284,X2285,X2286,X2287,X2288,X2289] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2289,X2288)),X2287),c_FuncSet_OPi(X2289,X2288,X2286,X2285)))
      | hBOOL(hAPP(hAPP(c_member(X2288),hAPP(X2287,X2284)),hAPP(X2285,X2284)))
      | ~ hBOOL(hAPP(hAPP(c_member(X2289),X2284),X2286)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_531])]) ).

fof(i_0_654,plain,
    ! [X3023,X3024,X3025,X3026,X3027] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X3026),hAPP(X3025,X3024)),c_Set_Oimage(X3027,X3026,X3025,X3023)))
        | hBOOL(hAPP(hAPP(c_member(X3027),X3024),X3023))
        | ~ c_Fun_Oinj__on(X3027,X3026,X3025,c_Orderings_Otop__class_Otop(tc_fun(X3027,tc_HOL_Obool))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X3027),X3024),X3023))
        | hBOOL(hAPP(hAPP(c_member(X3026),hAPP(X3025,X3024)),c_Set_Oimage(X3027,X3026,X3025,X3023)))
        | ~ c_Fun_Oinj__on(X3027,X3026,X3025,c_Orderings_Otop__class_Otop(tc_fun(X3027,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_655,plain,
    ! [X2928,X2929,X2930,X2931] :
      ( c_Set_Oimage(X2931,X2930,X2929,c_Orderings_Otop__class_Otop(tc_fun(X2931,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X2930,tc_HOL_Obool))
      | c_Set_Oimage(X2931,X2930,X2929,c_Set_Oimage(X2930,X2931,c_Hilbert__Choice_Oinv__into(X2931,X2930,c_Orderings_Otop__class_Otop(tc_fun(X2931,tc_HOL_Obool)),X2929),X2928)) = X2928 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__surj__f__inv__f])]) ).

fof(i_0_656,plain,
    ! [X2922,X2923,X2924,X2925,X2926,X2927] :
      ( c_Set_Oimage(X2927,X2926,X2925,X2924) != X2923
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2926,tc_HOL_Obool),X2922),X2923))
      | c_Set_Oimage(X2927,X2926,X2925,c_Set_Oimage(X2926,X2927,c_Hilbert__Choice_Oinv__into(X2927,X2926,X2924,X2925),X2922)) = X2922 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__inv__into__cancel])]) ).

fof(i_0_657,plain,
    ! [X2353,X2354,X2355,X2356,X2357,X2358,X2359,X2360,X2361,X2362] :
      ( ( ~ c_Fun_Oinj__on(X2356,X2355,X2354,X2353)
        | ~ hBOOL(hAPP(hAPP(c_member(X2356),X2357),X2353))
        | ~ hBOOL(hAPP(hAPP(c_member(X2356),X2358),X2353))
        | hAPP(X2354,X2357) != hAPP(X2354,X2358)
        | X2357 = X2358 )
      & ( hBOOL(hAPP(hAPP(c_member(X2362),esk25_4(X2359,X2360,X2361,X2362)),X2359))
        | c_Fun_Oinj__on(X2362,X2361,X2360,X2359) )
      & ( hBOOL(hAPP(hAPP(c_member(X2362),esk26_4(X2359,X2360,X2361,X2362)),X2359))
        | c_Fun_Oinj__on(X2362,X2361,X2360,X2359) )
      & ( hAPP(X2360,esk25_4(X2359,X2360,X2361,X2362)) = hAPP(X2360,esk26_4(X2359,X2360,X2361,X2362))
        | c_Fun_Oinj__on(X2362,X2361,X2360,X2359) )
      & ( esk25_4(X2359,X2360,X2361,X2362) != esk26_4(X2359,X2360,X2361,X2362)
        | c_Fun_Oinj__on(X2362,X2361,X2360,X2359) ) ),
    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_658,plain,
    ! [X1893,X1894,X1895] :
      ( X1895 = X1894
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1893),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,X1893),X1895),X1894)),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_above__Lin])]) ).

fof(i_0_659,plain,
    ! [X2949,X2950,X2951,X2952,X2953] : c_Set_Oimage(X2953,X2952,hAPP(c_COMBB(X2951,X2952,X2953,X2950),X2949),c_Orderings_Otop__class_Otop(tc_fun(X2953,tc_HOL_Obool))) = c_Set_Oimage(X2951,X2952,X2950,c_Set_Oimage(X2953,X2951,X2949,c_Orderings_Otop__class_Otop(tc_fun(X2953,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_range__composition]) ).

fof(i_0_660,plain,
    ! [X3017,X3018,X3019] :
      ( ~ c_Finite__Set_Ofinite(X3019,X3018)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3019,tc_HOL_Obool),X3018),c_Set_Oimage(X3019,X3019,X3017,X3018)))
      | c_Fun_Oinj__on(X3019,X3019,X3017,X3018) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__surj__inj])]) ).

fof(i_0_661,plain,
    ! [X2367,X2368,X2369,X2370,X2371] :
      ( ( ~ c_Arrow__Order__Mirabelle_Odictator(X2368,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))),X2369),c_Arrow__Order__Mirabelle_OProf))
        | hAPP(X2368,X2369) = hAPP(X2369,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))),esk27_2(X2370,X2371)),c_Arrow__Order__Mirabelle_OProf))
        | c_Arrow__Order__Mirabelle_Odictator(X2371,X2370) )
      & ( hAPP(X2371,esk27_2(X2370,X2371)) != hAPP(esk27_2(X2370,X2371),X2370)
        | c_Arrow__Order__Mirabelle_Odictator(X2371,X2370) ) ),
    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_662,plain,
    ! [X2334,X2335,X2336,X2337] :
      ( ~ c_Fun_Oinj__on(X2337,X2336,X2335,c_Orderings_Otop__class_Otop(tc_fun(X2337,tc_HOL_Obool)))
      | c_Fun_Oinj__on(X2337,tc_fun(X2334,X2336),hAPP(c_COMBB(X2336,tc_fun(X2334,X2336),X2337,c_COMBK(X2336,X2334)),X2335),c_Orderings_Otop__class_Otop(tc_fun(X2337,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__fun])]) ).

fof(i_0_663,plain,
    ! [X2318,X2319] : hBOOL(hAPP(hAPP(c_member(tc_fun(X2319,X2319)),c_COMBI(X2319)),c_FuncSet_OPi(X2319,X2319,X2318,hAPP(c_COMBK(tc_fun(X2319,tc_HOL_Obool),X2319),X2318)))),
    inference(variable_rename,[status(thm)],[fact_funcset__id]) ).

fof(i_0_664,plain,
    ! [X2959,X2960,X2961,X2962,X2963,X2964] : c_Set_Oimage(X2964,X2963,X2962,c_Set_Oimage(X2961,X2964,X2960,X2959)) = c_Set_Oimage(X2961,X2963,hAPP(c_COMBB(X2964,X2963,X2961,X2962),X2960),X2959),
    inference(variable_rename,[status(thm)],[fact_image__image]) ).

fof(i_0_665,plain,
    ! [X2217,X2218,X2219] :
      ( X2219 = X2218
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2217),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(X2217,X2219,X2218)),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_below__Lin])]) ).

fof(i_0_666,plain,
    ! [X2812,X2813,X2814,X2815] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2815,X2815)),hAPP(hAPP(c_Product__Type_OPair(X2815,X2815),X2814),X2813)),c_Wellfounded_Omeasure(X2815,X2812)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2812,X2814)),hAPP(X2812,X2813))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2812,X2814)),hAPP(X2812,X2813)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X2815,X2815)),hAPP(hAPP(c_Product__Type_OPair(X2815,X2815),X2814),X2813)),c_Wellfounded_Omeasure(X2815,X2812))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__measure])]) ).

fof(i_0_667,plain,
    ! [X3089,X3090,X3091,X3092,X3093] :
      ( ~ c_Fun_Oinj__on(X3093,X3092,X3091,X3090)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3093,tc_HOL_Obool),X3089),X3090))
      | c_Set_Oimage(X3092,X3093,c_Hilbert__Choice_Oinv__into(X3093,X3092,X3090,X3091),c_Set_Oimage(X3093,X3092,X3091,X3089)) = X3089 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__image__cancel])]) ).

fof(i_0_668,plain,
    ! [X2904,X2905,X2906,X2907,X2908] :
      ( ~ c_Finite__Set_Ofinite(X2908,X2907)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2906,tc_HOL_Obool),X2905),c_Set_Oimage(X2908,X2906,X2904,X2907)))
      | c_Finite__Set_Ofinite(X2906,X2905) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__surj])]) ).

fof(i_0_669,plain,
    ! [X1896,X1897] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1897),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,X1897),X1896)),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mkbot__Lin])]) ).

fof(i_0_670,plain,
    ! [X1898,X1899] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1899),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,X1899),X1898)),c_Arrow__Order__Mirabelle_OLin)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mktop__Lin])]) ).

fof(i_0_671,plain,
    ! [X3106,X3107,X3108,X3109] :
      ( ~ c_Fun_Oinj__on(X3109,X3108,X3107,c_Orderings_Otop__class_Otop(tc_fun(X3109,tc_HOL_Obool)))
      | c_Set_Oimage(X3108,X3109,c_Hilbert__Choice_Oinv__into(X3109,X3108,c_Orderings_Otop__class_Otop(tc_fun(X3109,tc_HOL_Obool)),X3107),c_Set_Oimage(X3109,X3108,X3107,X3106)) = X3106 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__inv__f__f])]) ).

fof(i_0_672,plain,
    ! [X3102,X3103,X3104,X3105] :
      ( ~ c_Fun_Oinj__on(X3105,X3104,X3103,c_Orderings_Otop__class_Otop(tc_fun(X3105,tc_HOL_Obool)))
      | c_Set_Oimage(X3104,X3105,c_Hilbert__Choice_Oinv__into(X3105,X3104,c_Orderings_Otop__class_Otop(tc_fun(X3105,tc_HOL_Obool)),X3103),c_Set_Oimage(X3105,X3104,X3103,X3102)) = X3102 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__image__comp])]) ).

fof(i_0_673,plain,
    ! [X2932,X2933,X2934,X2935] :
      ( c_Set_Oimage(X2935,X2934,X2933,c_Orderings_Otop__class_Otop(tc_fun(X2935,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X2934,tc_HOL_Obool))
      | hAPP(X2933,hAPP(c_Hilbert__Choice_Oinv__into(X2935,X2934,c_Orderings_Otop__class_Otop(tc_fun(X2935,tc_HOL_Obool)),X2933),X2932)) = X2932 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__f__inv__f])]) ).

fof(i_0_674,plain,
    ! [X2821,X2822,X2823,X2824,X2825] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2825,X2824)),hAPP(X2825,X2823)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X2822,X2822)),hAPP(hAPP(c_Product__Type_OPair(X2822,X2822),X2824),X2823)),c_Wellfounded_Omlex__prod(X2822,X2825,X2821))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mlex__less])]) ).

fof(i_0_675,plain,
    ! [X3170,X3171] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool),X3171),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3170,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3170),c_Finite__Set_Ocard(tc_Nat_Onat,X3171)))))
      | X3171 = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3170,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3170),c_Finite__Set_Ocard(tc_Nat_Onat,X3171))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__card__intvl__is__intvl])]) ).

fof(i_0_676,plain,
    ! [X3172,X3173,X3174,X3175,X3176] :
      ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3176,X3173),X3175))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3176,X3174),X3175))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3176,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(X3176,X3175,X3174)),c_SetInterval_Oord__class_OatLeastLessThan(X3176,X3173,X3172)))
        | ~ class_Orderings_Olinorder(X3176) )
      & ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3176,X3174),X3172))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3176,X3174),X3175))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3176,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(X3176,X3175,X3174)),c_SetInterval_Oord__class_OatLeastLessThan(X3176,X3173,X3172)))
        | ~ class_Orderings_Olinorder(X3176) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__subset__iff])])]) ).

fof(i_0_677,plain,
    ! [X3099,X3100,X3101] :
      ( c_Set_Oimage(X3101,X3100,X3099,c_Orderings_Otop__class_Otop(tc_fun(X3101,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X3100,tc_HOL_Obool))
      | c_Fun_Oinj__on(X3100,X3101,c_Hilbert__Choice_Oinv__into(X3101,X3100,c_Orderings_Otop__class_Otop(tc_fun(X3101,tc_HOL_Obool)),X3099),c_Orderings_Otop__class_Otop(tc_fun(X3100,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__imp__inj__inv])]) ).

fof(i_0_678,plain,
    ! [X3080,X3081,X3082,X3083] : hBOOL(hAPP(hAPP(c_member(X3083),hAPP(X3082,X3081)),c_Set_Oimage(X3080,X3083,X3082,c_Orderings_Otop__class_Otop(tc_fun(X3080,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[fact_rangeI]) ).

fof(i_0_679,plain,
    ! [X3110,X3111,X3112] :
      ( ~ c_Fun_Oinj__on(X3112,X3111,X3110,c_Orderings_Otop__class_Otop(tc_fun(X3112,tc_HOL_Obool)))
      | c_Set_Oimage(X3111,X3112,c_Hilbert__Choice_Oinv__into(X3112,X3111,c_Orderings_Otop__class_Otop(tc_fun(X3112,tc_HOL_Obool)),X3110),c_Orderings_Otop__class_Otop(tc_fun(X3111,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X3112,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__imp__surj__inv])]) ).

fof(i_0_680,plain,
    ! [X3042,X3043,X3044,X3045,X3046] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X3046),X3045),X3044))
      | hBOOL(hAPP(hAPP(c_member(X3043),hAPP(X3042,X3045)),c_Set_Oimage(X3046,X3043,X3042,X3044))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_imageI])]) ).

fof(i_0_681,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_682,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_683,plain,
    ! [X3075,X3076,X3077,X3078,X3079] :
      ( X3079 != hAPP(X3078,X3077)
      | hBOOL(hAPP(hAPP(c_member(X3076),X3079),c_Set_Oimage(X3075,X3076,X3078,c_Orderings_Otop__class_Otop(tc_fun(X3075,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_range__eqI])]) ).

fof(i_0_684,plain,
    ! [X2890,X2891,X2892,X2893,X2894,X2895] :
      ( X2895 != hAPP(X2894,X2893)
      | ~ hBOOL(hAPP(hAPP(c_member(X2892),X2893),X2891))
      | hBOOL(hAPP(hAPP(c_member(X2890),X2895),c_Set_Oimage(X2892,X2890,X2894,X2891))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__eqI])]) ).

fof(i_0_685,plain,
    ! [X3036,X3037,X3038,X3039,X3040,X3041] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X3041),X3040),X3039))
      | X3038 != hAPP(X3037,X3040)
      | hBOOL(hAPP(hAPP(c_member(X3036),X3038),c_Set_Oimage(X3041,X3036,X3037,X3039))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__image__eqI])]) ).

fof(i_0_686,plain,
    ! [X2913,X2914,X2915,X2916,X2917] :
      ( ( c_Set_Oimage(X2917,X2916,X2915,X2914) != c_Set_Oimage(X2917,X2916,X2915,X2913)
        | X2914 = X2913
        | ~ c_Fun_Oinj__on(X2917,X2916,X2915,c_Orderings_Otop__class_Otop(tc_fun(X2917,tc_HOL_Obool))) )
      & ( X2914 != X2913
        | c_Set_Oimage(X2917,X2916,X2915,X2914) = c_Set_Oimage(X2917,X2916,X2915,X2913)
        | ~ c_Fun_Oinj__on(X2917,X2916,X2915,c_Orderings_Otop__class_Otop(tc_fun(X2917,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_687,plain,
    ! [X2184,X2185,X2186,X2187] :
      ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2187)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2187),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2187),X2186),X2185)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2187),X2184),X2185)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2187),X2186),X2184)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__right])]) ).

fof(i_0_688,plain,
    ! [X2163,X2164,X2165,X2166] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2166),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2166),X2165),X2164)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2166),X2163),X2164)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2166),X2165),X2163))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2166) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2166),X2165),X2163))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2166),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2166),X2165),X2164)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2166),X2163),X2164)))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2166) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__right])])]) ).

fof(i_0_689,plain,
    ! [X2188,X2189,X2190,X2191] :
      ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2191)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2191),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2191),X2190),X2189)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2191),X2190),X2188)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2191),X2189),X2188)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__left])]) ).

fof(i_0_690,plain,
    ! [X2167,X2168,X2169,X2170] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2170),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2170),X2169),X2168)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2170),X2169),X2167)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2170),X2168),X2167))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2170) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2170),X2168),X2167))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2170),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2170),X2169),X2168)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2170),X2169),X2167)))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2170) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__left])])]) ).

fof(i_0_691,plain,
    ! [X2909,X2910,X2911,X2912] :
      ( ~ c_Finite__Set_Ofinite(X2912,c_Set_Oimage(X2911,X2912,X2910,X2909))
      | ~ c_Fun_Oinj__on(X2911,X2912,X2910,X2909)
      | c_Finite__Set_Ofinite(X2911,X2909) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageD])]) ).

fof(i_0_692,plain,
    ! [X1857,X1858,X1859,X1860] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1860,tc_HOL_Obool)),X1859),X1858))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1860,tc_HOL_Obool)),X1858),X1857))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1860,tc_HOL_Obool)),X1859),X1857)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__trans])]) ).

fof(i_0_693,plain,
    ! [X2155,X2156,X2157,X2158] :
      ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2158)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2158,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2158),X2157),X2156)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2158),X2155),X2156)))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2158,X2157),X2155)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__right])]) ).

fof(i_0_694,plain,
    ! [X2134,X2135,X2136,X2137] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2137,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2137),X2136),X2135)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2137),X2134),X2135)))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2137,X2136),X2134))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2137) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2137,X2136),X2134))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2137,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2137),X2136),X2135)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2137),X2134),X2135)))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2137) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__right])])]) ).

fof(i_0_695,plain,
    ! [X2159,X2160,X2161,X2162] :
      ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2162)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2162,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2162),X2161),X2160)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2162),X2161),X2159)))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2162,X2160),X2159)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__left])]) ).

fof(i_0_696,plain,
    ! [X2138,X2139,X2140,X2141] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2141,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2141),X2140),X2139)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2141),X2140),X2138)))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2141,X2139),X2138))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2141) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2141,X2139),X2138))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2141,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2141),X2140),X2139)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2141),X2140),X2138)))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2141) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__left])])]) ).

fof(i_0_697,plain,
    ! [X2565,X2566,X2567,X2568] :
      ( ( hBOOL(hAPP(hAPP(c_member(X2568),X2567),X2565))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2568,tc_HOL_Obool),c_Set_Oinsert(X2568,X2567,X2566)),X2565)) )
      & ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2568,tc_HOL_Obool),X2566),X2565))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2568,tc_HOL_Obool),c_Set_Oinsert(X2568,X2567,X2566)),X2565)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X2568),X2567),X2565))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2568,tc_HOL_Obool),X2566),X2565))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2568,tc_HOL_Obool),c_Set_Oinsert(X2568,X2567,X2566)),X2565)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__subset])])]) ).

fof(i_0_698,plain,
    ! [X2296,X2297,X2298,X2299] :
      ( ~ c_Fun_Oinj__on(X2299,X2298,X2297,c_Orderings_Otop__class_Otop(tc_fun(X2299,tc_HOL_Obool)))
      | hAPP(c_Hilbert__Choice_Oinv__into(X2299,X2298,c_Orderings_Otop__class_Otop(tc_fun(X2299,tc_HOL_Obool)),X2297),hAPP(X2297,X2296)) = X2296 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__f__f])]) ).

fof(i_0_699,plain,
    ! [X2300,X2301,X2302,X2303,X2304] :
      ( ~ c_Fun_Oinj__on(X2304,X2303,X2302,c_Orderings_Otop__class_Otop(tc_fun(X2304,tc_HOL_Obool)))
      | hAPP(X2302,X2301) != X2300
      | hAPP(c_Hilbert__Choice_Oinv__into(X2304,X2303,c_Orderings_Otop__class_Otop(tc_fun(X2304,tc_HOL_Obool)),X2302),X2300) = X2301 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__f__eq])]) ).

fof(i_0_700,plain,
    ! [X1765,X1766,X1767] :
      ( ( hAPP(hAPP(c_COMBC(X1767,tc_fun(X1767,tc_HOL_Obool),tc_HOL_Obool),c_member(X1767)),X1766) != hAPP(hAPP(c_COMBC(X1767,tc_fun(X1767,tc_HOL_Obool),tc_HOL_Obool),c_member(X1767)),X1765)
        | X1766 = X1765 )
      & ( X1766 != X1765
        | hAPP(hAPP(c_COMBC(X1767,tc_fun(X1767,tc_HOL_Obool),tc_HOL_Obool),c_member(X1767)),X1766) = hAPP(hAPP(c_COMBC(X1767,tc_fun(X1767,tc_HOL_Obool),tc_HOL_Obool),c_member(X1767)),X1765) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__equals__eq])]) ).

fof(i_0_701,plain,
    ! [X1652,X1653,X1654] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1654),X1653)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1654),X1652)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1653),X1652)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1653),X1652))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1654),X1653)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1654),X1652))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__less])]) ).

fof(i_0_702,plain,
    ! [X2329,X2330,X2331,X2332,X2333] :
      ( ~ c_Fun_Oinj__on(X2333,X2332,X2331,X2330)
      | ~ hBOOL(hAPP(hAPP(c_member(X2333),X2329),X2330))
      | hAPP(c_Hilbert__Choice_Oinv__into(X2333,X2332,X2330,X2331),hAPP(X2331,X2329)) = X2329 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__f__f])]) ).

fof(i_0_703,plain,
    ! [X2305,X2306,X2307,X2308,X2309,X2310] :
      ( ~ c_Fun_Oinj__on(X2310,X2309,X2308,X2307)
      | ~ hBOOL(hAPP(hAPP(c_member(X2310),X2306),X2307))
      | hAPP(X2308,X2306) != X2305
      | hAPP(c_Hilbert__Choice_Oinv__into(X2310,X2309,X2307,X2308),X2305) = X2306 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__f__eq])]) ).

fof(i_0_704,plain,
    ! [X2996,X2997,X2998,X2999] :
      ( ~ c_Finite__Set_Ofinite(X2999,X2998)
      | c_Finite__Set_Ocard(X2997,c_Set_Oimage(X2999,X2997,X2996,X2998)) != c_Finite__Set_Ocard(X2999,X2998)
      | c_Fun_Oinj__on(X2999,X2997,X2996,X2998) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__card__imp__inj__on])]) ).

fof(i_0_705,plain,
    ! [X3000,X3001,X3002,X3003] :
      ( ( ~ c_Fun_Oinj__on(X3003,X3001,X3000,X3002)
        | c_Finite__Set_Ocard(X3001,c_Set_Oimage(X3003,X3001,X3000,X3002)) = c_Finite__Set_Ocard(X3003,X3002)
        | ~ c_Finite__Set_Ofinite(X3003,X3002) )
      & ( c_Finite__Set_Ocard(X3001,c_Set_Oimage(X3003,X3001,X3000,X3002)) != c_Finite__Set_Ocard(X3003,X3002)
        | c_Fun_Oinj__on(X3003,X3001,X3000,X3002)
        | ~ c_Finite__Set_Ofinite(X3003,X3002) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__iff__eq__card])])]) ).

fof(i_0_706,plain,
    ! [X2505,X2506,X2507,X2508] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2508,tc_HOL_Obool),X2507),X2506))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2508,tc_HOL_Obool),c_Set_Oinsert(X2508,X2505,X2507)),c_Set_Oinsert(X2508,X2505,X2506))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__mono])]) ).

fof(i_0_707,plain,
    ! [X3198,X3199,X3200,X3201,X3202,X3203] : hAPP(hAPP(c_COMBB(X3203,X3202,X3201,X3200),X3199),X3198) = hAPP(X3200,hAPP(X3199,X3198)),
    inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).

fof(i_0_708,plain,
    ! [X2179,X2180,X2181,X2182,X2183] :
      ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X2183)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2183),X2182),X2181))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2183),X2180),X2179))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2183),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2183),X2182),X2180)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2183),X2181),X2179))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__mono])]) ).

fof(i_0_709,plain,
    ! [X3140,X3141,X3142] : 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)),X3142),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3141,X3140)) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3141),X3142),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3140),X3142)),
    inference(variable_rename,[status(thm)],[fact_image__add__atLeastLessThan]) ).

fof(i_0_710,plain,
    ! [X1704,X1705,X1706] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1706),X1705)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1706),X1704)))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1705),X1704)) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1705),X1704))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1706),X1705)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1706),X1704))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__le])]) ).

fof(i_0_711,plain,
    ! [X1817,X1818,X1819,X1820,X1821] :
      ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1821)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1821,X1820),X1819))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1821),X1818),X1817))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1821),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1821),X1820),X1818)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1821),X1819),X1817))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__less__mono])]) ).

fof(i_0_712,plain,
    ! [X1822,X1823,X1824,X1825,X1826] :
      ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1826)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1826),X1825),X1824))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1826,X1823),X1822))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1826),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1826),X1825),X1823)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1826),X1824),X1822))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__le__mono])]) ).

fof(i_0_713,plain,
    ! [X1865,X1866,X1867,X1868] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1868,tc_HOL_Obool),X1867),X1866))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1868,tc_HOL_Obool)),X1866),X1865))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1868,tc_HOL_Obool)),X1867),X1865)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__psubset__trans])]) ).

fof(i_0_714,plain,
    ! [X1861,X1862,X1863,X1864] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1864,tc_HOL_Obool)),X1863),X1862))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1864,tc_HOL_Obool),X1862),X1861))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1864,tc_HOL_Obool)),X1863),X1861)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__subset__trans])]) ).

fof(i_0_715,plain,
    ! [X2888,X2889] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2889)),X2888))
        | hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2889),X2888)) )
      & ( ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2889),X2888))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2889)),X2888)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__nat_Osimps_I2_J])]) ).

fof(i_0_716,plain,
    ! [X3084,X3085,X3086,X3087,X3088] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X3088),X3087),X3086))
      | c_Set_Oinsert(X3085,hAPP(X3084,X3087),c_Set_Oimage(X3088,X3085,X3084,X3086)) = c_Set_Oimage(X3088,X3085,X3084,X3086) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__image])]) ).

fof(i_0_717,plain,
    ! [X2421,X2422,X2423] :
      ( ~ c_Finite__Set_Ofinite(X2423,X2422)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2423,tc_HOL_Obool),X2421),X2422))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X2423,X2421)),c_Finite__Set_Ocard(X2423,X2422)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2423,tc_HOL_Obool)),X2421),X2422)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__psubset])]) ).

fof(i_0_718,plain,
    ! [X2150,X2151,X2152,X2153,X2154] :
      ( ~ class_Groups_Oordered__ab__semigroup__add(X2154)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2154,X2153),X2152))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2154,X2151),X2150))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2154,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2154),X2153),X2151)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2154),X2152),X2150))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__mono])]) ).

fof(i_0_719,plain,
    ! [X2654,X2655] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2655),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2655),X2654),X2654)),c_Groups_Ozero__class_Ozero(X2655)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2655),X2654),c_Groups_Ozero__class_Ozero(X2655)))
        | ~ class_Groups_Olinordered__ab__group__add(X2655) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2655),X2654),c_Groups_Ozero__class_Ozero(X2655)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2655),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2655),X2654),X2654)),c_Groups_Ozero__class_Ozero(X2655)))
        | ~ class_Groups_Olinordered__ab__group__add(X2655) ) ),
    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_720,plain,
    ! [X2690,X2691] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2691),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2691),X2690),X2690)),c_Groups_Ozero__class_Ozero(X2691)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2691),X2690),c_Groups_Ozero__class_Ozero(X2691)))
        | ~ class_Rings_Olinordered__idom(X2691) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2691),X2690),c_Groups_Ozero__class_Ozero(X2691)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2691),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2691),X2690),X2690)),c_Groups_Ozero__class_Ozero(X2691)))
        | ~ class_Rings_Olinordered__idom(X2691) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_even__less__0__iff])])]) ).

fof(i_0_721,plain,
    ! [X1775,X1776,X1777,X1778] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1778),X1777))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1776),X1775))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1778),X1776)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1777),X1775))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono])]) ).

fof(i_0_722,plain,
    ! [X2954,X2955,X2956,X2957,X2958] : c_Set_Oimage(X2958,X2957,X2956,c_Set_Oinsert(X2958,X2955,X2954)) = c_Set_Oinsert(X2957,hAPP(X2956,X2955),c_Set_Oimage(X2958,X2957,X2956,X2954)),
    inference(variable_rename,[status(thm)],[fact_image__insert]) ).

fof(i_0_723,plain,
    ! [X3013,X3014] :
      ( ~ c_Finite__Set_Ofinite(X3014,c_Orderings_Otop__class_Otop(tc_fun(X3014,tc_HOL_Obool)))
      | c_Set_Oimage(X3014,X3014,X3013,c_Orderings_Otop__class_Otop(tc_fun(X3014,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X3014,tc_HOL_Obool))
      | c_Fun_Oinj__on(X3014,X3014,X3013,c_Orderings_Otop__class_Otop(tc_fun(X3014,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__surj__inj])]) ).

fof(i_0_724,plain,
    ! [X2391,X2392,X2393,X2394,X2395] :
      ( ~ c_Fun_Oinj__on(X2395,X2394,X2393,X2392)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2395,tc_HOL_Obool),X2391),X2392))
      | c_Fun_Oinj__on(X2395,X2394,X2393,X2391) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__inj__on])]) ).

fof(i_0_725,plain,
    ! [X2918,X2919,X2920,X2921] :
      ( ~ c_Fun_Oinj__on(X2921,X2920,X2919,X2918)
      | c_Finite__Set_Ocard(X2920,c_Set_Oimage(X2921,X2920,X2919,X2918)) = c_Finite__Set_Ocard(X2921,X2918) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__image])]) ).

fof(i_0_726,plain,
    ! [X2648,X2649,X2650] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X2650)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2650),X2649),c_Groups_Ozero__class_Ozero(X2650)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2650),X2648),c_Groups_Ozero__class_Ozero(X2650)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2650),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2650),X2649),X2648)),c_Groups_Ozero__class_Ozero(X2650))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__neg])]) ).

fof(i_0_727,plain,
    ! [X2831,X2832,X2833] :
      ( ~ class_Rings_Oring__1(X2833)
      | ~ hBOOL(hAPP(hAPP(c_member(X2833),X2832),c_Int_Oring__1__class_OInts(X2833)))
      | ~ hBOOL(hAPP(hAPP(c_member(X2833),X2831),c_Int_Oring__1__class_OInts(X2833)))
      | hBOOL(hAPP(hAPP(c_member(X2833),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2833),X2832),X2831)),c_Int_Oring__1__class_OInts(X2833))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__add])]) ).

fof(i_0_728,plain,
    ! [X3015,X3016] :
      ( ~ c_Finite__Set_Ofinite(X3016,c_Orderings_Otop__class_Otop(tc_fun(X3016,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(X3016,X3016,X3015,c_Orderings_Otop__class_Otop(tc_fun(X3016,tc_HOL_Obool)))
      | c_Set_Oimage(X3016,X3016,X3015,c_Orderings_Otop__class_Otop(tc_fun(X3016,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X3016,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__inj__surj])]) ).

fof(i_0_729,plain,
    ! [X2171,X2172,X2173,X2174] :
      ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X2174)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2174),X2173),X2172))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2174),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2174),X2173),X2171)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2174),X2172),X2171))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__right__mono])]) ).

fof(i_0_730,plain,
    ! [X2175,X2176,X2177,X2178] :
      ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X2178)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2178),X2177),X2176))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2178),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2178),X2175),X2177)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2178),X2175),X2176))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__left__mono])]) ).

fof(i_0_731,plain,
    ! [X2625,X2626] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2626,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2626),X2625),X2625)),c_Groups_Ozero__class_Ozero(X2626)))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2626,X2625),c_Groups_Ozero__class_Ozero(X2626)))
        | ~ class_Groups_Olinordered__ab__group__add(X2626) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2626,X2625),c_Groups_Ozero__class_Ozero(X2626)))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2626,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2626),X2625),X2625)),c_Groups_Ozero__class_Ozero(X2626)))
        | ~ class_Groups_Olinordered__ab__group__add(X2626) ) ),
    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_732,plain,
    ! [X2561,X2562,X2563,X2564] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2564,tc_HOL_Obool),X2562),c_Set_Oinsert(X2564,X2563,X2561)))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2564,tc_HOL_Obool),X2562),X2561))
        | hBOOL(hAPP(hAPP(c_member(X2564),X2563),X2562)) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2564,tc_HOL_Obool),X2562),X2561))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2564,tc_HOL_Obool),X2562),c_Set_Oinsert(X2564,X2563,X2561)))
        | hBOOL(hAPP(hAPP(c_member(X2564),X2563),X2562)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_532])])]) ).

fof(i_0_733,plain,
    ! [X2666,X2667,X2668] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X2668)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2668,X2667),c_Groups_Ozero__class_Ozero(X2668)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2668),X2666),c_Groups_Ozero__class_Ozero(X2668)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2668),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2668),X2667),X2666)),c_Groups_Ozero__class_Ozero(X2668))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__neg])]) ).

fof(i_0_734,plain,
    ! [X2669,X2670,X2671] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X2671)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2671),X2670),c_Groups_Ozero__class_Ozero(X2671)))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2671,X2669),c_Groups_Ozero__class_Ozero(X2671)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2671),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2671),X2670),X2669)),c_Groups_Ozero__class_Ozero(X2671))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__nonpos])]) ).

fof(i_0_735,plain,
    ! [X1691,X1692,X1693,X1694] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1694),X1693))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1692),X1691))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1694),X1692)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1693),X1691))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono])]) ).

fof(i_0_736,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_533])])]) ).

fof(i_0_737,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_534])])]) ).

fof(i_0_738,plain,
    ! [X2545,X2546,X2547,X2548] :
      ( ( c_Finite__Set_Ofinite(X2548,X2546)
        | ~ c_Finite__Set_Ofinite(tc_sum(X2548,X2547),c_Sum__Type_OPlus(X2548,X2547,X2546,X2545)) )
      & ( c_Finite__Set_Ofinite(X2547,X2545)
        | ~ c_Finite__Set_Ofinite(tc_sum(X2548,X2547),c_Sum__Type_OPlus(X2548,X2547,X2546,X2545)) )
      & ( ~ c_Finite__Set_Ofinite(X2548,X2546)
        | ~ c_Finite__Set_Ofinite(X2547,X2545)
        | c_Finite__Set_Ofinite(tc_sum(X2548,X2547),c_Sum__Type_OPlus(X2548,X2547,X2546,X2545)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Plus__iff])])]) ).

fof(i_0_739,plain,
    ! [X2553,X2554,X2555,X2556] :
      ( ~ c_Finite__Set_Ofinite(tc_sum(X2556,X2555),c_Sum__Type_OPlus(X2556,X2555,X2554,X2553))
      | c_Finite__Set_Ofinite(X2556,X2554) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__PlusD_I1_J])]) ).

fof(i_0_740,plain,
    ! [X2557,X2558,X2559,X2560] :
      ( ~ c_Finite__Set_Ofinite(tc_sum(X2560,X2559),c_Sum__Type_OPlus(X2560,X2559,X2558,X2557))
      | c_Finite__Set_Ofinite(X2559,X2557) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__PlusD_I2_J])]) ).

fof(i_0_741,plain,
    ! [X2142,X2143,X2144,X2145] :
      ( ~ class_Groups_Oordered__ab__semigroup__add(X2145)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2145,X2144),X2143))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2145,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2145),X2144),X2142)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2145),X2143),X2142))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__mono])]) ).

fof(i_0_742,plain,
    ! [X2146,X2147,X2148,X2149] :
      ( ~ class_Groups_Oordered__ab__semigroup__add(X2149)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2149,X2148),X2147))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2149,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2149),X2146),X2148)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2149),X2146),X2147))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__mono])]) ).

fof(i_0_743,plain,
    ! [X1768,X1769,X1770] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1770),X1769)),X1768))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1770),X1768)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__lessD1])]) ).

fof(i_0_744,plain,
    ! [X2641,X2642,X2643] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X2643)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2643,X2642),c_Groups_Ozero__class_Ozero(X2643)))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2643,X2641),c_Groups_Ozero__class_Ozero(X2643)))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2643,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2643),X2642),X2641)),c_Groups_Ozero__class_Ozero(X2643))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__nonpos])]) ).

fof(i_0_745,plain,
    ! [X1847,X1848,X1849,X1850] :
      ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1849,X1850),X1848),X1847))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1849,X1850)),X1848),X1847))
        | ~ class_Orderings_Oord(X1850) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1849,X1850),X1847),X1848))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1849,X1850)),X1848),X1847))
        | ~ class_Orderings_Oord(X1850) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1849,X1850),X1848),X1847))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1849,X1850),X1847),X1848))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1849,X1850)),X1848),X1847))
        | ~ class_Orderings_Oord(X1850) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_535])])]) ).

fof(i_0_746,plain,
    ! [X2269,X2270,X2271,X2272,X2273,X2274] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2274,tc_fun(X2273,tc_HOL_Obool)),X2272),X2271))
      | ~ hBOOL(hAPP(hAPP(X2272,X2270),X2269))
      | hBOOL(hAPP(hAPP(X2271,X2270),X2269)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_predicate2D])]) ).

fof(i_0_747,plain,
    ! [X2278,X2279,X2280,X2281,X2282,X2283] :
      ( ~ hBOOL(hAPP(hAPP(X2283,X2282),X2281))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2280,tc_fun(X2279,tc_HOL_Obool)),X2283),X2278))
      | hBOOL(hAPP(hAPP(X2278,X2282),X2281)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__predicate2D])]) ).

fof(i_0_748,plain,
    ! [X1779,X1780,X1781] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1781),X1780))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1781),X1779)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1780),X1779))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono1])]) ).

fof(i_0_749,plain,
    ! [X2379,X2380,X2381,X2382,X2383,X2384] :
      ( ( hAPP(X2382,X2380) != hAPP(X2382,X2379)
        | X2380 = X2379
        | ~ hBOOL(hAPP(hAPP(c_member(X2384),X2379),X2381))
        | ~ hBOOL(hAPP(hAPP(c_member(X2384),X2380),X2381))
        | ~ c_Fun_Oinj__on(X2384,X2383,X2382,X2381) )
      & ( X2380 != X2379
        | hAPP(X2382,X2380) = hAPP(X2382,X2379)
        | ~ hBOOL(hAPP(hAPP(c_member(X2384),X2379),X2381))
        | ~ hBOOL(hAPP(hAPP(c_member(X2384),X2380),X2381))
        | ~ c_Fun_Oinj__on(X2384,X2383,X2382,X2381) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__iff])])]) ).

fof(i_0_750,plain,
    ! [X2385,X2386,X2387,X2388,X2389,X2390] :
      ( ~ c_Fun_Oinj__on(X2390,X2389,X2388,X2387)
      | hAPP(X2388,X2386) != hAPP(X2388,X2385)
      | ~ hBOOL(hAPP(hAPP(c_member(X2390),X2386),X2387))
      | ~ hBOOL(hAPP(hAPP(c_member(X2390),X2385),X2387))
      | X2386 = X2385 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__onD])]) ).

fof(i_0_751,plain,
    ! [X2373,X2374,X2375,X2376,X2377,X2378] :
      ( ~ c_Fun_Oinj__on(X2378,X2377,X2376,X2375)
      | X2374 = X2373
      | ~ hBOOL(hAPP(hAPP(c_member(X2378),X2374),X2375))
      | ~ hBOOL(hAPP(hAPP(c_member(X2378),X2373),X2375))
      | hAPP(X2376,X2374) != hAPP(X2376,X2373) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__contraD])]) ).

fof(i_0_752,plain,
    ! [X1682,X1683,X1684] :
      ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1684),X1682))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1684),X1683)),X1682)) )
      & ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1683),X1682))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1684),X1683)),X1682)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_536])])]) ).

fof(i_0_753,plain,
    ! [X1685,X1686,X1687] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1687),X1686)),X1685))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1687),X1685)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD1])]) ).

fof(i_0_754,plain,
    ! [X1688,X1689,X1690] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1690),X1689)),X1688))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1689),X1688)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD2])]) ).

fof(i_0_755,plain,
    ! [X2651,X2652,X2653] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X2653)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2653),c_Groups_Ozero__class_Ozero(X2653)),X2652))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2653),c_Groups_Ozero__class_Ozero(X2653)),X2651))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2653),c_Groups_Ozero__class_Ozero(X2653)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2653),X2652),X2651))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__pos])]) ).

fof(i_0_756,plain,
    ! [X1695,X1696,X1697] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1697),X1696))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1697),X1695)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1696),X1695))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono1])]) ).

fof(i_0_757,plain,
    ! [X1668,X1669,X1670,X1671] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1671,tc_HOL_Obool)),X1670),X1669))
      | ~ hBOOL(hAPP(hAPP(c_member(X1671),X1668),X1670))
      | hBOOL(hAPP(hAPP(c_member(X1671),X1668),X1669)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubsetD])]) ).

fof(i_0_758,plain,
    ! [X2424,X2425,X2426] :
      ( ~ c_Finite__Set_Ofinite(X2426,X2425)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2426,tc_HOL_Obool)),X2424),X2425))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X2426,X2424)),c_Finite__Set_Ocard(X2426,X2425))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__card__mono])]) ).

fof(i_0_759,plain,
    ! [X2311,X2312] : 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)),X2312),X2311),
    inference(variable_rename,[status(thm)],[fact_inj__on__add__nat]) ).

fof(i_0_760,plain,
    ! [X2862,X2863,X2864,X2865,X2866] :
      ( ~ class_Rings_Ocomm__semiring__1(X2866)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2866),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2866),X2865),X2864)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2866),X2863),X2862)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2866),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2866),X2865),X2863)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2866),X2864),X2862)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J])]) ).

fof(i_0_761,plain,
    ! [X2265,X2266,X2267,X2268] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2268,tc_HOL_Obool),X2267),X2266))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2268,tc_HOL_Obool),X2266),X2265))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2268,tc_HOL_Obool),X2267),X2265)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__trans])]) ).

fof(i_0_762,plain,
    ! [X2680,X2681,X2682] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X2682)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2682,c_Groups_Ozero__class_Ozero(X2682)),X2681))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2682),c_Groups_Ozero__class_Ozero(X2682)),X2680))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2682),c_Groups_Ozero__class_Ozero(X2682)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2682),X2681),X2680))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__pos])]) ).

fof(i_0_763,plain,
    ! [X2683,X2684,X2685] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X2685)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2685),c_Groups_Ozero__class_Ozero(X2685)),X2684))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2685,c_Groups_Ozero__class_Ozero(X2685)),X2683))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2685),c_Groups_Ozero__class_Ozero(X2685)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2685),X2684),X2683))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__nonneg])]) ).

fof(i_0_764,plain,
    ! [X1648,X1649] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1649),X1648)),X1649)),
    inference(variable_rename,[status(thm)],[i_0_537]) ).

fof(i_0_765,plain,
    ! [X1650,X1651] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1651),X1650)),X1650)),
    inference(variable_rename,[status(thm)],[i_0_538]) ).

fof(i_0_766,plain,
    ! [X2574,X2575,X2576,X2577] :
      ( ( ~ c_Finite__Set_Ofinite(X2577,X2576)
        | ~ c_Finite__Set_Ofinite(X2575,X2574)
        | c_Finite__Set_Ocard(tc_sum(X2577,X2575),c_Sum__Type_OPlus(X2577,X2575,X2576,X2574)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Finite__Set_Ocard(X2577,X2576)),c_Finite__Set_Ocard(X2575,X2574)) )
      & ( c_Finite__Set_Ofinite(X2577,X2576)
        | c_Finite__Set_Ocard(tc_sum(X2577,X2575),c_Sum__Type_OPlus(X2577,X2575,X2576,X2574)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( c_Finite__Set_Ofinite(X2575,X2574)
        | c_Finite__Set_Ocard(tc_sum(X2577,X2575),c_Sum__Type_OPlus(X2577,X2575,X2576,X2574)) = 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_767,plain,
    ! [X2453,X2454,X2455,X2456] :
      ( ~ c_Finite__Set_Ofinite(X2456,X2455)
      | ~ c_Finite__Set_Ofinite(X2454,X2453)
      | c_Finite__Set_Ocard(tc_sum(X2456,X2454),c_Sum__Type_OPlus(X2456,X2454,X2455,X2453)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Finite__Set_Ocard(X2456,X2455)),c_Finite__Set_Ocard(X2454,X2453)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Plus])]) ).

fof(i_0_768,plain,
    ! [X2644,X2645,X2646,X2647] :
      ( ~ class_Rings_Olinordered__semidom(X2647)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2647),c_Groups_Ozero__class_Ozero(X2647)),X2646))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2647),X2645),X2644))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2647),X2645),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2647),X2646),X2644))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__add__strict])]) ).

fof(i_0_769,plain,
    ! [X2569,X2570,X2571] :
      ( ~ c_Finite__Set_Ofinite(X2571,X2570)
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2571,X2570)),c_Finite__Set_Ocard(X2571,c_Set_Oinsert(X2571,X2569,X2570)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__insert__le])]) ).

fof(i_0_770,plain,
    ! [X2837,X2838] :
      ( ~ class_Int_Oring__char__0(X2838)
      | ~ hBOOL(hAPP(hAPP(c_member(X2838),X2837),c_Int_Oring__1__class_OInts(X2838)))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2838),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2838),c_Groups_Oone__class_Oone(X2838)),X2837)),X2837) != c_Groups_Ozero__class_Ozero(X2838) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__odd__nonzero])]) ).

fof(i_0_771,plain,
    ! [X2656,X2657] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2657),c_Groups_Ozero__class_Ozero(X2657)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2657),X2656),X2656)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2657),c_Groups_Ozero__class_Ozero(X2657)),X2656))
        | ~ class_Groups_Olinordered__ab__group__add(X2657) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2657),c_Groups_Ozero__class_Ozero(X2657)),X2656))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2657),c_Groups_Ozero__class_Ozero(X2657)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2657),X2656),X2656)))
        | ~ class_Groups_Olinordered__ab__group__add(X2657) ) ),
    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_772,plain,
    ! [X2662,X2663] :
      ( ( ~ 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),X2663),X2662)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2663))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2662)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2663))
        | 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),X2663),X2662))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2662))
        | 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),X2663),X2662))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__gr__0])])]) ).

fof(i_0_773,plain,
    ! [X2430,X2431,X2432] :
      ( ~ c_Finite__Set_Ofinite(X2432,X2431)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2432,tc_HOL_Obool),X2430),X2431))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2432,X2431)),c_Finite__Set_Ocard(X2432,X2430)))
      | X2430 = X2431 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__seteq])]) ).

fof(i_0_774,plain,
    ! [X2509,X2510,X2511,X2512] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2512,tc_HOL_Obool),X2511),X2510))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2512,tc_HOL_Obool),X2511),c_Set_Oinsert(X2512,X2509,X2510))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__insertI2])]) ).

fof(i_0_775,plain,
    ! [X2672,X2673,X2674,X2675] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X2675)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2675,c_Groups_Ozero__class_Ozero(X2675)),X2674))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2675),X2673),X2672))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2675),X2673),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2675),X2674),X2672))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing2])]) ).

fof(i_0_776,plain,
    ! [X2676,X2677,X2678,X2679] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X2679)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2679),c_Groups_Ozero__class_Ozero(X2679)),X2678))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2679,X2677),X2676))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2679),X2677),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2679),X2678),X2676))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing])]) ).

fof(i_0_777,plain,
    ! [X2627,X2628,X2629] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X2629)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2629,c_Groups_Ozero__class_Ozero(X2629)),X2628))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2629,c_Groups_Ozero__class_Ozero(X2629)),X2627))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2629,c_Groups_Ozero__class_Ozero(X2629)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2629),X2628),X2627))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__nonneg])]) ).

fof(i_0_778,plain,
    ! [X1854,X1855,X1856] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1856,tc_HOL_Obool)),X1855),X1854))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1856,tc_HOL_Obool),X1855),X1854)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__imp__subset])]) ).

fof(i_0_779,plain,
    ! [X1851,X1852,X1853] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1853,tc_HOL_Obool),X1852),X1851))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1853,tc_HOL_Obool)),X1852),X1851))
        | X1852 = X1851 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1853,tc_HOL_Obool)),X1852),X1851))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1853,tc_HOL_Obool),X1852),X1851)) )
      & ( X1852 != X1851
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1853,tc_HOL_Obool),X1852),X1851)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__iff__psubset__eq])])]) ).

fof(i_0_780,plain,
    ! [X1844,X1845,X1846] :
      ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1846,tc_HOL_Obool),X1845),X1844))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1846,tc_HOL_Obool)),X1845),X1844)) )
      & ( X1845 != X1844
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1846,tc_HOL_Obool)),X1845),X1844)) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1846,tc_HOL_Obool),X1845),X1844))
        | X1845 = X1844
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1846,tc_HOL_Obool)),X1845),X1844)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__eq])])]) ).

fof(i_0_781,plain,
    ! [X2530,X2531,X2532,X2533] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X2533),X2532),c_Set_Oinsert(X2533,X2531,X2530)))
        | X2532 = X2531
        | hBOOL(hAPP(hAPP(c_member(X2533),X2532),X2530)) )
      & ( X2532 != X2531
        | hBOOL(hAPP(hAPP(c_member(X2533),X2532),c_Set_Oinsert(X2533,X2531,X2530))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X2533),X2532),X2530))
        | hBOOL(hAPP(hAPP(c_member(X2533),X2532),c_Set_Oinsert(X2533,X2531,X2530))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__iff])])]) ).

fof(i_0_782,plain,
    ! [X2480,X2481,X2482,X2483] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X2483),X2482),c_Set_Oinsert(X2483,X2481,X2480)))
      | X2482 = X2481
      | hBOOL(hAPP(hAPP(c_member(X2483),X2482),X2480)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insertE])]) ).

fof(i_0_783,plain,
    ! [X2623,X2624] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2624,c_Groups_Ozero__class_Ozero(X2624)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2624),X2623),X2623)))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2624,c_Groups_Ozero__class_Ozero(X2624)),X2623))
        | ~ class_Groups_Olinordered__ab__group__add(X2624) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2624,c_Groups_Ozero__class_Ozero(X2624)),X2623))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2624,c_Groups_Ozero__class_Ozero(X2624)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2624),X2623),X2623)))
        | ~ class_Groups_Olinordered__ab__group__add(X2624) ) ),
    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_784,plain,
    ! [X2320,X2321,X2322] : c_FuncSet_OPi(X2322,X2321,X2320,hAPP(c_COMBK(tc_fun(X2321,tc_HOL_Obool),X2322),c_Orderings_Otop__class_Otop(tc_fun(X2321,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X2322,X2321),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Pi__UNIV]) ).

fof(i_0_785,plain,
    ! [X2633,X2634,X2635,X2636] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X2636)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2636,c_Groups_Ozero__class_Ozero(X2636)),X2635))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2636,X2634),X2633))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2636,X2634),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2636),X2635),X2633))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing])]) ).

fof(i_0_786,plain,
    ! [X2637,X2638,X2639,X2640] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X2640)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2640,c_Groups_Ozero__class_Ozero(X2640)),X2639))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2640,X2638),X2637))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2640,X2638),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2640),X2637),X2639))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing2])]) ).

fof(i_0_787,plain,
    ! [X2549,X2550,X2551,X2552] :
      ( ~ c_Finite__Set_Ofinite(X2552,X2551)
      | ~ c_Finite__Set_Ofinite(X2550,X2549)
      | c_Finite__Set_Ofinite(tc_sum(X2552,X2550),c_Sum__Type_OPlus(X2552,X2550,X2551,X2549)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Plus])]) ).

fof(i_0_788,plain,
    ! [X3204,X3205,X3206,X3207,X3208,X3209] : hAPP(hAPP(hAPP(c_COMBC(X3209,X3208,X3207),X3206),X3205),X3204) = hAPP(hAPP(X3206,X3204),X3205),
    inference(variable_rename,[status(thm)],[help_c__COMBC__1]) ).

fof(i_0_789,plain,
    ! [X2248,X2249,X2250] :
      ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2248,tc_HOL_Obool),X2250),X2249))
        | X2250 != X2249 )
      & ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2248,tc_HOL_Obool),X2249),X2250))
        | X2250 != X2249 )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2248,tc_HOL_Obool),X2250),X2249))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2248,tc_HOL_Obool),X2249),X2250))
        | X2250 = X2249 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__eq__subset])])]) ).

fof(i_0_790,plain,
    ! [X2243,X2244,X2245] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2245,tc_HOL_Obool),X2244),X2243))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2245,tc_HOL_Obool),X2243),X2244))
      | X2244 = X2243 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityI])]) ).

fof(i_0_791,plain,
    ! [X1882,X1883,X1884,X1885] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X1885),X1884),X1883))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1885,tc_HOL_Obool),X1883),X1882))
      | hBOOL(hAPP(hAPP(c_member(X1885),X1884),X1882)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__rev__mp])]) ).

fof(i_0_792,plain,
    ! [X1886,X1887,X1888,X1889] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1889,tc_HOL_Obool),X1888),X1887))
      | ~ hBOOL(hAPP(hAPP(c_member(X1889),X1886),X1888))
      | hBOOL(hAPP(hAPP(c_member(X1889),X1886),X1887)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__mp])]) ).

fof(i_0_793,plain,
    ! [X1878,X1879,X1880,X1881] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1881,tc_HOL_Obool),X1880),X1879))
      | ~ hBOOL(hAPP(hAPP(c_member(X1881),X1878),X1880))
      | hBOOL(hAPP(hAPP(c_member(X1881),X1878),X1879)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__mono])]) ).

fof(i_0_794,plain,
    ! [X1834,X1835,X1836,X1837] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1837,tc_HOL_Obool),X1836),X1835))
      | ~ hBOOL(hAPP(hAPP(c_member(X1837),X1834),X1836))
      | hBOOL(hAPP(hAPP(c_member(X1837),X1834),X1835)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subsetD])]) ).

fof(i_0_795,plain,
    ! [X1941,X1942,X1943,X1944,X1945] :
      ( ~ class_Orderings_Oord(X1945)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1944,X1945),X1943),X1942))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1945,hAPP(X1943,X1941)),hAPP(X1942,X1941))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funD])]) ).

fof(i_0_796,plain,
    ! [X1903,X1904,X1905,X1906,X1907] :
      ( ~ class_Orderings_Oord(X1907)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1906,X1907),X1905),X1904))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1907,hAPP(X1905,X1903)),hAPP(X1904,X1903))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funE])]) ).

fof(i_0_797,plain,
    ! [X2896,X2897,X2898,X2899] :
      ( ~ c_Finite__Set_Ofinite(X2899,X2898)
      | c_Finite__Set_Ofinite(X2897,c_Set_Oimage(X2899,X2897,X2896,X2898)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageI])]) ).

fof(i_0_798,plain,
    ! [X2427,X2428,X2429] :
      ( ~ c_Finite__Set_Ofinite(X2429,X2428)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2429,tc_HOL_Obool),X2427),X2428))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2429,X2427)),c_Finite__Set_Ocard(X2429,X2428))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__mono])]) ).

fof(i_0_799,plain,
    ! [X2858,X2859,X2860,X2861] :
      ( ~ class_Rings_Ocomm__semiring__1(X2861)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2861),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2861),X2860),X2859)),X2858) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2861),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2861),X2860),X2858)),X2859) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J])]) ).

fof(i_0_800,plain,
    ! [X2343,X2344,X2345,X2346,X2347] :
      ( ( hAPP(X2345,X2344) != hAPP(X2345,X2343)
        | X2344 = X2343
        | ~ c_Fun_Oinj__on(X2347,X2346,X2345,c_Orderings_Otop__class_Otop(tc_fun(X2347,tc_HOL_Obool))) )
      & ( X2344 != X2343
        | hAPP(X2345,X2344) = hAPP(X2345,X2343)
        | ~ c_Fun_Oinj__on(X2347,X2346,X2345,c_Orderings_Otop__class_Otop(tc_fun(X2347,tc_HOL_Obool))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__eq])])]) ).

fof(i_0_801,plain,
    ! [X2348,X2349,X2350,X2351,X2352] :
      ( ~ c_Fun_Oinj__on(X2352,X2351,X2350,c_Orderings_Otop__class_Otop(tc_fun(X2352,tc_HOL_Obool)))
      | hAPP(X2350,X2349) != hAPP(X2350,X2348)
      | X2349 = X2348 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_injD])]) ).

fof(i_0_802,plain,
    ! [X3155,X3156,X3157,X3158,X3159] :
      ( ( X3158 = X3156
        | c_SetInterval_Oord__class_OatLeastLessThan(X3159,X3158,X3157) != c_SetInterval_Oord__class_OatLeastLessThan(X3159,X3156,X3155)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3159),X3156),X3155))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3159),X3158),X3157))
        | ~ class_Orderings_Olinorder(X3159) )
      & ( X3157 = X3155
        | c_SetInterval_Oord__class_OatLeastLessThan(X3159,X3158,X3157) != c_SetInterval_Oord__class_OatLeastLessThan(X3159,X3156,X3155)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3159),X3156),X3155))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3159),X3158),X3157))
        | ~ class_Orderings_Olinorder(X3159) )
      & ( X3158 != X3156
        | X3157 != X3155
        | c_SetInterval_Oord__class_OatLeastLessThan(X3159,X3158,X3157) = c_SetInterval_Oord__class_OatLeastLessThan(X3159,X3156,X3155)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3159),X3156),X3155))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3159),X3158),X3157))
        | ~ class_Orderings_Olinorder(X3159) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__eq__iff])])]) ).

fof(i_0_803,plain,
    ! [X3160,X3161,X3162,X3163,X3164] :
      ( ~ class_Orderings_Olinorder(X3164)
      | c_SetInterval_Oord__class_OatLeastLessThan(X3164,X3163,X3162) != c_SetInterval_Oord__class_OatLeastLessThan(X3164,X3161,X3160)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3164),X3163),X3162))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3164),X3161),X3160))
      | X3163 = X3161 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__inj_I1_J])]) ).

fof(i_0_804,plain,
    ! [X3165,X3166,X3167,X3168,X3169] :
      ( ~ class_Orderings_Olinorder(X3169)
      | c_SetInterval_Oord__class_OatLeastLessThan(X3169,X3168,X3167) != c_SetInterval_Oord__class_OatLeastLessThan(X3169,X3166,X3165)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3169),X3168),X3167))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3169),X3166),X3165))
      | X3167 = X3165 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__inj_I2_J])]) ).

fof(i_0_805,plain,
    ! [X2873,X2874,X2876] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk33_2(X2873,X2874)),X2873))
        | ~ hBOOL(hAPP(X2874,X2873))
        | hBOOL(hAPP(X2874,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2876),esk33_2(X2873,X2874)))
        | ~ hBOOL(hAPP(X2874,X2876))
        | ~ hBOOL(hAPP(X2874,X2873))
        | hBOOL(hAPP(X2874,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
      & ( hBOOL(hAPP(X2874,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk33_2(X2873,X2874)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | ~ hBOOL(hAPP(X2874,X2873))
        | hBOOL(hAPP(X2874,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_539])])])])]) ).

fof(i_0_806,plain,
    ! [X2776,X2777] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2777),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2777),X2776)))),
    inference(variable_rename,[status(thm)],[fact_less__add__Suc1]) ).

fof(i_0_807,plain,
    ! [X2778,X2779] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2779),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2778),X2779)))),
    inference(variable_rename,[status(thm)],[fact_less__add__Suc2]) ).

fof(i_0_808,plain,
    ! [X2538,X2539,X2540,X2541] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X2541),X2540),X2539))
      | hBOOL(hAPP(hAPP(c_member(X2541),X2540),c_Set_Oinsert(X2541,X2538,X2539))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insertI2])]) ).

fof(i_0_809,plain,
    ! [X2476,X2477,X2478,X2479] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X2479),X2478),X2477))
        | hBOOL(hAPP(hAPP(c_member(X2479),X2478),c_Set_Oinsert(X2479,X2476,X2477))) )
      & ( X2478 != X2476
        | hBOOL(hAPP(hAPP(c_member(X2479),X2478),c_Set_Oinsert(X2479,X2476,X2477))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_540])])]) ).

fof(i_0_810,plain,
    ! [X2731,X2732,X2733] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2733),X2732))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2732),X2731))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2733)),X2731)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__trans__Suc])]) ).

fof(i_0_811,plain,
    ! [X2689] :
      ( ~ c_Finite__Set_Ofinite(X2689,c_Orderings_Otop__class_Otop(tc_fun(X2689,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(X2689,c_Orderings_Otop__class_Otop(tc_fun(X2689,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__card__ge__0])]) ).

fof(i_0_812,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_813,plain,
    ! [X2742,X2743] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2743)),hAPP(c_Nat_OSuc,X2742)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2743),X2742)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2743),X2742))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2743)),hAPP(c_Nat_OSuc,X2742))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__less__eq])]) ).

fof(i_0_814,plain,
    ! [X2725,X2726] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2726)),hAPP(c_Nat_OSuc,X2725)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2726),X2725)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__less__SucD])]) ).

fof(i_0_815,plain,
    ! [X2700,X2701] :
      ( ~ c_Finite__Set_Ofinite(tc_fun(X2701,X2700),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X2701,X2700),tc_HOL_Obool)))
      | c_Finite__Set_Ocard(X2700,c_Orderings_Otop__class_Otop(tc_fun(X2700,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | c_Finite__Set_Ofinite(X2701,c_Orderings_Otop__class_Otop(tc_fun(X2701,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__fun__UNIVD1])]) ).

fof(i_0_816,plain,
    ! [X2021,X2022,X2023,X2024] :
      ( ~ class_Orderings_Opreorder(X2024)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2024),X2023),X2022))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2024),X2022),X2021))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2024),X2023),X2021)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__trans])]) ).

fof(i_0_817,plain,
    ! [X2025,X2026,X2027,X2028] :
      ( ~ class_Orderings_Oorder(X2028)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2028),X2027),X2026))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2028),X2025),X2027))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2028),X2025),X2026)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I10_J])]) ).

fof(i_0_818,plain,
    ! [X3138,X3139] : c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3139,X3138)) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X3139),hAPP(c_Nat_OSuc,X3138)),
    inference(variable_rename,[status(thm)],[fact_image__Suc__atLeastLessThan]) ).

fof(i_0_819,plain,
    ! [X2630,X2631,X2632] :
      ( ( X2631 = c_Groups_Ozero__class_Ozero(X2632)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2632),X2631),X2630) != c_Groups_Ozero__class_Ozero(X2632)
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2632,c_Groups_Ozero__class_Ozero(X2632)),X2630))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2632,c_Groups_Ozero__class_Ozero(X2632)),X2631))
        | ~ class_Groups_Oordered__comm__monoid__add(X2632) )
      & ( X2630 = c_Groups_Ozero__class_Ozero(X2632)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2632),X2631),X2630) != c_Groups_Ozero__class_Ozero(X2632)
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2632,c_Groups_Ozero__class_Ozero(X2632)),X2630))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2632,c_Groups_Ozero__class_Ozero(X2632)),X2631))
        | ~ class_Groups_Oordered__comm__monoid__add(X2632) )
      & ( X2631 != c_Groups_Ozero__class_Ozero(X2632)
        | X2630 != c_Groups_Ozero__class_Ozero(X2632)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2632),X2631),X2630) = c_Groups_Ozero__class_Ozero(X2632)
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2632,c_Groups_Ozero__class_Ozero(X2632)),X2630))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2632,c_Groups_Ozero__class_Ozero(X2632)),X2631))
        | ~ class_Groups_Oordered__comm__monoid__add(X2632) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__eq__0__iff])])]) ).

fof(i_0_820,plain,
    ! [X2572,X2573] : c_Sum__Type_OPlus(X2573,X2572,c_Orderings_Otop__class_Otop(tc_fun(X2573,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2572,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X2573,X2572),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_UNIV__Plus__UNIV]) ).

fof(i_0_821,plain,
    ! [X2192,X2193,X2194] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2194),X2193))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2194),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2193),X2192))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I1_J])]) ).

fof(i_0_822,plain,
    ! [X1655,X1656,X1657] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1657),X1656))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1657),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1656),X1655))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add1])]) ).

fof(i_0_823,plain,
    ! [X2195,X2196,X2197] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2197),X2196))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2197),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2195),X2196))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I2_J])]) ).

fof(i_0_824,plain,
    ! [X1782,X1783,X1784] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1784),X1783))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1784),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1782),X1783))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add2])]) ).

fof(i_0_825,plain,
    ! [X2761,X2762,X2764,X2765,X2766] :
      ( ( X2762 = hAPP(c_Nat_OSuc,esk30_2(X2761,X2762))
        | X2762 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2762),hAPP(c_Nat_OSuc,X2761))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk30_2(X2761,X2762)),X2761))
        | X2762 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2762),hAPP(c_Nat_OSuc,X2761))) )
      & ( X2765 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2765),hAPP(c_Nat_OSuc,X2764))) )
      & ( X2765 != hAPP(c_Nat_OSuc,X2766)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2766),X2764))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2765),hAPP(c_Nat_OSuc,X2764))) ) ),
    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_826,plain,
    ! [X2854,X2855,X2856,X2857] :
      ( ~ class_Rings_Ocomm__semiring__1(X2857)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2857),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2857),X2856),X2855)),X2854) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2857),X2856),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2857),X2855),X2854)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J])]) ).

fof(i_0_827,plain,
    ! [X2035,X2036,X2037,X2038] :
      ( ~ class_Groups_Oab__semigroup__add(X2038)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2038),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2038),X2037),X2036)),X2035) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2038),X2037),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2038),X2036),X2035)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__semigroup__add__class_Oadd__ac_I1_J])]) ).

fof(i_0_828,plain,
    ! [X2850,X2851,X2852,X2853] :
      ( ~ class_Rings_Ocomm__semiring__1(X2853)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2853),X2852),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2853),X2851),X2850)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2853),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2853),X2852),X2851)),X2850) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J])]) ).

fof(i_0_829,plain,
    ! [X2523,X2524,X2525,X2526] :
      ( ( ~ hBOOL(hAPP(c_Set_Oinsert(X2526,X2525,X2524),X2523))
        | X2525 = X2523
        | hBOOL(hAPP(X2524,X2523)) )
      & ( X2525 != X2523
        | hBOOL(hAPP(c_Set_Oinsert(X2526,X2525,X2524),X2523)) )
      & ( ~ hBOOL(hAPP(X2524,X2523))
        | hBOOL(hAPP(c_Set_Oinsert(X2526,X2525,X2524),X2523)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__code])])]) ).

fof(i_0_830,plain,
    ! [X2686] :
      ( ~ class_Rings_Olinordered__semidom(X2686)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2686),c_Groups_Ozero__class_Ozero(X2686)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2686),c_Groups_Oone__class_Oone(X2686)),c_Groups_Oone__class_Oone(X2686)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__two])]) ).

fof(i_0_831,plain,
    ! [X2718,X2719] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2719)),hAPP(c_Nat_OSuc,X2718)))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2719),X2718)) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2719),X2718))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2719)),hAPP(c_Nat_OSuc,X2718))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__mono])]) ).

fof(i_0_832,plain,
    ! [X2126,X2127,X2128,X2129] :
      ( ~ class_Orderings_Opreorder(X2129)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2129,X2128),X2127))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2129),X2127),X2126))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2129),X2128),X2126)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less__trans])]) ).

fof(i_0_833,plain,
    ! [X2118,X2119,X2120,X2121] :
      ( ~ class_Orderings_Opreorder(X2121)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2121),X2120),X2119))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2121,X2119),X2118))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2121),X2120),X2118)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le__trans])]) ).

fof(i_0_834,plain,
    ! [X2130,X2131,X2132,X2133] :
      ( ~ class_Orderings_Oorder(X2133)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2133,X2132),X2131))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2133),X2130),X2132))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2133),X2130),X2131)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I8_J])]) ).

fof(i_0_835,plain,
    ! [X2122,X2123,X2124,X2125] :
      ( ~ class_Orderings_Oorder(X2125)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2125),X2124),X2123))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2125,X2122),X2124))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2125),X2122),X2123)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I7_J])]) ).

fof(i_0_836,plain,
    ! [X2445,X2446] :
      ( ( c_Finite__Set_Ofinite(X2446,c_Orderings_Otop__class_Otop(tc_fun(X2446,tc_HOL_Obool)))
        | ~ c_Finite__Set_Ofinite(tc_sum(X2446,X2445),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X2446,X2445),tc_HOL_Obool))) )
      & ( c_Finite__Set_Ofinite(X2445,c_Orderings_Otop__class_Otop(tc_fun(X2445,tc_HOL_Obool)))
        | ~ c_Finite__Set_Ofinite(tc_sum(X2446,X2445),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X2446,X2445),tc_HOL_Obool))) )
      & ( ~ c_Finite__Set_Ofinite(X2446,c_Orderings_Otop__class_Otop(tc_fun(X2446,tc_HOL_Obool)))
        | ~ c_Finite__Set_Ofinite(X2445,c_Orderings_Otop__class_Otop(tc_fun(X2445,tc_HOL_Obool)))
        | c_Finite__Set_Ofinite(tc_sum(X2446,X2445),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X2446,X2445),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_837,plain,
    ! [X2443,X2444] :
      ( ~ c_Finite__Set_Ofinite(X2444,c_Orderings_Otop__class_Otop(tc_fun(X2444,tc_HOL_Obool)))
      | ~ c_Finite__Set_Ofinite(X2443,c_Orderings_Otop__class_Otop(tc_fun(X2443,tc_HOL_Obool)))
      | c_Finite__Set_Ofinite(tc_prod(X2444,X2443),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X2444,X2443),tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Prod__UNIV])]) ).

fof(i_0_838,plain,
    ! [X1771,X1772,X1773,X1774] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1774),X1773))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1772),X1773) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1774),X1771)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1772),X1771)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__eq__less])]) ).

fof(i_0_839,plain,
    ! [X2513,X2514,X2515] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2515,tc_HOL_Obool),X2514),c_Set_Oinsert(X2515,X2513,X2514))),
    inference(variable_rename,[status(thm)],[fact_subset__insertI]) ).

fof(i_0_840,plain,
    ! [X2534,X2535,X2536,X2537] :
      ( ( c_Set_Oinsert(X2537,X2536,X2535) != c_Set_Oinsert(X2537,X2536,X2534)
        | X2535 = X2534
        | hBOOL(hAPP(hAPP(c_member(X2537),X2536),X2534))
        | hBOOL(hAPP(hAPP(c_member(X2537),X2536),X2535)) )
      & ( X2535 != X2534
        | c_Set_Oinsert(X2537,X2536,X2535) = c_Set_Oinsert(X2537,X2536,X2534)
        | hBOOL(hAPP(hAPP(c_member(X2537),X2536),X2534))
        | hBOOL(hAPP(hAPP(c_member(X2537),X2536),X2535)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_541])])]) ).

fof(i_0_841,plain,
    ! [X2727,X2728] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2728)),X2727))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2728),X2727)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__lessD])]) ).

fof(i_0_842,plain,
    ! [X2722,X2723] :
      ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2723),X2722))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2722)),X2723)) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2722)),X2723))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2723),X2722)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_542])]) ).

fof(i_0_843,plain,
    ! [X2702,X2703] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2703),X2702))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2703)),hAPP(c_Nat_OSuc,X2702))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mono])]) ).

fof(i_0_844,plain,
    ! [X2200,X2201,X2202] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2202),X2201))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2202),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2201),X2200))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I3_J])]) ).

fof(i_0_845,plain,
    ! [X1701,X1702,X1703] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1703),X1702))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1703),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1702),X1701))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add1])]) ).

fof(i_0_846,plain,
    ! [X1831,X1832,X1833] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1833),X1832))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1833),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1831),X1832))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I4_J])]) ).

fof(i_0_847,plain,
    ! [X1698,X1699,X1700] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1700),X1699))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1700),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1698),X1699))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add2])]) ).

fof(i_0_848,plain,
    ! [X2451,X2452] :
      ( ~ c_Finite__Set_Ofinite(tc_fun(X2452,X2451),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X2452,X2451),tc_HOL_Obool)))
      | c_Finite__Set_Ofinite(X2451,c_Orderings_Otop__class_Otop(tc_fun(X2451,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__fun__UNIVD2])]) ).

fof(i_0_849,plain,
    ! [X2746,X2747] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2747),X2746))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2746),hAPP(c_Nat_OSuc,X2747))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2746),hAPP(c_Nat_OSuc,X2747)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2747),X2746)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_543])]) ).

fof(i_0_850,plain,
    ! [X1757,X1758,X1759] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1759),X1758)),X1757) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1759),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1758),X1757)),
    inference(variable_rename,[status(thm)],[fact_nat__add__assoc]) ).

fof(i_0_851,plain,
    ! [X2798,X2799] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2799),X2798))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2799)),X2798)) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2799)),X2798))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2799),X2798)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__Suc__le])]) ).

fof(i_0_852,plain,
    ! [X2794,X2795] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2795)),X2794))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2795),X2794)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2795),X2794))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2795)),X2794)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__eq])]) ).

fof(i_0_853,plain,
    ! [X2786,X2787] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2787)),X2786))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2787),X2786)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__lessD])]) ).

fof(i_0_854,plain,
    ! [X2261,X2262,X2263,X2264] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2264,tc_HOL_Obool),X2263),X2262))
      | ~ hBOOL(hAPP(X2263,X2261))
      | hBOOL(hAPP(X2262,X2261)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_predicate1D])]) ).

fof(i_0_855,plain,
    ! [X2251,X2252,X2253,X2254] :
      ( ~ hBOOL(hAPP(X2254,X2253))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2252,tc_HOL_Obool),X2254),X2251))
      | hBOOL(hAPP(X2251,X2253)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__predicate1D])]) ).

fof(i_0_856,plain,
    ! [X1915,X1916,X1917,X1918] :
      ( ~ class_Orderings_Opreorder(X1918)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1918,X1917),X1916))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1918,X1916),X1915))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1918,X1917),X1915)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__trans])]) ).

fof(i_0_857,plain,
    ! [X1908,X1909,X1910,X1911] :
      ( ~ class_Orderings_Oorder(X1911)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1911,X1910),X1909))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1911,X1908),X1910))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1911,X1908),X1909)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I6_J])]) ).

fof(i_0_858,plain,
    ! [X2734,X2735] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2735),X2734))
      | hAPP(c_Nat_OSuc,X2735) = X2734
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2735)),X2734)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__lessI])]) ).

fof(i_0_859,plain,
    ! [X2002,X2003,X2004] :
      ( ~ class_Orderings_Oorder(X2004)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2004),X2003),X2002))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2004),X2002),X2003)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_544])]) ).

fof(i_0_860,plain,
    ! [X1972,X1973,X1974] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1974),X1973),X1972))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1974),X1972),X1973))
        | X1973 = X1972
        | ~ class_Orderings_Olinorder(X1974) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1974),X1972),X1973))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1974),X1973),X1972))
        | ~ class_Orderings_Olinorder(X1974) )
      & ( X1973 != X1972
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1974),X1973),X1972))
        | ~ class_Orderings_Olinorder(X1974) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_545])])]) ).

fof(i_0_861,plain,
    ! [X2029,X2030,X2031] :
      ( ~ class_Orderings_Opreorder(X2031)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2031),X2030),X2029))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2031),X2029),X2030)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_546])]) ).

fof(i_0_862,plain,
    ! [X1999,X2000,X2001] :
      ( ~ class_Orderings_Opreorder(X2001)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2001),X2000),X1999))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2001),X1999),X2000)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_547])]) ).

fof(i_0_863,plain,
    ! [X1990,X1991,X1992] :
      ( ~ class_Orderings_Opreorder(X1992)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1992),X1991),X1990))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1992),X1990),X1991)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_548])]) ).

fof(i_0_864,plain,
    ! [X1987,X1988,X1989] :
      ( ~ class_Orderings_Opreorder(X1989)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1989),X1988),X1987))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1989),X1987),X1988)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_549])]) ).

fof(i_0_865,plain,
    ! [X1638,X1639] :
      ( ~ class_Rings_Olinordered__semidom(X1639)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1639),X1638),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1639),X1638),c_Groups_Oone__class_Oone(X1639)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__one])]) ).

fof(i_0_866,plain,
    ! [X2788,X2789] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2788),hAPP(c_Nat_OSuc,X2789)))
        | X2788 = X2789
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2789),X2788)) )
      & ( X2788 != X2789
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2788),hAPP(c_Nat_OSuc,X2789)))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2789),X2788)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__less__Suc__eq])])]) ).

fof(i_0_867,plain,
    ! [X2712,X2713] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2713)),X2712))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2713),X2712)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__leD])]) ).

fof(i_0_868,plain,
    ! [X2457,X2458,X2459] :
      ( ~ c_Finite__Set_Ofinite(X2459,X2458)
      | hBOOL(hAPP(hAPP(c_member(X2459),X2457),X2458))
      | c_Finite__Set_Ocard(X2459,c_Set_Oinsert(X2459,X2457,X2458)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Finite__Set_Ocard(X2459,X2458)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_550])]) ).

fof(i_0_869,plain,
    ! [X2079,X2080,X2081] :
      ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2081,X2080),X2079))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2081),X2080),X2079))
        | ~ class_Orderings_Opreorder(X2081) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2081,X2079),X2080))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2081),X2080),X2079))
        | ~ class_Orderings_Opreorder(X2081) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2081,X2080),X2079))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2081,X2079),X2080))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2081),X2080),X2079))
        | ~ class_Orderings_Opreorder(X2081) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_551])])]) ).

fof(i_0_870,plain,
    ! [X2804,X2805,X2806] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X2806),X2804),X2805))
        | c_Finite__Set_Ocard(X2806,c_Set_Oinsert(X2806,X2804,X2805)) = c_Finite__Set_Ocard(X2806,X2805)
        | ~ c_Finite__Set_Ofinite(X2806,X2805) )
      & ( hBOOL(hAPP(hAPP(c_member(X2806),X2804),X2805))
        | c_Finite__Set_Ocard(X2806,c_Set_Oinsert(X2806,X2804,X2805)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X2806,X2805))
        | ~ c_Finite__Set_Ofinite(X2806,X2805) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_552])])]) ).

fof(i_0_871,plain,
    ! [X3143,X3145,X3146,X3147] :
      ( ( ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X3143)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3145),X3143))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3145),esk41_1(X3143))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk42_2(X3146,X3147)),X3146))
        | c_Finite__Set_Ofinite(tc_Nat_Onat,X3146) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk42_2(X3146,X3147)),X3147))
        | c_Finite__Set_Ofinite(tc_Nat_Onat,X3146) ) ),
    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_872,plain,
    ! [X2519,X2520,X2521,X2522] : c_Set_Oinsert(X2522,X2521,c_Set_Oinsert(X2522,X2520,X2519)) = c_Set_Oinsert(X2522,X2520,c_Set_Oinsert(X2522,X2521,X2519)),
    inference(variable_rename,[status(thm)],[fact_insert__commute]) ).

fof(i_0_873,plain,
    ! [X2527,X2528,X2529] : hBOOL(hAPP(hAPP(c_member(X2529),X2528),c_Set_Oinsert(X2529,X2528,X2527))),
    inference(variable_rename,[status(thm)],[fact_insertI1]) ).

fof(i_0_874,plain,
    ! [X2744,X2745] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2745),hAPP(c_Nat_OSuc,X2744)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2745),X2744))
        | X2745 = X2744 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2745),X2744))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2745),hAPP(c_Nat_OSuc,X2744))) )
      & ( X2745 != X2744
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2745),hAPP(c_Nat_OSuc,X2744))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq])])]) ).

fof(i_0_875,plain,
    ! [X2740,X2741] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2741),hAPP(c_Nat_OSuc,X2740)))
        | X2741 = X2740
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2741),X2740)) )
      & ( X2741 != X2740
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2741),hAPP(c_Nat_OSuc,X2740)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2741),X2740)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_553])])]) ).

fof(i_0_876,plain,
    ! [X2738,X2739] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2739),X2738))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2739),hAPP(c_Nat_OSuc,X2738)))
      | X2738 = X2739 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_554])]) ).

fof(i_0_877,plain,
    ! [X2729,X2730] :
      ( ~ 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),X2730),X2729))
      | X2730 = X2729 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_555])]) ).

fof(i_0_878,plain,
    ! [X2790,X2791] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2791),X2790))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2791)),X2790)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__leI])]) ).

fof(i_0_879,plain,
    ! [X2846,X2847,X2848,X2849] :
      ( ~ class_Rings_Ocomm__semiring__1(X2849)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2849),X2848),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2849),X2847),X2846)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2849),X2847),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2849),X2848),X2846)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J])]) ).

fof(i_0_880,plain,
    ! [X1663,X1664,X1665] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1665),X1664))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1664),X1663))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1665),X1663)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__trans])]) ).

fof(i_0_881,plain,
    ! [X2440,X2441,X2442] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2442,tc_HOL_Obool),X2441),X2440))
      | ~ c_Finite__Set_Ofinite(X2442,X2440)
      | c_Finite__Set_Ofinite(X2442,X2441) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__subset])]) ).

fof(i_0_882,plain,
    ! [X2437,X2438,X2439] :
      ( ~ c_Finite__Set_Ofinite(X2439,X2438)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2439,tc_HOL_Obool),X2437),X2438))
      | c_Finite__Set_Ofinite(X2439,X2437) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__finite__subset])]) ).

fof(i_0_883,plain,
    ! [X2106,X2107,X2108] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2108),X2107),X2106))
        | X2107 = X2106
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2108,X2107),X2106))
        | ~ class_Orderings_Olinorder(X2108) )
      & ( X2107 != X2106
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2108),X2107),X2106))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2108,X2107),X2106))
        | ~ class_Orderings_Olinorder(X2108) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_556])])]) ).

fof(i_0_884,plain,
    ! [X2100,X2101,X2102] :
      ( ~ class_Orderings_Olinorder(X2102)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2102,X2101),X2100))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2102),X2100),X2101)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_557])]) ).

fof(i_0_885,plain,
    ! [X2067,X2068,X2069] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2069),X2068),X2067))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2069,X2067),X2068))
        | ~ class_Orderings_Olinorder(X2069) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2069,X2067),X2068))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2069),X2068),X2067))
        | ~ class_Orderings_Olinorder(X2069) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_558])])]) ).

fof(i_0_886,plain,
    ! [X2070,X2071,X2072] :
      ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2072,X2071),X2070))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2072),X2070),X2071))
        | ~ class_Orderings_Olinorder(X2072) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2072),X2070),X2071))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2072,X2071),X2070))
        | ~ class_Orderings_Olinorder(X2072) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_559])])]) ).

fof(i_0_887,plain,
    ! [X2780,X2781,X2783,X2784,X2785] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2781),X2780))
        | X2780 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2781),esk32_2(X2780,X2781))) )
      & ( X2783 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2784),X2785))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2784),X2783)) ) ),
    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_888,plain,
    ! [X2796,X2797] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2797),hAPP(c_Nat_OSuc,X2796)))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2797),X2796)) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2797),X2796))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2797),hAPP(c_Nat_OSuc,X2796))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__le])]) ).

fof(i_0_889,plain,
    ! [X3149,X3151,X3152,X3153] :
      ( ( ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X3149)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3151),X3149))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3151),esk43_1(X3149))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk44_2(X3152,X3153)),X3152))
        | c_Finite__Set_Ofinite(tc_Nat_Onat,X3152) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk44_2(X3152,X3153)),X3153))
        | c_Finite__Set_Ofinite(tc_Nat_Onat,X3152) ) ),
    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_890,plain,
    ! [X2801,X2802,X2803] :
      ( ~ c_Finite__Set_Ofinite(X2803,X2802)
      | hBOOL(hAPP(hAPP(c_member(X2803),X2801),X2802))
      | c_Finite__Set_Ocard(X2803,c_Set_Oinsert(X2803,X2801,X2802)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X2803,X2802)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_560])]) ).

fof(i_0_891,plain,
    ! [X2736,X2737] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2737),X2736))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2737),hAPP(c_Nat_OSuc,X2736))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__SucI])]) ).

fof(i_0_892,plain,
    ! [X2835,X2836] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2836),X2835),X2835) != c_Groups_Ozero__class_Ozero(X2836)
        | X2835 = c_Groups_Ozero__class_Ozero(X2836)
        | ~ hBOOL(hAPP(hAPP(c_member(X2836),X2835),c_Int_Oring__1__class_OInts(X2836)))
        | ~ class_Int_Oring__char__0(X2836) )
      & ( X2835 != c_Groups_Ozero__class_Ozero(X2836)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2836),X2835),X2835) = c_Groups_Ozero__class_Ozero(X2836)
        | ~ hBOOL(hAPP(hAPP(c_member(X2836),X2835),c_Int_Oring__1__class_OInts(X2836)))
        | ~ class_Int_Oring__char__0(X2836) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__double__eq__0__iff])])]) ).

fof(i_0_893,plain,
    ! [X2984,X2985,X2986,X2987] : c_Nat_Onat_Onat__case(X2987,X2986,X2985,hAPP(c_Nat_OSuc,X2984)) = hAPP(X2985,X2984),
    inference(variable_rename,[status(thm)],[fact_nat__case__Suc]) ).

fof(i_0_894,plain,
    ! [X2720,X2721] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2721),hAPP(c_Nat_OSuc,X2720)))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2721),X2720))
        | X2721 = hAPP(c_Nat_OSuc,X2720) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2721),X2720))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2721),hAPP(c_Nat_OSuc,X2720))) )
      & ( X2721 != hAPP(c_Nat_OSuc,X2720)
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2721),hAPP(c_Nat_OSuc,X2720))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__Suc__eq])])]) ).

fof(i_0_895,plain,
    ! [X2714,X2715] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2715),hAPP(c_Nat_OSuc,X2714)))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2715),X2714))
      | X2715 = hAPP(c_Nat_OSuc,X2714) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_561])]) ).

fof(i_0_896,plain,
    ! [X1842,X1843] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1843,tc_HOL_Obool),X1842),c_Orderings_Otop__class_Otop(tc_fun(X1843,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_subset__UNIV]) ).

fof(i_0_897,plain,
    ! [X1738,X1739,X1740] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1739),X1740))
        | hBOOL(hAPP(hAPP(X1738,X1739),X1740))
        | X1740 = X1739
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1740),X1739)) )
      & ( ~ hBOOL(hAPP(hAPP(X1738,X1739),X1740))
        | hBOOL(hAPP(hAPP(X1738,X1739),X1740))
        | X1740 = X1739
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1740),X1739)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1739),X1740))
        | hBOOL(hAPP(hAPP(X1738,X1739),X1740))
        | ~ hBOOL(hAPP(hAPP(X1738,X1739),X1740))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1740),X1739)) )
      & ( ~ hBOOL(hAPP(hAPP(X1738,X1739),X1740))
        | hBOOL(hAPP(hAPP(X1738,X1739),X1740))
        | ~ hBOOL(hAPP(hAPP(X1738,X1739),X1740))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1740),X1739)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1739),X1740))
        | hBOOL(hAPP(hAPP(X1738,X1739),X1740))
        | X1740 = X1739
        | ~ hBOOL(hAPP(hAPP(X1738,X1739),X1740)) )
      & ( ~ hBOOL(hAPP(hAPP(X1738,X1739),X1740))
        | hBOOL(hAPP(hAPP(X1738,X1739),X1740))
        | X1740 = X1739
        | ~ hBOOL(hAPP(hAPP(X1738,X1739),X1740)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1739),X1740))
        | hBOOL(hAPP(hAPP(X1738,X1739),X1740))
        | ~ hBOOL(hAPP(hAPP(X1738,X1739),X1740))
        | ~ hBOOL(hAPP(hAPP(X1738,X1739),X1740)) )
      & ( ~ hBOOL(hAPP(hAPP(X1738,X1739),X1740))
        | hBOOL(hAPP(hAPP(X1738,X1739),X1740))
        | ~ hBOOL(hAPP(hAPP(X1738,X1739),X1740))
        | ~ hBOOL(hAPP(hAPP(X1738,X1739),X1740)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__cases])])]) ).

fof(i_0_898,plain,
    ! [X1760,X1761,X1762] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1762),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1761),X1760)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1761),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1762),X1760)),
    inference(variable_rename,[status(thm)],[fact_nat__add__left__commute]) ).

fof(i_0_899,plain,
    ! [X1949,X1950,X1951] :
      ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1951,X1950),X1949))
        | X1950 != X1949
        | ~ class_Orderings_Oorder(X1951) )
      & ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1951,X1949),X1950))
        | X1950 != X1949
        | ~ class_Orderings_Oorder(X1951) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1951,X1950),X1949))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1951,X1949),X1950))
        | X1950 = X1949
        | ~ class_Orderings_Oorder(X1951) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__iff])])]) ).

fof(i_0_900,plain,
    ! [X1938,X1939,X1940] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1940,X1938),X1939))
        | X1938 = X1939
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1940,X1939),X1938))
        | ~ class_Orderings_Oorder(X1940) )
      & ( X1938 != X1939
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1940,X1938),X1939))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1940,X1939),X1938))
        | ~ class_Orderings_Oorder(X1940) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym__conv])])]) ).

fof(i_0_901,plain,
    ! [X1919,X1920,X1921] :
      ( ~ class_Orderings_Oorder(X1921)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1921,X1920),X1919))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1921,X1919),X1920))
      | X1920 = X1919 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym])]) ).

fof(i_0_902,plain,
    ! [X1912,X1913,X1914] :
      ( ~ class_Orderings_Oorder(X1914)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1914,X1913),X1912))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1914,X1912),X1913))
      | X1912 = X1913 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I5_J])]) ).

fof(i_0_903,plain,
    ! [X2687,X2688] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Finite__Set_Ocard(X2688,X2687)))
      | c_Finite__Set_Ofinite(X2688,X2687) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__ge__0__finite])]) ).

fof(i_0_904,plain,
    ! [X2724] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2724)),X2724)),
    inference(variable_rename,[status(thm)],[i_0_562]) ).

fof(i_0_905,plain,
    ! [X2792,X2793] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2793),X2792))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2793),hAPP(c_Nat_OSuc,X2792))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__less__Suc])]) ).

fof(i_0_906,plain,
    ! [X2449,X2450] :
      ( ~ c_Finite__Set_Ofinite(X2450,c_Orderings_Otop__class_Otop(tc_fun(X2450,tc_HOL_Obool)))
      | c_Finite__Set_Ocard(X2450,X2449) != c_Finite__Set_Ocard(X2450,c_Orderings_Otop__class_Otop(tc_fun(X2450,tc_HOL_Obool)))
      | X2449 = c_Orderings_Otop__class_Otop(tc_fun(X2450,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__eq__UNIV__imp__eq__UNIV])]) ).

fof(i_0_907,plain,
    ! [X2082,X2083,X2084] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2084,X2083),X2082))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2084),X2083),X2082))
        | X2083 = X2082
        | ~ class_Orderings_Oorder(X2084) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2084),X2083),X2082))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2084,X2083),X2082))
        | ~ class_Orderings_Oorder(X2084) )
      & ( X2083 != X2082
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2084,X2083),X2082))
        | ~ class_Orderings_Oorder(X2084) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less])])]) ).

fof(i_0_908,plain,
    ! [X2076,X2077,X2078] :
      ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2078,X2077),X2076))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2078),X2077),X2076))
        | ~ class_Orderings_Oorder(X2078) )
      & ( X2077 != X2076
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2078),X2077),X2076))
        | ~ class_Orderings_Oorder(X2078) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2078,X2077),X2076))
        | X2077 = X2076
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2078),X2077),X2076))
        | ~ class_Orderings_Oorder(X2078) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le])])]) ).

fof(i_0_909,plain,
    ! [X2103,X2104,X2105] :
      ( ~ class_Orderings_Opreorder(X2105)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2105),X2104),X2103))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2105,X2104),X2103)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__le])]) ).

fof(i_0_910,plain,
    ! [X1713,X1714] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1714),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1714),X1713))),
    inference(variable_rename,[status(thm)],[fact_le__add1]) ).

fof(i_0_911,plain,
    ! [X1715,X1716] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1716),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1715),X1716))),
    inference(variable_rename,[status(thm)],[fact_le__add2]) ).

fof(i_0_912,plain,
    ! [X2982,X2983] : c_Set_Oimage(X2983,X2983,c_COMBI(X2983),X2982) = X2982,
    inference(variable_rename,[status(thm)],[fact_image__ident]) ).

fof(i_0_913,plain,
    ! [X2365,X2366] : c_Fun_Oinj__on(X2366,X2366,c_COMBI(X2366),X2365),
    inference(variable_rename,[status(thm)],[fact_inj__on__id2]) ).

fof(i_0_914,plain,
    ! [X2988,X2989,X2990] : c_Nat_Onat_Onat__case(X2990,X2989,X2988,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2989,
    inference(variable_rename,[status(thm)],[fact_nat__case__0]) ).

fof(i_0_915,plain,
    ! [X2115,X2116,X2117] :
      ( ~ class_Orderings_Oorder(X2117)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2117,X2116),X2115))
      | X2115 = X2116
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2117),X2116),X2115)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I11_J])]) ).

fof(i_0_916,plain,
    ! [X2112,X2113,X2114] :
      ( ~ class_Orderings_Oorder(X2114)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2114,X2113),X2112))
      | X2113 = X2112
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2114),X2113),X2112)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__neq__trans])]) ).

fof(i_0_917,plain,
    ! [X2109,X2110,X2111] :
      ( ~ class_Orderings_Oorder(X2111)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2111,X2110),X2109))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2111),X2110),X2109))
      | X2110 = X2109 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__imp__less__or__eq])]) ).

fof(i_0_918,plain,
    ! [X2094,X2095,X2096] :
      ( ~ class_Orderings_Oorder(X2096)
      | X2095 = X2094
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2096,X2095),X2094))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2096),X2095),X2094)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__neq__le__trans])]) ).

fof(i_0_919,plain,
    ! [X2091,X2092,X2093] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2093,X2092),X2091))
        | X2092 = X2091
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2093),X2092),X2091))
        | ~ class_Orderings_Olinorder(X2093) )
      & ( X2092 != X2091
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2093,X2092),X2091))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2093),X2092),X2091))
        | ~ class_Orderings_Olinorder(X2093) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_563])])]) ).

fof(i_0_920,plain,
    ! [X2097,X2098,X2099] :
      ( ~ class_Orderings_Oorder(X2099)
      | X2098 = X2097
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2099,X2097),X2098))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2099),X2097),X2098)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I12_J])]) ).

fof(i_0_921,plain,
    ! [X2767] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2767),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
        | X2767 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X2767 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2767),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_922,plain,
    ! [X2760] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X2760),
    inference(variable_rename,[status(thm)],[fact_inj__Suc]) ).

fof(i_0_923,plain,
    ! [X1666,X1667] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1667),X1666))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1666),X1667))
      | X1667 = X1666 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__antisym])]) ).

fof(i_0_924,plain,
    ! [X1729,X1730,X1731] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X1731),X1730),hAPP(c_fequal,X1729)))
        | X1730 = X1729 )
      & ( X1730 != X1729
        | hBOOL(hAPP(hAPP(c_member(X1731),X1730),hAPP(c_fequal,X1729))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__mem])]) ).

fof(i_0_925,plain,
    ! [X2716,X2717] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2717),X2716))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2717),hAPP(c_Nat_OSuc,X2716))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__SucI])]) ).

fof(i_0_926,plain,
    ! [X2661] :
      ( ~ class_Rings_Olinordered__semidom(X2661)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2661),c_Groups_Oone__class_Oone(X2661)),c_Groups_Ozero__class_Ozero(X2661))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_564])]) ).

fof(i_0_927,plain,
    ! [X2198,X2199] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2199),X2198))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2199),X2198)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I5_J])]) ).

fof(i_0_928,plain,
    ! [X1680,X1681] :
      ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1681),X1680))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1681),X1680)) )
      & ( X1681 != X1680
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1681),X1680)) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1681),X1680))
        | X1681 = X1680
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1681),X1680)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__le])])]) ).

fof(i_0_929,plain,
    ! [X1678,X1679] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1679),X1678))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1679),X1678))
        | X1679 = X1678 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1679),X1678))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1679),X1678)) )
      & ( X1679 != X1678
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1679),X1678)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__eq__less__or__eq])])]) ).

fof(i_0_930,plain,
    ! [X1676,X1677] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1677),X1676))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1677),X1676)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__le__nat])]) ).

fof(i_0_931,plain,
    ! [X1672,X1673] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1673),X1672))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1673),X1672)) )
      & ( X1673 != X1672
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1673),X1672)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__or__eq__imp__le])])]) ).

fof(i_0_932,plain,
    ! [X2542,X2543,X2544] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X2544),X2543),X2542))
      | c_Set_Oinsert(X2544,X2543,X2542) = X2542 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__absorb])]) ).

fof(i_0_933,plain,
    ! [X1969,X1970,X1971] :
      ( ( X1970 = X1969
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1971),X1970),X1969))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1971),X1969),X1970))
        | ~ class_Orderings_Olinorder(X1971) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1971),X1970),X1969))
        | X1970 != X1969
        | ~ class_Orderings_Olinorder(X1971) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1971),X1969),X1970))
        | X1970 != X1969
        | ~ class_Orderings_Olinorder(X1971) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__neq__iff])])]) ).

fof(i_0_934,plain,
    ! [X2032,X2033,X2034] :
      ( ~ class_Orderings_Olinorder(X2034)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2034),X2033),X2032))
      | X2033 = X2032
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2034),X2032),X2033)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_565])]) ).

fof(i_0_935,plain,
    ! [X1981,X1982,X1983] :
      ( ~ class_Orderings_Olinorder(X1983)
      | X1982 = X1981
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1983),X1982),X1981))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1983),X1981),X1982)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_566])]) ).

fof(i_0_936,plain,
    ! [X1978,X1979,X1980] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1980),X1978),X1979))
        | X1978 = X1979
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1980),X1979),X1978))
        | ~ class_Orderings_Olinorder(X1980) )
      & ( X1978 != X1979
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1980),X1978),X1979))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1980),X1979),X1978))
        | ~ class_Orderings_Olinorder(X1980) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_567])])]) ).

fof(i_0_937,plain,
    ! [X1975,X1976,X1977] :
      ( ~ class_Orderings_Olinorder(X1977)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1977),X1976),X1975))
      | X1976 = X1975
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1977),X1975),X1976)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__less__linear])]) ).

fof(i_0_938,plain,
    ! [X1735,X1736,X1737] :
      ( ~ class_Rings_Olinordered__idom(X1737)
      | X1736 = X1735
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1737),X1736),X1735))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1737),X1735),X1736)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_568])]) ).

fof(i_0_939,plain,
    ! [X2447] :
      ( ( ~ c_Finite__Set_Ofinite(tc_Option_Ooption(X2447),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X2447),tc_HOL_Obool)))
        | c_Finite__Set_Ofinite(X2447,c_Orderings_Otop__class_Otop(tc_fun(X2447,tc_HOL_Obool))) )
      & ( ~ c_Finite__Set_Ofinite(X2447,c_Orderings_Otop__class_Otop(tc_fun(X2447,tc_HOL_Obool)))
        | c_Finite__Set_Ofinite(tc_Option_Ooption(X2447),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X2447),tc_HOL_Obool))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__option__UNIV])]) ).

fof(i_0_940,plain,
    ! [X1674,X1675] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1675),X1674))
      | X1675 = X1674
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1675),X1674)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__neq__implies__less])]) ).

fof(i_0_941,plain,
    ! [X2516,X2517,X2518] : c_Set_Oinsert(X2518,X2517,c_Set_Oinsert(X2518,X2517,X2516)) = c_Set_Oinsert(X2518,X2517,X2516),
    inference(variable_rename,[status(thm)],[fact_insert__absorb2]) ).

fof(i_0_942,plain,
    ! [X2396,X2397] : hBOOL(hAPP(hAPP(c_member(X2397),X2396),c_Orderings_Otop__class_Otop(tc_fun(X2397,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_iso__tuple__UNIV__I]) ).

fof(i_0_943,plain,
    ! [X1840,X1841] : hBOOL(hAPP(hAPP(c_member(X1841),X1840),c_Orderings_Otop__class_Otop(tc_fun(X1841,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_UNIV__I]) ).

fof(i_0_944,plain,
    ! [X2495,X2496,X2497] :
      ( ( ~ c_Finite__Set_Ofinite(X2497,c_Set_Oinsert(X2497,X2496,X2495))
        | c_Finite__Set_Ofinite(X2497,X2495) )
      & ( ~ c_Finite__Set_Ofinite(X2497,X2495)
        | c_Finite__Set_Ofinite(X2497,c_Set_Oinsert(X2497,X2496,X2495)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__insert])]) ).

fof(i_0_945,plain,
    ! [X1732,X1733,X1734] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X1734),X1733),X1732))
        | hBOOL(hAPP(X1732,X1733)) )
      & ( ~ hBOOL(hAPP(X1732,X1733))
        | hBOOL(hAPP(hAPP(c_member(X1734),X1733),X1732)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__def])]) ).

fof(i_0_946,plain,
    ! [X2088,X2089,X2090] :
      ( ~ class_Orderings_Olinorder(X2090)
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2090,X2089),X2088))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2090),X2088),X2089)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_569])]) ).

fof(i_0_947,plain,
    ! [X2073,X2074,X2075] :
      ( ~ class_Orderings_Olinorder(X2075)
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2075,X2074),X2073))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2075),X2073),X2074)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__le__less__linear])]) ).

fof(i_0_948,plain,
    ! [X2085,X2086,X2087] :
      ( ~ class_Orderings_Olinorder(X2087)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2087),X2086),X2085))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2087,X2085),X2086)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_570])]) ).

fof(i_0_949,plain,
    ! [X2750,X2751] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2751)),X2750) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2751),X2750)),
    inference(variable_rename,[status(thm)],[fact_add__Suc]) ).

fof(i_0_950,plain,
    ! [X2658] :
      ( ~ class_Rings_Olinordered__semidom(X2658)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2658,c_Groups_Oone__class_Oone(X2658)),c_Groups_Ozero__class_Ozero(X2658))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_571])]) ).

fof(i_0_951,plain,
    ! [X1707,X1708,X1710,X1711,X1712] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1708),X1707))
        | X1707 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1708),esk2_2(X1707,X1708)) )
      & ( X1710 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1711),X1712)
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1711),X1710)) ) ),
    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_952,plain,
    ! [X1748,X1749] :
      ( ( X1749 = X1748
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1749),X1748))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1748),X1749)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1749),X1748))
        | X1749 != X1748 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1748),X1749))
        | X1749 != X1748 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__neq__iff])])]) ).

fof(i_0_953,plain,
    ! [X1746,X1747] :
      ( X1747 = X1746
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1747),X1746))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1746),X1747)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_572])]) ).

fof(i_0_954,plain,
    ! [X2768,X2770,X2771] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2768))
        | X2768 = hAPP(c_Nat_OSuc,esk31_1(X2768)) )
      & ( X2770 != hAPP(c_Nat_OSuc,X2771)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2770)) ) ),
    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_955,plain,
    ! [X1996,X1997,X1998] :
      ( ~ class_Orderings_Oorder(X1998)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1998),X1997),X1996))
      | X1996 != X1997 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq2])]) ).

fof(i_0_956,plain,
    ! [X1993,X1994,X1995] :
      ( ~ class_Orderings_Oorder(X1995)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1995),X1994),X1993))
      | X1994 != X1993 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq])]) ).

fof(i_0_957,plain,
    ! [X1984,X1985,X1986] :
      ( ~ class_Orderings_Oorder(X1986)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1986),X1985),X1984))
      | X1985 != X1984 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__neq])]) ).

fof(i_0_958,plain,
    ! [X2275,X2276,X2277] :
      ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2275,tc_HOL_Obool),X2277),X2276))
        | X2277 != X2276 )
      & ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2275,tc_HOL_Obool),X2276),X2277))
        | X2277 != X2276 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_573])])]) ).

fof(i_0_959,plain,
    ! [X2255,X2256,X2257] :
      ( X2257 != X2256
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2255,tc_HOL_Obool),X2257),X2256)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityD1])]) ).

fof(i_0_960,plain,
    ! [X2258,X2259,X2260] :
      ( X2260 != X2259
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2258,tc_HOL_Obool),X2259),X2260)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityD2])]) ).

fof(i_0_961,plain,
    ! [X1967,X1968] :
      ( ~ class_Orderings_Opreorder(X1968)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1968),X1967),X1967)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_574])]) ).

fof(i_0_962,plain,
    ! [X2246,X2247] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2247,tc_HOL_Obool),X2246),X2246)),
    inference(variable_rename,[status(thm)],[fact_subset__refl]) ).

fof(i_0_963,plain,
    ! [X2596] :
      ( ( X2596 = 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)),X2596)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2596))
        | X2596 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neq0__conv])]) ).

fof(i_0_964,plain,
    ! [X2055,X2056,X2057,X2058] :
      ( ~ class_Groups_Ocancel__semigroup__add(X2058)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2058),X2057),X2056) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2058),X2055),X2056)
      | X2057 = X2055 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__imp__eq])]) ).

fof(i_0_965,plain,
    ! [X2043,X2044,X2045,X2046] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2046),X2045),X2044) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2046),X2043),X2044)
        | X2045 = X2043
        | ~ class_Groups_Ocancel__semigroup__add(X2046) )
      & ( X2045 != X2043
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2046),X2045),X2044) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2046),X2043),X2044)
        | ~ class_Groups_Ocancel__semigroup__add(X2046) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__cancel])])]) ).

fof(i_0_966,plain,
    ! [X2051,X2052,X2053,X2054] :
      ( ~ class_Groups_Ocancel__ab__semigroup__add(X2054)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2054),X2053),X2052) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2054),X2053),X2051)
      | X2052 = X2051 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__imp__eq])]) ).

fof(i_0_967,plain,
    ! [X2047,X2048,X2049,X2050] :
      ( ~ class_Groups_Ocancel__semigroup__add(X2050)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2050),X2049),X2048) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2050),X2049),X2047)
      | X2048 = X2047 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__imp__eq])]) ).

fof(i_0_968,plain,
    ! [X2039,X2040,X2041,X2042] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2042),X2041),X2040) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2042),X2041),X2039)
        | X2040 = X2039
        | ~ class_Groups_Ocancel__semigroup__add(X2042) )
      & ( X2040 != X2039
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2042),X2041),X2040) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2042),X2041),X2039)
        | ~ class_Groups_Ocancel__semigroup__add(X2042) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__cancel])])]) ).

fof(i_0_969,plain,
    ! [X1952,X1953,X1954] :
      ( ~ class_Orderings_Olinorder(X1954)
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1954,X1953),X1952))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1954,X1952),X1953)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__linear])]) ).

fof(i_0_970,plain,
    ! [X1900,X1901,X1902] :
      ( ~ class_Orderings_Olinorder(X1902)
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1902,X1901),X1900))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1902,X1900),X1901)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_575])]) ).

fof(i_0_971,plain,
    ! [X2752,X2753] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2753),hAPP(c_Nat_OSuc,X2752)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2753),X2752)),
    inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).

fof(i_0_972,plain,
    ! [X2748,X2749] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2749)),X2748) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2749),hAPP(c_Nat_OSuc,X2748)),
    inference(variable_rename,[status(thm)],[fact_add__Suc__shift]) ).

fof(i_0_973,plain,
    ! [X2597] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2597),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[i_0_576]) ).

fof(i_0_974,plain,
    ! [X2595] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2595),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[i_0_577]) ).

fof(i_0_975,plain,
    ! [X2593] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2593),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[i_0_578]) ).

fof(i_0_976,plain,
    ! [X2826] : c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2826)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_Nat_Onat,X2826)),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_977,plain,
    ! [X2598,X2599] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2599),X2598))
      | X2598 != 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_978,plain,
    ! [X1659,X1660] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1660),X1659))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1659),X1660)) ),
    inference(variable_rename,[status(thm)],[fact_nat__le__linear]) ).

fof(i_0_979,plain,
    ! [X2705] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X2705))),
    inference(variable_rename,[status(thm)],[fact_zero__less__Suc]) ).

fof(i_0_980,plain,
    ! [X1743,X1744] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1744),X1743))
      | X1743 != X1744 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl2])]) ).

fof(i_0_981,plain,
    ! [X1741,X1742] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1742),X1741))
      | X1742 != X1741 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl3])]) ).

fof(i_0_982,plain,
    ! [X2660] :
      ( ~ class_Rings_Olinordered__semidom(X2660)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2660),c_Groups_Ozero__class_Ozero(X2660)),c_Groups_Oone__class_Oone(X2660))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__one])]) ).

fof(i_0_983,plain,
    ! [X2830] :
      ( ~ class_Rings_Oring__1(X2830)
      | hBOOL(hAPP(hAPP(c_member(X2830),c_Groups_Ozero__class_Ozero(X2830)),c_Int_Oring__1__class_OInts(X2830))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__0])]) ).

fof(i_0_984,plain,
    ! [X2834] :
      ( ~ class_Rings_Oring__1(X2834)
      | hBOOL(hAPP(hAPP(c_member(X2834),c_Groups_Oone__class_Oone(X2834)),c_Int_Oring__1__class_OInts(X2834))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__1])]) ).

fof(i_0_985,plain,
    ! [X1750] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1750),X1750)),
    inference(variable_rename,[status(thm)],[i_0_579]) ).

fof(i_0_986,plain,
    ! [X1745] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1745),X1745)),
    inference(variable_rename,[status(thm)],[i_0_580]) ).

fof(i_0_987,plain,
    ! [X1751,X1752,X1753] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1753),X1752) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1751),X1752)
        | X1753 = X1751 )
      & ( X1753 != X1751
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1753),X1752) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1751),X1752) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__right__cancel])]) ).

fof(i_0_988,plain,
    ! [X1754,X1755,X1756] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1756),X1755) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1756),X1754)
        | X1755 = X1754 )
      & ( X1755 != X1754
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1756),X1755) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1756),X1754) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel])]) ).

fof(i_0_989,plain,
    ! [X2484,X2485,X2486] :
      ( ~ c_Finite__Set_Ofinite(X2486,X2485)
      | c_Finite__Set_Ofinite(X2486,c_Set_Oinsert(X2486,X2484,X2485)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite_OinsertI])]) ).

fof(i_0_990,plain,
    ! [X2704] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2704),hAPP(c_Nat_OSuc,X2704))),
    inference(variable_rename,[status(thm)],[fact_lessI]) ).

fof(i_0_991,plain,
    ! [X1838,X1839] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1839,tc_HOL_Obool)),X1838)),
    inference(variable_rename,[status(thm)],[fact_top1I]) ).

fof(i_0_992,plain,
    ! [X2622] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2622),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | X2622 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X2622 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2622),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_993,plain,
    ! [X2774,X2775] :
      ( ( X2775 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X2775 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2775),X2774) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X2774 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X2775 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2775),X2774) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X2775 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X2774 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2775),X2774) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X2774 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X2774 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2775),X2774) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X2775 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X2774 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2775),X2774) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X2775 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X2774 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2775),X2774) = 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_994,plain,
    ! [X2772,X2773] :
      ( ( X2773 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X2773 = 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),X2773),X2772) )
      & ( X2772 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X2773 = 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),X2773),X2772) )
      & ( X2773 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X2772 = 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),X2773),X2772) )
      & ( X2772 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X2772 = 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),X2773),X2772) )
      & ( X2773 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X2772 != 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),X2773),X2772) )
      & ( X2773 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X2772 != 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),X2773),X2772) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__is__add])])]) ).

fof(i_0_995,plain,
    ! [X1623,X1624] :
      ( hAPP(X1624,esk1_2(X1623,X1624)) != hAPP(X1623,esk1_2(X1623,X1624))
      | X1624 = X1623 ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])]) ).

fof(i_0_996,plain,
    ! [X2659] :
      ( ~ class_Rings_Olinordered__semidom(X2659)
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2659,c_Groups_Ozero__class_Ozero(X2659)),c_Groups_Oone__class_Oone(X2659))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__one])]) ).

fof(i_0_997,plain,
    ! [X3216,X3217] :
      ( ~ hBOOL(hAPP(hAPP(c_fequal,X3217),X3216))
      | X3217 = X3216 ),
    inference(variable_rename,[status(thm)],[i_0_581]) ).

fof(i_0_998,plain,
    ! [X3136,X3137] : c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3137,X3136)),
    inference(variable_rename,[status(thm)],[fact_finite__atLeastLessThan]) ).

fof(i_0_999,plain,
    ! [X2811] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X2811)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(X2811)),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_1000,plain,
    ! [X2843,X2844,X2845] :
      ( ~ class_Rings_Ocomm__semiring__1(X2845)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2845),X2844),X2843) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2845),X2843),X2844) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])]) ).

fof(i_0_1001,plain,
    ! [X2600] :
      ( X2600 = 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)),X2600)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr0I])]) ).

fof(i_0_1002,plain,
    ! [X1872,X1873] :
      ( ~ class_Orderings_Otop(X1873)
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1873,X1872),c_Orderings_Otop__class_Otop(X1873))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_top__greatest])]) ).

fof(i_0_1003,plain,
    ! [X2807,X2808] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2808),X2807),X2807) != c_Groups_Ozero__class_Ozero(X2808)
        | X2807 = c_Groups_Ozero__class_Ozero(X2808)
        | ~ class_Groups_Olinordered__ab__group__add(X2808) )
      & ( X2807 != c_Groups_Ozero__class_Ozero(X2808)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2808),X2807),X2807) = c_Groups_Ozero__class_Ozero(X2808)
        | ~ class_Groups_Olinordered__ab__group__add(X2808) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__eq__0__iff])])]) ).

fof(i_0_1004,plain,
    ! [X2615,X2616] :
      ( ( c_Groups_Ozero__class_Ozero(X2616) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2616),X2615),X2615)
        | X2615 = c_Groups_Ozero__class_Ozero(X2616)
        | ~ class_Groups_Olinordered__ab__group__add(X2616) )
      & ( X2615 != c_Groups_Ozero__class_Ozero(X2616)
        | c_Groups_Ozero__class_Ozero(X2616) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2616),X2615),X2615)
        | ~ class_Groups_Olinordered__ab__group__add(X2616) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__zero__sym])])]) ).

fof(i_0_1005,plain,
    ! [X2867,X2868,X2869] :
      ( ( X2868 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2869),X2868),X2867)
        | X2867 = c_Groups_Ozero__class_Ozero(X2869)
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2869) )
      & ( X2867 != c_Groups_Ozero__class_Ozero(X2869)
        | X2868 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2869),X2868),X2867)
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2869) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__iff])])]) ).

fof(i_0_1006,plain,
    ! [X1946,X1947,X1948] :
      ( ~ class_Orderings_Opreorder(X1948)
      | X1947 != X1946
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1948,X1947),X1946)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__refl])]) ).

fof(i_0_1007,plain,
    ! [X3194,X3195,X3196,X3197] : hAPP(hAPP(c_COMBK(X3197,X3196),X3195),X3194) = X3195,
    inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).

fof(i_0_1008,plain,
    ! [X1763,X1764] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1764),X1763) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1763),X1764),
    inference(variable_rename,[status(thm)],[fact_nat__add__commute]) ).

fof(i_0_1009,plain,
    ! [X1827,X1828] :
      ( ~ class_Orderings_Opreorder(X1828)
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1828,X1827),X1827)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__refl])]) ).

fof(i_0_1010,plain,
    ! [X2621] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2621)),
    inference(variable_rename,[status(thm)],[fact_less__eq__nat_Osimps_I1_J]) ).

fof(i_0_1011,plain,
    ! [X2594] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2594)),
    inference(variable_rename,[status(thm)],[fact_le0]) ).

fof(i_0_1012,plain,
    ! [X1869,X1870,X1871] :
      ( ~ class_Orderings_Otop(X1871)
      | hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1870,X1871)),X1869) = c_Orderings_Otop__class_Otop(X1871) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_top__apply])]) ).

fof(i_0_1013,plain,
    ! [X2603,X2604] :
      ( ( X2604 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2604),X2603) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X2603 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2604),X2603) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X2604 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X2603 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2604),X2603) = 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_1014,plain,
    ! [X1661,X1662] :
      ( X1662 != X1661
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1662),X1661)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__imp__le])]) ).

fof(i_0_1015,plain,
    ! [X3218,X3219] :
      ( X3219 != X3218
      | hBOOL(hAPP(hAPP(c_fequal,X3219),X3218)) ),
    inference(variable_rename,[status(thm)],[help_c__fequal__2]) ).

fof(i_0_1016,plain,
    ! [X2605,X2606] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2606),X2605) != X2606
      | X2605 = 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_1017,plain,
    ! [X1658] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1658),X1658)),
    inference(variable_rename,[status(thm)],[fact_le__refl]) ).

fof(i_0_1018,plain,
    ! [X2448] :
      ( ~ class_Finite__Set_Ofinite(X2448)
      | c_Finite__Set_Ofinite(X2448,c_Orderings_Otop__class_Otop(tc_fun(X2448,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV])]) ).

fof(i_0_1019,plain,
    ! [X2839,X2840] :
      ( ~ class_Rings_Ocomm__semiring__1(X2840)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2840),c_Groups_Ozero__class_Ozero(X2840)),X2839) = X2839 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J])]) ).

fof(i_0_1020,plain,
    ! [X2613,X2614] :
      ( ~ class_Groups_Ocomm__monoid__add(X2614)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2614),c_Groups_Ozero__class_Ozero(X2614)),X2613) = X2613 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0])]) ).

fof(i_0_1021,plain,
    ! [X2611,X2612] :
      ( ~ class_Groups_Omonoid__add(X2612)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2612),c_Groups_Ozero__class_Ozero(X2612)),X2611) = X2611 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__left])]) ).

fof(i_0_1022,plain,
    ! [X2841,X2842] :
      ( ~ class_Rings_Ocomm__semiring__1(X2842)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2842),X2841),c_Groups_Ozero__class_Ozero(X2842)) = X2841 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J])]) ).

fof(i_0_1023,plain,
    ! [X2619,X2620] :
      ( ~ class_Groups_Ocomm__monoid__add(X2620)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2620),X2619),c_Groups_Ozero__class_Ozero(X2620)) = X2619 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add_Ocomm__neutral])]) ).

fof(i_0_1024,plain,
    ! [X2617,X2618] :
      ( ~ class_Groups_Omonoid__add(X2618)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2618),X2617),c_Groups_Ozero__class_Ozero(X2618)) = X2617 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__right])]) ).

fof(i_0_1025,plain,
    ! [X2810] : hAPP(c_Nat_OSuc,X2810) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2810),
    inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1__left]) ).

fof(i_0_1026,plain,
    ! [X2809] : hAPP(c_Nat_OSuc,X2809) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2809),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1]) ).

fof(i_0_1027,plain,
    ! [X2601] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2601) = X2601,
    inference(variable_rename,[status(thm)],[fact_plus__nat_Oadd__0]) ).

fof(i_0_1028,plain,
    ! [X2800] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2800) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2800)),
    inference(variable_rename,[status(thm)],[fact_less__eq__Suc__le__raw]) ).

fof(i_0_1029,plain,
    ! [X2602] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2602),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2602,
    inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).

fof(i_0_1030,plain,
    ! [X3187,X3188] :
      ( ~ class_Finite__Set_Ofinite(X3188)
      | ~ class_Finite__Set_Ofinite(X3187)
      | class_Finite__Set_Ofinite(tc_sum(X3188,X3187)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_sum__Finite__Set_Ofinite])]) ).

fof(i_0_1031,plain,
    ! [X3179,X3180] :
      ( ~ class_Finite__Set_Ofinite(X3180)
      | ~ class_Finite__Set_Ofinite(X3179)
      | class_Finite__Set_Ofinite(tc_fun(X3180,X3179)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Finite__Set_Ofinite])]) ).

fof(i_0_1032,plain,
    ! [X3190,X3191] :
      ( ~ class_Finite__Set_Ofinite(X3191)
      | ~ class_Finite__Set_Ofinite(X3190)
      | class_Finite__Set_Ofinite(tc_prod(X3191,X3190)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_prod__Finite__Set_Ofinite])]) ).

fof(i_0_1033,plain,
    ! [X2758,X2759] :
      ( hAPP(c_Nat_OSuc,X2759) != hAPP(c_Nat_OSuc,X2758)
      | X2759 = X2758 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__inject])]) ).

fof(i_0_1034,plain,
    ! [X2756,X2757] :
      ( ( hAPP(c_Nat_OSuc,X2757) != hAPP(c_Nat_OSuc,X2756)
        | X2757 = X2756 )
      & ( X2757 != X2756
        | hAPP(c_Nat_OSuc,X2757) = hAPP(c_Nat_OSuc,X2756) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat_Oinject])]) ).

fof(i_0_1035,plain,
    ! [X3181,X3182] :
      ( ~ class_Orderings_Oorder(X3182)
      | class_Orderings_Oorder(tc_fun(X3181,X3182)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oorder])]) ).

fof(i_0_1036,plain,
    ! [X3183,X3184] :
      ( ~ class_Orderings_Otop(X3184)
      | class_Orderings_Otop(tc_fun(X3183,X3184)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Otop])]) ).

fof(i_0_1037,plain,
    ! [X3185,X3186] :
      ( ~ class_Orderings_Oord(X3186)
      | class_Orderings_Oord(tc_fun(X3185,X3186)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oord])]) ).

fof(i_0_1038,plain,
    ! [X3177,X3178] :
      ( ~ class_Orderings_Opreorder(X3178)
      | class_Orderings_Opreorder(tc_fun(X3177,X3178)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Opreorder])]) ).

fof(i_0_1039,plain,
    ! [X2664,X2665] :
      ( c_Finite__Set_Ofinite(X2665,X2664)
      | c_Finite__Set_Ocard(X2665,X2664) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_582])]) ).

fof(i_0_1040,plain,
    ! [X2709] : hAPP(c_Nat_OSuc,X2709) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_Suc__not__Zero]) ).

fof(i_0_1041,plain,
    ! [X2708] : hAPP(c_Nat_OSuc,X2708) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_nat_Osimps_I3_J]) ).

fof(i_0_1042,plain,
    ! [X2706] : hAPP(c_Nat_OSuc,X2706) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_Suc__neq__Zero]) ).

fof(i_0_1043,plain,
    ! [X2711] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X2711),
    inference(variable_rename,[status(thm)],[fact_Zero__not__Suc]) ).

fof(i_0_1044,plain,
    ! [X2710] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X2710),
    inference(variable_rename,[status(thm)],[fact_nat_Osimps_I2_J]) ).

fof(i_0_1045,plain,
    ! [X2707] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X2707),
    inference(variable_rename,[status(thm)],[fact_Zero__neq__Suc]) ).

fof(i_0_1046,plain,
    ! [X2435,X2436] :
      ( ~ class_Finite__Set_Ofinite(X2436)
      | c_Finite__Set_Ofinite(X2436,X2435) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__code])]) ).

fof(i_0_1047,plain,
    ! [X2433,X2434] :
      ( ~ class_Finite__Set_Ofinite(X2434)
      | c_Finite__Set_Ofinite(X2434,X2433) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite])]) ).

fof(i_0_1048,plain,
    ! [X2755] : hAPP(c_Nat_OSuc,X2755) != X2755,
    inference(variable_rename,[status(thm)],[fact_Suc__n__not__n]) ).

fof(i_0_1049,plain,
    ! [X2754] : X2754 != hAPP(c_Nat_OSuc,X2754),
    inference(variable_rename,[status(thm)],[fact_n__not__Suc__n]) ).

fof(i_0_1050,plain,
    ! [X3192,X3193] : hAPP(c_COMBI(X3193),X3192) = X3192,
    inference(variable_rename,[status(thm)],[help_c__COMBI__1]) ).

fof(i_0_1051,plain,
    ! [X2610] :
      ( ~ class_Rings_Ozero__neq__one(X2610)
      | c_Groups_Ozero__class_Ozero(X2610) != c_Groups_Oone__class_Oone(X2610) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__neq__one])]) ).

fof(i_0_1052,plain,
    ! [X2609] :
      ( ~ class_Rings_Ozero__neq__one(X2609)
      | c_Groups_Oone__class_Oone(X2609) != c_Groups_Ozero__class_Ozero(X2609) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__neq__zero])]) ).

fof(i_0_1053,plain,
    ! [X3189] :
      ( ~ class_Finite__Set_Ofinite(X3189)
      | class_Finite__Set_Ofinite(tc_Option_Ooption(X3189)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Option__Ooption__Finite__Set_Ofinite])]) ).

fof(i_0_1054,plain,
    ! [X2829] : c_Nat_Osize__class_Osize(tc_Nat_Onat,X2829) = X2829,
    inference(variable_rename,[status(thm)],[fact_nat__size]) ).

fof(i_0_1055,plain,
    ~ hBOOL(c_fFalse),
    inference(fof_simplification,[status(thm)],[help_c__fFalse__1]) ).

cnf(i_0_1056,plain,
    ( v_c____ = v_e____
    | v_a____ = v_b____
    | 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____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)),c_Arrow__Order__Mirabelle_OProf)) ),
    inference(split_conjunct,[status(thm)],[i_0_583]),
    [final] ).

cnf(i_0_1057,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_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_584]),
    [final] ).

cnf(i_0_1058,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____))))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [final] ).

cnf(i_0_1059,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____))))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [final] ).

cnf(i_0_1060,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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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(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____)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [final] ).

cnf(i_0_1061,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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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____)),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____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [final] ).

cnf(i_0_1062,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____))))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [final] ).

cnf(i_0_1063,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____))))
    | hAPP(v_h____,esk45_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_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____)),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____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [final] ).

cnf(i_0_1064,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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [final] ).

cnf(i_0_1065,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____))))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [final] ).

cnf(i_0_1066,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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_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_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____)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [final] ).

cnf(i_0_1067,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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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(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____)),v_Lba____))
    | hAPP(v_h____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [final] ).

cnf(i_0_1068,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____))))
    | hAPP(v_h____,esk45_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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [final] ).

cnf(i_0_1069,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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | hAPP(v_h____,esk45_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_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____)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [final] ).

cnf(i_0_1070,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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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____)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [final] ).

cnf(i_0_1071,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____))))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [final] ).

cnf(i_0_1072,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____))))
    | hAPP(v_h____,esk45_0) = v_n____
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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____)),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____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,esk45_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [final] ).

cnf(i_0_1073,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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [final] ).

cnf(i_0_1074,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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_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_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____)),v_Lba____))
    | hAPP(v_h____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [final] ).

cnf(i_0_1075,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____))))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [final] ).

cnf(i_0_1076,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____))))
    | hAPP(v_h____,esk45_0) = v_n____
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [final] ).

cnf(i_0_1077,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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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(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____)),v_Lba____))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [final] ).

cnf(i_0_1078,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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | hAPP(v_h____,esk45_0) = v_n____
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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____)),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____,esk45_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [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_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(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | hAPP(v_h____,esk45_0) != v_n____
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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____))))))
    | hAPP(v_h____,esk45_0) != v_n____
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [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_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____)),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_Omktop,hAPP(v_P____,esk45_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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_0)),v_n____))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [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_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____)),v_Lab____))
    | hAPP(v_h____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk45_0)),v_e____)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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_Omktop,hAPP(v_P____,esk45_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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk45_0)),v_e____)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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____))))))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [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_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____)),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____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____)),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____)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [final] ).

cnf(i_0_1088,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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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____)),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____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [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_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____)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [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_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____))))))
    | hAPP(v_h____,esk45_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_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____)),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____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_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_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____)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [final] ).

cnf(i_0_1094,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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____)),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____)),v_Lba____))
    | hAPP(v_h____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [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_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____))))))
    | hAPP(v_h____,esk45_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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [final] ).

cnf(i_0_1096,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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | hAPP(v_h____,esk45_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_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____)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [final] ).

cnf(i_0_1097,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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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____)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [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_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____)),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____))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [final] ).

cnf(i_0_1099,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____))))))
    | hAPP(v_h____,esk45_0) = v_n____
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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____)),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____))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____,esk45_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_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_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____)),v_Lba____))
    | hAPP(v_h____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [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_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____))))))
    | hAPP(v_h____,esk45_0) = v_n____
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____)),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____)),v_Lba____))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | hAPP(v_h____,esk45_0) = v_n____
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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____)),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____,esk45_0)),v_e____)))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [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_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____)),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(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | hAPP(v_h____,esk45_0) != v_n____
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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____))))
    | hAPP(v_h____,esk45_0) != v_n____
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [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_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____)),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_Omktop,hAPP(v_P____,esk45_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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_0)),v_n____))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [final] ).

cnf(i_0_1109,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____)),v_Lab____))
    | hAPP(v_h____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk45_0)),v_e____)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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_Omktop,hAPP(v_P____,esk45_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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [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_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_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk45_0)),v_e____)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_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_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____))))
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_585]),
    [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_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_586]),
    [final] ).

cnf(i_0_1113,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_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_584]),
    [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_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_586]),
    [final] ).

cnf(i_0_1115,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_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_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),esk12_0),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))),
    inference(split_conjunct,[status(thm)],[i_0_587]),
    [final] ).

cnf(i_0_1117,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_588]),
    [final] ).

cnf(i_0_1118,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_1119,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_589]),
    [final] ).

cnf(i_0_1120,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),esk12_0)) ),
    inference(split_conjunct,[status(thm)],[i_0_587]),
    [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_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_588]),
    [final] ).

cnf(i_0_1122,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_590]),
    [final] ).

cnf(i_0_1123,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_591]),
    [final] ).

cnf(i_0_1124,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_591]),
    [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),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,esk7_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,esk7_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_592]),
    [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),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,esk7_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,esk7_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_592]),
    [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),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,esk6_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,esk6_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_593]),
    [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),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,esk4_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,esk4_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_594]),
    [final] ).

cnf(i_0_1129,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,esk4_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,esk4_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_594]),
    [final] ).

cnf(i_0_1130,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_595]),
    [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),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,esk7_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,esk7_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_592]),
    [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),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,esk7_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,esk7_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_592]),
    [final] ).

cnf(i_0_1133,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,esk6_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,esk6_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_593]),
    [final] ).

cnf(i_0_1134,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,esk4_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,esk4_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_594]),
    [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)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_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,esk4_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_594]),
    [final] ).

cnf(i_0_1136,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_596]),
    [final] ).

cnf(i_0_1137,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_597]),
    [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),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,esk17_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,esk17_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_598]),
    [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),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,esk17_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,esk17_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_598]),
    [final] ).

cnf(i_0_1140,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,esk5_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,esk5_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_599]),
    [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),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,esk5_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,esk5_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_599]),
    [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),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,esk17_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,esk17_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_598]),
    [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,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,esk17_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,esk17_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_598]),
    [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),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,esk5_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,esk5_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_599]),
    [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),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,esk5_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,esk5_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_599]),
    [final] ).

cnf(i_0_1146,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),esk23_2(X1,X2)),esk24_2(X1,X2))),hAPP(X2,esk22_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_600]),
    [final] ).

cnf(i_0_1147,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),esk23_2(X1,X2)),esk24_2(X1,X2))),hAPP(esk22_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_600]),
    [final] ).

cnf(i_0_1148,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))),esk22_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_600]),
    [final] ).

cnf(i_0_1149,plain,
    ( c_Arrow__Order__Mirabelle_Odictator(X2,X1)
    | esk23_2(X1,X2) != esk24_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_600]),
    [final] ).

cnf(i_0_1150,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_601]),
    [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),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,esk3_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,esk3_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_602]),
    [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),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,esk3_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,esk3_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_602]),
    [final] ).

cnf(i_0_1153,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_603]),
    [final] ).

cnf(i_0_1154,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_601]),
    [final] ).

cnf(i_0_1155,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_596]),
    [final] ).

cnf(i_0_1156,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,esk3_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,esk3_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_602]),
    [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),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,esk3_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,esk3_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_602]),
    [final] ).

cnf(i_0_1158,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),esk35_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_604]),
    [final] ).

cnf(i_0_1159,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_597]),
    [final] ).

cnf(i_0_1160,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_605]),
    [final] ).

cnf(i_0_1161,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_1162,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_601]),
    [final] ).

cnf(i_0_1163,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_601]),
    [final] ).

cnf(i_0_1164,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_606]),
    [final] ).

cnf(i_0_1165,plain,
    ( hAPP(hAPP(X3,hAPP(X6,X8)),hAPP(X6,X7)) = hAPP(X6,X7)
    | ~ c_Finite__Set_Ofolding__image__simple__idem(X1,X2,X3,X4,X5,X6)
    | ~ c_Finite__Set_Ofinite(X2,X7)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X8),X7)) ),
    inference(split_conjunct,[status(thm)],[i_0_607]),
    [final] ).

cnf(i_0_1166,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_608]),
    [final] ).

cnf(i_0_1167,plain,
    ( hAPP(hAPP(X3,hAPP(X5,X8)),hAPP(X6,X7)) = hAPP(X6,X7)
    | ~ c_Finite__Set_Ofolding__image__simple__idem(X1,X2,X3,X4,X5,X6)
    | ~ c_Finite__Set_Ofinite(X2,X7)
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X8),X7)) ),
    inference(split_conjunct,[status(thm)],[i_0_609]),
    [final] ).

cnf(i_0_1168,plain,
    ( hAPP(X6,c_Set_Oinsert(X2,X8,X7)) = hAPP(hAPP(X3,hAPP(X5,X8)),hAPP(X6,X7))
    | ~ c_Finite__Set_Ofolding__image__simple__idem(X1,X2,X3,X4,X5,X6)
    | ~ c_Finite__Set_Ofinite(X2,X7) ),
    inference(split_conjunct,[status(thm)],[i_0_610]),
    [final] ).

cnf(i_0_1169,plain,
    ( hAPP(hAPP(X3,X7),X7) = X7
    | ~ c_Finite__Set_Ofolding__image__simple__idem(X1,X2,X3,X4,X5,X6) ),
    inference(split_conjunct,[status(thm)],[i_0_611]),
    [final] ).

cnf(i_0_1170,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_612]),
    [final] ).

cnf(i_0_1171,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,esk13_4(X1,X2,X3,X4)))) ),
    inference(split_conjunct,[status(thm)],[i_0_613]),
    [final] ).

cnf(i_0_1172,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_614]),
    [final] ).

cnf(i_0_1173,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_614]),
    [final] ).

cnf(i_0_1174,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_615]),
    [final] ).

cnf(i_0_1175,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_616]),
    [final] ).

cnf(i_0_1176,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_617]),
    [final] ).

cnf(i_0_1177,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_618]),
    [final] ).

cnf(i_0_1178,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_619]),
    [final] ).

cnf(i_0_1179,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_620]),
    [final] ).

cnf(i_0_1180,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_621]),
    [final] ).

cnf(i_0_1181,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_622]),
    [final] ).

cnf(i_0_1182,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_623]),
    [final] ).

cnf(i_0_1183,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_614]),
    [final] ).

cnf(i_0_1184,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_624]),
    [final] ).

cnf(i_0_1185,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_614]),
    [final] ).

cnf(i_0_1186,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_614]),
    [final] ).

cnf(i_0_1187,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_1188,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_625]),
    [final] ).

cnf(i_0_1189,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_614]),
    [final] ).

cnf(i_0_1190,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_626]),
    [final] ).

cnf(i_0_1191,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_617]),
    [final] ).

cnf(i_0_1192,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_627]),
    [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_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_617]),
    [final] ).

cnf(i_0_1194,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_614]),
    [final] ).

cnf(i_0_1195,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_626]),
    [final] ).

cnf(i_0_1196,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_628]),
    [final] ).

cnf(i_0_1197,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_620]),
    [final] ).

cnf(i_0_1198,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_620]),
    [final] ).

cnf(i_0_1199,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_620]),
    [final] ).

cnf(i_0_1200,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_620]),
    [final] ).

cnf(i_0_1201,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_614]),
    [final] ).

cnf(i_0_1202,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_621]),
    [final] ).

cnf(i_0_1203,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_621]),
    [final] ).

cnf(i_0_1204,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_621]),
    [final] ).

cnf(i_0_1205,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_621]),
    [final] ).

cnf(i_0_1206,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_616]),
    [final] ).

cnf(i_0_1207,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_617]),
    [final] ).

cnf(i_0_1208,plain,
    ( X1 = c_Set_Oimage(X2,X3,X4,esk35_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_604]),
    [final] ).

cnf(i_0_1209,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_614]),
    [final] ).

cnf(i_0_1210,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_629]),
    [final] ).

cnf(i_0_1211,plain,
    ( X1 = hAPP(X2,esk37_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_630]),
    [final] ).

cnf(i_0_1212,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_631]),
    [final] ).

cnf(i_0_1213,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_614]),
    [final] ).

cnf(i_0_1214,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_632]),
    [final] ).

cnf(i_0_1215,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_614]),
    [final] ).

cnf(i_0_1216,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_614]),
    [final] ).

cnf(i_0_1217,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_619]),
    [final] ).

cnf(i_0_1218,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_633]),
    [final] ).

cnf(i_0_1219,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_634]),
    [final] ).

cnf(i_0_1220,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_625]),
    [final] ).

cnf(i_0_1221,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_614]),
    [final] ).

cnf(i_0_1222,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk38_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_635]),
    [final] ).

cnf(i_0_1223,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_620]),
    [final] ).

cnf(i_0_1224,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_620]),
    [final] ).

cnf(i_0_1225,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_620]),
    [final] ).

cnf(i_0_1226,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_636]),
    [final] ).

cnf(i_0_1227,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_637]),
    [final] ).

cnf(i_0_1228,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_638]),
    [final] ).

cnf(i_0_1229,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_626]),
    [final] ).

cnf(i_0_1230,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)))))
    | esk37_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_630]),
    [final] ).

cnf(i_0_1231,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_614]),
    [final] ).

cnf(i_0_1232,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_639]),
    [final] ).

cnf(i_0_1233,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_620]),
    [final] ).

cnf(i_0_1234,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_620]),
    [final] ).

cnf(i_0_1235,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_620]),
    [final] ).

cnf(i_0_1236,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_620]),
    [final] ).

cnf(i_0_1237,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_620]),
    [final] ).

cnf(i_0_1238,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_621]),
    [final] ).

cnf(i_0_1239,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_640]),
    [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),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_621]),
    [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))
    | 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_621]),
    [final] ).

cnf(i_0_1242,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_614]),
    [final] ).

cnf(i_0_1243,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_617]),
    [final] ).

cnf(i_0_1244,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_641]),
    [final] ).

cnf(i_0_1245,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),esk20_1(X1)),esk21_1(X1))),hAPP(X1,esk18_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),esk20_1(X1)),esk21_1(X1))),hAPP(X1,esk19_1(X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_598]),
    [final] ).

cnf(i_0_1246,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_642]),
    [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_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_614]),
    [final] ).

cnf(i_0_1248,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_621]),
    [final] ).

cnf(i_0_1249,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_621]),
    [final] ).

cnf(i_0_1250,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_621]),
    [final] ).

cnf(i_0_1251,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_621]),
    [final] ).

cnf(i_0_1252,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_621]),
    [final] ).

cnf(i_0_1253,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_614]),
    [final] ).

cnf(i_0_1254,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_643]),
    [final] ).

cnf(i_0_1255,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_614]),
    [final] ).

cnf(i_0_1256,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_614]),
    [final] ).

cnf(i_0_1257,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_614]),
    [final] ).

cnf(i_0_1258,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_614]),
    [final] ).

cnf(i_0_1259,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_644]),
    [final] ).

cnf(i_0_1260,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_614]),
    [final] ).

cnf(i_0_1261,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_617]),
    [final] ).

cnf(i_0_1262,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_614]),
    [final] ).

cnf(i_0_1263,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_617]),
    [final] ).

cnf(i_0_1264,plain,
    ( X1 = hAPP(X2,esk36_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_630]),
    [final] ).

cnf(i_0_1265,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_617]),
    [final] ).

cnf(i_0_1266,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_629]),
    [final] ).

cnf(i_0_1267,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_645]),
    [final] ).

cnf(i_0_1268,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_620]),
    [final] ).

cnf(i_0_1269,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_617]),
    [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),esk20_1(X1)),esk21_1(X1))),hAPP(esk19_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),esk20_1(X1)),esk21_1(X1))),hAPP(esk18_1(X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_598]),
    [final] ).

cnf(i_0_1271,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),esk20_1(X1)),esk21_1(X1))),hAPP(esk18_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),esk20_1(X1)),esk21_1(X1))),hAPP(esk19_1(X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_598]),
    [final] ).

cnf(i_0_1272,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_645]),
    [final] ).

cnf(i_0_1273,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_617]),
    [final] ).

cnf(i_0_1274,plain,
    ( X3 = esk36_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_630]),
    [final] ).

cnf(i_0_1275,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_646]),
    [final] ).

cnf(i_0_1276,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_636]),
    [final] ).

cnf(i_0_1277,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_621]),
    [final] ).

cnf(i_0_1278,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),esk34_3(X1,X3,X2))) != esk34_3(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_647]),
    [final] ).

cnf(i_0_1279,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_648]),
    [final] ).

cnf(i_0_1280,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_649]),
    [final] ).

cnf(i_0_1281,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_650]),
    [final] ).

cnf(i_0_1282,plain,
    hAPP(c_COMBS(X1,X2,X3,X4,X5),X6) = hAPP(hAPP(X4,X6),hAPP(X5,X6)),
    inference(split_conjunct,[status(thm)],[i_0_651]),
    [final] ).

cnf(i_0_1283,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_652]),
    [final] ).

cnf(i_0_1284,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_653]),
    [final] ).

cnf(i_0_1285,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_654]),
    [final] ).

cnf(i_0_1286,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_655]),
    [final] ).

cnf(i_0_1287,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_650]),
    [final] ).

cnf(i_0_1288,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_649]),
    [final] ).

cnf(i_0_1289,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_649]),
    [final] ).

cnf(i_0_1290,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_650]),
    [final] ).

cnf(i_0_1291,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_656]),
    [final] ).

cnf(i_0_1292,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk26_4(X2,X3,X4,X1)),X2))
    | c_Fun_Oinj__on(X1,X4,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_657]),
    [final] ).

cnf(i_0_1293,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk25_4(X2,X3,X4,X1)),X2))
    | c_Fun_Oinj__on(X1,X4,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_657]),
    [final] ).

cnf(i_0_1294,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),esk20_1(X1)),esk21_1(X1))),hAPP(X1,esk18_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),esk20_1(X1)),esk21_1(X1))),hAPP(X1,esk19_1(X1))))
    | c_Arrow__Order__Mirabelle_OIIA(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_598]),
    [final] ).

cnf(i_0_1295,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_658]),
    [final] ).

cnf(i_0_1296,plain,
    ( X1 = hAPP(X2,esk38_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_635]),
    [final] ).

cnf(i_0_1297,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_620]),
    [final] ).

cnf(i_0_1298,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_659]),
    [final] ).

cnf(i_0_1299,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_660]),
    [final] ).

cnf(i_0_1300,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_661]),
    [final] ).

cnf(i_0_1301,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_621]),
    [final] ).

cnf(i_0_1302,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_662]),
    [final] ).

cnf(i_0_1303,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_663]),
    [final] ).

cnf(i_0_1304,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_664]),
    [final] ).

cnf(i_0_1305,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_665]),
    [final] ).

cnf(i_0_1306,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_666]),
    [final] ).

cnf(i_0_1307,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_667]),
    [final] ).

cnf(i_0_1308,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_668]),
    [final] ).

cnf(i_0_1309,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_669]),
    [final] ).

cnf(i_0_1310,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_670]),
    [final] ).

cnf(i_0_1311,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_654]),
    [final] ).

cnf(i_0_1312,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_604]),
    [final] ).

cnf(i_0_1313,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_671]),
    [final] ).

cnf(i_0_1314,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_672]),
    [final] ).

cnf(i_0_1315,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),esk15_1(X1)),esk16_1(X1))),hAPP(X1,esk14_1(X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_613]),
    [final] ).

cnf(i_0_1316,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_647]),
    [final] ).

cnf(i_0_1317,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_673]),
    [final] ).

cnf(i_0_1318,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_674]),
    [final] ).

cnf(i_0_1319,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_649]),
    [final] ).

cnf(i_0_1320,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_650]),
    [final] ).

cnf(i_0_1321,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_650]),
    [final] ).

cnf(i_0_1322,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_649]),
    [final] ).

cnf(i_0_1323,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_675]),
    [final] ).

cnf(i_0_1324,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_666]),
    [final] ).

cnf(i_0_1325,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_676]),
    [final] ).

cnf(i_0_1326,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_676]),
    [final] ).

cnf(i_0_1327,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_677]),
    [final] ).

cnf(i_0_1328,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))),esk27_2(X1,X2)),c_Arrow__Order__Mirabelle_OProf))
    | c_Arrow__Order__Mirabelle_Odictator(X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_661]),
    [final] ).

cnf(i_0_1329,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_678]),
    [final] ).

cnf(i_0_1330,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_679]),
    [final] ).

cnf(i_0_1331,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_680]),
    [final] ).

cnf(i_0_1332,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_681]),
    [final] ).

cnf(i_0_1333,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_682]),
    [final] ).

cnf(i_0_1334,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_683]),
    [final] ).

cnf(i_0_1335,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_1(X1)),c_Arrow__Order__Mirabelle_OProf))
    | c_Arrow__Order__Mirabelle_Ounanimity(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_613]),
    [final] ).

cnf(i_0_1336,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))),esk19_1(X1)),c_Arrow__Order__Mirabelle_OProf))
    | c_Arrow__Order__Mirabelle_OIIA(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_598]),
    [final] ).

cnf(i_0_1337,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))),esk18_1(X1)),c_Arrow__Order__Mirabelle_OProf))
    | c_Arrow__Order__Mirabelle_OIIA(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_598]),
    [final] ).

cnf(i_0_1338,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_684]),
    [final] ).

cnf(i_0_1339,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_635]),
    [final] ).

cnf(i_0_1340,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_685]),
    [final] ).

cnf(i_0_1341,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_1342,plain,
    ( hAPP(X1,esk25_4(X2,X1,X3,X4)) = hAPP(X1,esk26_4(X2,X1,X3,X4))
    | c_Fun_Oinj__on(X4,X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_657]),
    [final] ).

cnf(i_0_1343,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_686]),
    [final] ).

cnf(i_0_1344,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_687]),
    [final] ).

cnf(i_0_1345,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_688]),
    [final] ).

cnf(i_0_1346,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_689]),
    [final] ).

cnf(i_0_1347,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_690]),
    [final] ).

cnf(i_0_1348,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_691]),
    [final] ).

cnf(i_0_1349,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_692]),
    [final] ).

cnf(i_0_1350,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_693]),
    [final] ).

cnf(i_0_1351,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_694]),
    [final] ).

cnf(i_0_1352,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_695]),
    [final] ).

cnf(i_0_1353,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_696]),
    [final] ).

cnf(i_0_1354,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_619]),
    [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),esk15_1(X1)),esk16_1(X1))),hAPP(esk14_1(X1),X2)))
    | c_Arrow__Order__Mirabelle_Ounanimity(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_613]),
    [final] ).

cnf(i_0_1356,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_697]),
    [final] ).

cnf(i_0_1357,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_698]),
    [final] ).

cnf(i_0_1358,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_699]),
    [final] ).

cnf(i_0_1359,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_700]),
    [final] ).

cnf(i_0_1360,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_701]),
    [final] ).

cnf(i_0_1361,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_702]),
    [final] ).

cnf(i_0_1362,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_703]),
    [final] ).

cnf(i_0_1363,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_704]),
    [final] ).

cnf(i_0_1364,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_705]),
    [final] ).

cnf(i_0_1365,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_706]),
    [final] ).

cnf(i_0_1366,plain,
    hAPP(hAPP(c_COMBB(X1,X2,X3,X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
    inference(split_conjunct,[status(thm)],[i_0_707]),
    [final] ).

cnf(i_0_1367,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_708]),
    [final] ).

cnf(i_0_1368,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_709]),
    [final] ).

cnf(i_0_1369,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_697]),
    [final] ).

cnf(i_0_1370,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_649]),
    [final] ).

cnf(i_0_1371,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_650]),
    [final] ).

cnf(i_0_1372,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_710]),
    [final] ).

cnf(i_0_1373,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_697]),
    [final] ).

cnf(i_0_1374,plain,
    ( c_Fun_Oinj__on(X4,X3,X2,X1)
    | esk25_4(X1,X2,X3,X4) != esk26_4(X1,X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_657]),
    [final] ).

cnf(i_0_1375,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_711]),
    [final] ).

cnf(i_0_1376,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_712]),
    [final] ).

cnf(i_0_1377,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_713]),
    [final] ).

cnf(i_0_1378,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_714]),
    [final] ).

cnf(i_0_1379,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_1380,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_715]),
    [final] ).

cnf(i_0_1381,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_716]),
    [final] ).

cnf(i_0_1382,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_717]),
    [final] ).

cnf(i_0_1383,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_718]),
    [final] ).

cnf(i_0_1384,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_719]),
    [final] ).

cnf(i_0_1385,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_720]),
    [final] ).

cnf(i_0_1386,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_705]),
    [final] ).

cnf(i_0_1387,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_721]),
    [final] ).

cnf(i_0_1388,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_722]),
    [final] ).

cnf(i_0_1389,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_723]),
    [final] ).

cnf(i_0_1390,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_724]),
    [final] ).

cnf(i_0_1391,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_725]),
    [final] ).

cnf(i_0_1392,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_726]),
    [final] ).

cnf(i_0_1393,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_727]),
    [final] ).

cnf(i_0_1394,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_728]),
    [final] ).

cnf(i_0_1395,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_688]),
    [final] ).

cnf(i_0_1396,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_729]),
    [final] ).

cnf(i_0_1397,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_690]),
    [final] ).

cnf(i_0_1398,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_730]),
    [final] ).

cnf(i_0_1399,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_731]),
    [final] ).

cnf(i_0_1400,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_732]),
    [final] ).

cnf(i_0_1401,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_733]),
    [final] ).

cnf(i_0_1402,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_734]),
    [final] ).

cnf(i_0_1403,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_735]),
    [final] ).

cnf(i_0_1404,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_736]),
    [final] ).

cnf(i_0_1405,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_1406,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_737]),
    [final] ).

cnf(i_0_1407,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_1408,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_738]),
    [final] ).

cnf(i_0_1409,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_738]),
    [final] ).

cnf(i_0_1410,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_739]),
    [final] ).

cnf(i_0_1411,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_740]),
    [final] ).

cnf(i_0_1412,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_741]),
    [final] ).

cnf(i_0_1413,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_694]),
    [final] ).

cnf(i_0_1414,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_742]),
    [final] ).

cnf(i_0_1415,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_696]),
    [final] ).

cnf(i_0_1416,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_743]),
    [final] ).

cnf(i_0_1417,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_744]),
    [final] ).

cnf(i_0_1418,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_715]),
    [final] ).

cnf(i_0_1419,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_745]),
    [final] ).

cnf(i_0_1420,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_745]),
    [final] ).

cnf(i_0_1421,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_746]),
    [final] ).

cnf(i_0_1422,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_747]),
    [final] ).

cnf(i_0_1423,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_748]),
    [final] ).

cnf(i_0_1424,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_701]),
    [final] ).

cnf(i_0_1425,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_749]),
    [final] ).

cnf(i_0_1426,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_750]),
    [final] ).

cnf(i_0_1427,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_751]),
    [final] ).

cnf(i_0_1428,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_657]),
    [final] ).

cnf(i_0_1429,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_732]),
    [final] ).

cnf(i_0_1430,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_752]),
    [final] ).

cnf(i_0_1431,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_752]),
    [final] ).

cnf(i_0_1432,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_753]),
    [final] ).

cnf(i_0_1433,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_754]),
    [final] ).

cnf(i_0_1434,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_755]),
    [final] ).

cnf(i_0_1435,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_756]),
    [final] ).

cnf(i_0_1436,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_710]),
    [final] ).

cnf(i_0_1437,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_757]),
    [final] ).

cnf(i_0_1438,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_758]),
    [final] ).

cnf(i_0_1439,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_759]),
    [final] ).

cnf(i_0_1440,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_760]),
    [final] ).

cnf(i_0_1441,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_719]),
    [final] ).

cnf(i_0_1442,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_720]),
    [final] ).

cnf(i_0_1443,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_761]),
    [final] ).

cnf(i_0_1444,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_762]),
    [final] ).

cnf(i_0_1445,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_763]),
    [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),X1),X2)),X1)),
    inference(split_conjunct,[status(thm)],[i_0_764]),
    [final] ).

cnf(i_0_1447,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_765]),
    [final] ).

cnf(i_0_1448,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_766]),
    [final] ).

cnf(i_0_1449,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_767]),
    [final] ).

cnf(i_0_1450,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_768]),
    [final] ).

cnf(i_0_1451,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_745]),
    [final] ).

cnf(i_0_1452,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_769]),
    [final] ).

cnf(i_0_1453,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_770]),
    [final] ).

cnf(i_0_1454,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_771]),
    [final] ).

cnf(i_0_1455,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_772]),
    [final] ).

cnf(i_0_1456,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_773]),
    [final] ).

cnf(i_0_1457,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_774]),
    [final] ).

cnf(i_0_1458,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_731]),
    [final] ).

cnf(i_0_1459,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_775]),
    [final] ).

cnf(i_0_1460,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_776]),
    [final] ).

cnf(i_0_1461,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_777]),
    [final] ).

cnf(i_0_1462,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_778]),
    [final] ).

cnf(i_0_1463,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_779]),
    [final] ).

cnf(i_0_1464,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_780]),
    [final] ).

cnf(i_0_1465,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_781]),
    [final] ).

cnf(i_0_1466,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_782]),
    [final] ).

cnf(i_0_1467,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_783]),
    [final] ).

cnf(i_0_1468,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_784]),
    [final] ).

cnf(i_0_1469,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_736]),
    [final] ).

cnf(i_0_1470,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_737]),
    [final] ).

cnf(i_0_1471,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_1472,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_1473,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_785]),
    [final] ).

cnf(i_0_1474,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_786]),
    [final] ).

cnf(i_0_1475,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_787]),
    [final] ).

cnf(i_0_1476,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_738]),
    [final] ).

cnf(i_0_1477,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_779]),
    [final] ).

cnf(i_0_1478,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_780]),
    [final] ).

cnf(i_0_1479,plain,
    hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
    inference(split_conjunct,[status(thm)],[i_0_788]),
    [final] ).

cnf(i_0_1480,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_766]),
    [final] ).

cnf(i_0_1481,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_766]),
    [final] ).

cnf(i_0_1482,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_771]),
    [final] ).

cnf(i_0_1483,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_789]),
    [final] ).

cnf(i_0_1484,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_790]),
    [final] ).

cnf(i_0_1485,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_791]),
    [final] ).

cnf(i_0_1486,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_792]),
    [final] ).

cnf(i_0_1487,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_793]),
    [final] ).

cnf(i_0_1488,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_794]),
    [final] ).

cnf(i_0_1489,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_795]),
    [final] ).

cnf(i_0_1490,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_796]),
    [final] ).

cnf(i_0_1491,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_606]),
    [final] ).

cnf(i_0_1492,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_797]),
    [final] ).

cnf(i_0_1493,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_798]),
    [final] ).

cnf(i_0_1494,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_799]),
    [final] ).

cnf(i_0_1495,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_800]),
    [final] ).

cnf(i_0_1496,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_801]),
    [final] ).

cnf(i_0_1497,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_802]),
    [final] ).

cnf(i_0_1498,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_802]),
    [final] ).

cnf(i_0_1499,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_803]),
    [final] ).

cnf(i_0_1500,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_804]),
    [final] ).

cnf(i_0_1501,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_805]),
    [final] ).

cnf(i_0_1502,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_806]),
    [final] ).

cnf(i_0_1503,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_807]),
    [final] ).

cnf(i_0_1504,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_808]),
    [final] ).

cnf(i_0_1505,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_781]),
    [final] ).

cnf(i_0_1506,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_809]),
    [final] ).

cnf(i_0_1507,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_783]),
    [final] ).

cnf(i_0_1508,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_810]),
    [final] ).

cnf(i_0_1509,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_811]),
    [final] ).

cnf(i_0_1510,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_812]),
    [final] ).

cnf(i_0_1511,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_1512,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_780]),
    [final] ).

cnf(i_0_1513,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_813]),
    [final] ).

cnf(i_0_1514,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_814]),
    [final] ).

cnf(i_0_1515,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_815]),
    [final] ).

cnf(i_0_1516,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_772]),
    [final] ).

cnf(i_0_1517,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_772]),
    [final] ).

cnf(i_0_1518,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_816]),
    [final] ).

cnf(i_0_1519,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_817]),
    [final] ).

cnf(i_0_1520,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_818]),
    [final] ).

cnf(i_0_1521,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_819]),
    [final] ).

cnf(i_0_1522,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_819]),
    [final] ).

cnf(i_0_1523,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_820]),
    [final] ).

cnf(i_0_1524,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_821]),
    [final] ).

cnf(i_0_1525,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_822]),
    [final] ).

cnf(i_0_1526,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_823]),
    [final] ).

cnf(i_0_1527,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_824]),
    [final] ).

cnf(i_0_1528,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk30_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_825]),
    [final] ).

cnf(i_0_1529,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_826]),
    [final] ).

cnf(i_0_1530,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_827]),
    [final] ).

cnf(i_0_1531,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_828]),
    [final] ).

cnf(i_0_1532,plain,
    ( X2 = X4
    | hBOOL(hAPP(X3,X4))
    | ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_829]),
    [final] ).

cnf(i_0_1533,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_819]),
    [final] ).

cnf(i_0_1534,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_830]),
    [final] ).

cnf(i_0_1535,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_831]),
    [final] ).

cnf(i_0_1536,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_832]),
    [final] ).

cnf(i_0_1537,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_833]),
    [final] ).

cnf(i_0_1538,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_834]),
    [final] ).

cnf(i_0_1539,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_835]),
    [final] ).

cnf(i_0_1540,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_836]),
    [final] ).

cnf(i_0_1541,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_837]),
    [final] ).

cnf(i_0_1542,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_838]),
    [final] ).

cnf(i_0_1543,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_839]),
    [final] ).

cnf(i_0_1544,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_840]),
    [final] ).

cnf(i_0_1545,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_841]),
    [final] ).

cnf(i_0_1546,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_842]),
    [final] ).

cnf(i_0_1547,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_813]),
    [final] ).

cnf(i_0_1548,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_843]),
    [final] ).

cnf(i_0_1549,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_844]),
    [final] ).

cnf(i_0_1550,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_845]),
    [final] ).

cnf(i_0_1551,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_846]),
    [final] ).

cnf(i_0_1552,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_847]),
    [final] ).

cnf(i_0_1553,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_836]),
    [final] ).

cnf(i_0_1554,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_836]),
    [final] ).

cnf(i_0_1555,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_848]),
    [final] ).

cnf(i_0_1556,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_849]),
    [final] ).

cnf(i_0_1557,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_850]),
    [final] ).

cnf(i_0_1558,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_851]),
    [final] ).

cnf(i_0_1559,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_852]),
    [final] ).

cnf(i_0_1560,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_853]),
    [final] ).

cnf(i_0_1561,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_854]),
    [final] ).

cnf(i_0_1562,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_855]),
    [final] ).

cnf(i_0_1563,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_856]),
    [final] ).

cnf(i_0_1564,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_857]),
    [final] ).

cnf(i_0_1565,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_858]),
    [final] ).

cnf(i_0_1566,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_859]),
    [final] ).

cnf(i_0_1567,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_860]),
    [final] ).

cnf(i_0_1568,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_861]),
    [final] ).

cnf(i_0_1569,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_862]),
    [final] ).

cnf(i_0_1570,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_863]),
    [final] ).

cnf(i_0_1571,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_864]),
    [final] ).

cnf(i_0_1572,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_865]),
    [final] ).

cnf(i_0_1573,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_866]),
    [final] ).

cnf(i_0_1574,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_867]),
    [final] ).

cnf(i_0_1575,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_805]),
    [final] ).

cnf(i_0_1576,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_831]),
    [final] ).

cnf(i_0_1577,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_868]),
    [final] ).

cnf(i_0_1578,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_869]),
    [final] ).

cnf(i_0_1579,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_870]),
    [final] ).

cnf(i_0_1580,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_871]),
    [final] ).

cnf(i_0_1581,plain,
    ( hBOOL(hAPP(hAPP(c_member(X3),X1),c_Set_Oinsert(X3,X2,X4)))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_781]),
    [final] ).

cnf(i_0_1582,plain,
    ( hBOOL(hAPP(hAPP(c_member(X3),X1),c_Set_Oinsert(X3,X2,X4)))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_809]),
    [final] ).

cnf(i_0_1583,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_872]),
    [final] ).

cnf(i_0_1584,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X2,X3))),
    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))
    | 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_874]),
    [final] ).

cnf(i_0_1586,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_875]),
    [final] ).

cnf(i_0_1587,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_876]),
    [final] ).

cnf(i_0_1588,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_877]),
    [final] ).

cnf(i_0_1589,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk12_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_587]),
    [final] ).

cnf(i_0_1590,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_588]),
    [final] ).

cnf(i_0_1591,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_1592,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_851]),
    [final] ).

cnf(i_0_1593,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_852]),
    [final] ).

cnf(i_0_1594,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_878]),
    [final] ).

cnf(i_0_1595,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_879]),
    [final] ).

cnf(i_0_1596,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_880]),
    [final] ).

cnf(i_0_1597,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_825]),
    [final] ).

cnf(i_0_1598,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_881]),
    [final] ).

cnf(i_0_1599,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_882]),
    [final] ).

cnf(i_0_1600,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_883]),
    [final] ).

cnf(i_0_1601,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_884]),
    [final] ).

cnf(i_0_1602,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_885]),
    [final] ).

cnf(i_0_1603,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_886]),
    [final] ).

cnf(i_0_1604,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_869]),
    [final] ).

cnf(i_0_1605,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_887]),
    [final] ).

cnf(i_0_1606,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_888]),
    [final] ).

cnf(i_0_1607,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_889]),
    [final] ).

cnf(i_0_1608,plain,
    ( hBOOL(hAPP(c_Set_Oinsert(X3,X4,X1),X2))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_829]),
    [final] ).

cnf(i_0_1609,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_812]),
    [final] ).

cnf(i_0_1610,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_1611,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_870]),
    [final] ).

cnf(i_0_1612,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_890]),
    [final] ).

cnf(i_0_1613,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_874]),
    [final] ).

cnf(i_0_1614,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_891]),
    [final] ).

cnf(i_0_1615,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_892]),
    [final] ).

cnf(i_0_1616,plain,
    c_Nat_Onat_Onat__case(X1,X2,X3,hAPP(c_Nat_OSuc,X4)) = hAPP(X3,X4),
    inference(split_conjunct,[status(thm)],[i_0_893]),
    [final] ).

cnf(i_0_1617,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_805]),
    [final] ).

cnf(i_0_1618,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_894]),
    [final] ).

cnf(i_0_1619,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_895]),
    [final] ).

cnf(i_0_1620,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_896]),
    [final] ).

cnf(i_0_1621,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_871]),
    [final] ).

cnf(i_0_1622,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_897]),
    [final] ).

cnf(i_0_1623,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_898]),
    [final] ).

cnf(i_0_1624,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_899]),
    [final] ).

cnf(i_0_1625,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_900]),
    [final] ).

cnf(i_0_1626,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_901]),
    [final] ).

cnf(i_0_1627,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_902]),
    [final] ).

cnf(i_0_1628,plain,
    ( X1 = hAPP(c_Nat_OSuc,esk30_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_825]),
    [final] ).

cnf(i_0_1629,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_866]),
    [final] ).

cnf(i_0_1630,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_903]),
    [final] ).

cnf(i_0_1631,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_904]),
    [final] ).

cnf(i_0_1632,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_888]),
    [final] ).

cnf(i_0_1633,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_905]),
    [final] ).

cnf(i_0_1634,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_892]),
    [final] ).

cnf(i_0_1635,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_906]),
    [final] ).

cnf(i_0_1636,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_887]),
    [final] ).

cnf(i_0_1637,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_889]),
    [final] ).

cnf(i_0_1638,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_907]),
    [final] ).

cnf(i_0_1639,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_908]),
    [final] ).

cnf(i_0_1640,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_909]),
    [final] ).

cnf(i_0_1641,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_869]),
    [final] ).

cnf(i_0_1642,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_910]),
    [final] ).

cnf(i_0_1643,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_911]),
    [final] ).

cnf(i_0_1644,plain,
    c_Set_Oimage(X1,X1,c_COMBI(X1),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_912]),
    [final] ).

cnf(i_0_1645,plain,
    c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
    inference(split_conjunct,[status(thm)],[i_0_913]),
    [final] ).

cnf(i_0_1646,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_914]),
    [final] ).

cnf(i_0_1647,plain,
    ( hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_829]),
    [final] ).

cnf(i_0_1648,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_915]),
    [final] ).

cnf(i_0_1649,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_916]),
    [final] ).

cnf(i_0_1650,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_917]),
    [final] ).

cnf(i_0_1651,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_918]),
    [final] ).

cnf(i_0_1652,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_907]),
    [final] ).

cnf(i_0_1653,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_908]),
    [final] ).

cnf(i_0_1654,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_883]),
    [final] ).

cnf(i_0_1655,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_919]),
    [final] ).

cnf(i_0_1656,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_920]),
    [final] ).

cnf(i_0_1657,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_842]),
    [final] ).

cnf(i_0_1658,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_921]),
    [final] ).

cnf(i_0_1659,plain,
    c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1),
    inference(split_conjunct,[status(thm)],[i_0_922]),
    [final] ).

cnf(i_0_1660,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_923]),
    [final] ).

cnf(i_0_1661,plain,
    ( X2 = X3
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_924]),
    [final] ).

cnf(i_0_1662,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_894]),
    [final] ).

cnf(i_0_1663,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_925]),
    [final] ).

cnf(i_0_1664,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_875]),
    [final] ).

cnf(i_0_1665,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_849]),
    [final] ).

cnf(i_0_1666,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_926]),
    [final] ).

cnf(i_0_1667,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_927]),
    [final] ).

cnf(i_0_1668,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_928]),
    [final] ).

cnf(i_0_1669,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_929]),
    [final] ).

cnf(i_0_1670,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_930]),
    [final] ).

cnf(i_0_1671,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_931]),
    [final] ).

cnf(i_0_1672,plain,
    ( c_Set_Oinsert(X1,X2,X3) = X3
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_932]),
    [final] ).

cnf(i_0_1673,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_933]),
    [final] ).

cnf(i_0_1674,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_934]),
    [final] ).

cnf(i_0_1675,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_935]),
    [final] ).

cnf(i_0_1676,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_936]),
    [final] ).

cnf(i_0_1677,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_937]),
    [final] ).

cnf(i_0_1678,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_860]),
    [final] ).

cnf(i_0_1679,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_938]),
    [final] ).

cnf(i_0_1680,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_939]),
    [final] ).

cnf(i_0_1681,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_928]),
    [final] ).

cnf(i_0_1682,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_929]),
    [final] ).

cnf(i_0_1683,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_940]),
    [final] ).

cnf(i_0_1684,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_941]),
    [final] ).

cnf(i_0_1685,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_889]),
    [final] ).

cnf(i_0_1686,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_871]),
    [final] ).

cnf(i_0_1687,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_942]),
    [final] ).

cnf(i_0_1688,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_943]),
    [final] ).

cnf(i_0_1689,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_944]),
    [final] ).

cnf(i_0_1690,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_939]),
    [final] ).

cnf(i_0_1691,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_919]),
    [final] ).

cnf(i_0_1692,plain,
    ( hBOOL(hAPP(X3,X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_945]),
    [final] ).

cnf(i_0_1693,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_946]),
    [final] ).

cnf(i_0_1694,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_947]),
    [final] ).

cnf(i_0_1695,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_886]),
    [final] ).

cnf(i_0_1696,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_948]),
    [final] ).

cnf(i_0_1697,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_885]),
    [final] ).

cnf(i_0_1698,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_949]),
    [final] ).

cnf(i_0_1699,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_950]),
    [final] ).

cnf(i_0_1700,plain,
    ( X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk2_2(X2,X1))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_951]),
    [final] ).

cnf(i_0_1701,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_952]),
    [final] ).

cnf(i_0_1702,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_953]),
    [final] ).

cnf(i_0_1703,plain,
    ( X1 = hAPP(c_Nat_OSuc,esk31_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_954]),
    [final] ).

cnf(i_0_1704,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_908]),
    [final] ).

cnf(i_0_1705,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_860]),
    [final] ).

cnf(i_0_1706,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_955]),
    [final] ).

cnf(i_0_1707,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_956]),
    [final] ).

cnf(i_0_1708,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_957]),
    [final] ).

cnf(i_0_1709,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_933]),
    [final] ).

cnf(i_0_1710,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_933]),
    [final] ).

cnf(i_0_1711,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_958]),
    [final] ).

cnf(i_0_1712,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_958]),
    [final] ).

cnf(i_0_1713,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_789]),
    [final] ).

cnf(i_0_1714,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_789]),
    [final] ).

cnf(i_0_1715,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_959]),
    [final] ).

cnf(i_0_1716,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_779]),
    [final] ).

cnf(i_0_1717,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_960]),
    [final] ).

cnf(i_0_1718,plain,
    ( ~ class_Orderings_Opreorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_961]),
    [final] ).

cnf(i_0_1719,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
    inference(split_conjunct,[status(thm)],[i_0_962]),
    [final] ).

cnf(i_0_1720,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_963]),
    [final] ).

cnf(i_0_1721,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_964]),
    [final] ).

cnf(i_0_1722,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_965]),
    [final] ).

cnf(i_0_1723,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_966]),
    [final] ).

cnf(i_0_1724,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_967]),
    [final] ).

cnf(i_0_1725,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_968]),
    [final] ).

cnf(i_0_1726,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_969]),
    [final] ).

cnf(i_0_1727,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_970]),
    [final] ).

cnf(i_0_1728,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_971]),
    [final] ).

cnf(i_0_1729,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_972]),
    [final] ).

cnf(i_0_1730,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_921]),
    [final] ).

cnf(i_0_1731,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_973]),
    [final] ).

cnf(i_0_1732,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_974]),
    [final] ).

cnf(i_0_1733,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_975]),
    [final] ).

cnf(i_0_1734,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_976]),
    [final] ).

cnf(i_0_1735,plain,
    ( hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(c_fequal,X2)))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_924]),
    [final] ).

cnf(i_0_1736,plain,
    ( hBOOL(hAPP(hAPP(c_member(X3),X2),X1))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_945]),
    [final] ).

cnf(i_0_1737,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_977]),
    [final] ).

cnf(i_0_1738,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_978]),
    [final] ).

cnf(i_0_1739,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_979]),
    [final] ).

cnf(i_0_1740,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_952]),
    [final] ).

cnf(i_0_1741,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X2 != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_952]),
    [final] ).

cnf(i_0_1742,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X2 != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_980]),
    [final] ).

cnf(i_0_1743,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_981]),
    [final] ).

cnf(i_0_1744,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_928]),
    [final] ).

cnf(i_0_1745,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_951]),
    [final] ).

cnf(i_0_1746,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_982]),
    [final] ).

cnf(i_0_1747,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_983]),
    [final] ).

cnf(i_0_1748,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_984]),
    [final] ).

cnf(i_0_1749,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_985]),
    [final] ).

cnf(i_0_1750,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_986]),
    [final] ).

cnf(i_0_1751,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_987]),
    [final] ).

cnf(i_0_1752,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_988]),
    [final] ).

cnf(i_0_1753,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_825]),
    [final] ).

cnf(i_0_1754,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_944]),
    [final] ).

cnf(i_0_1755,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_989]),
    [final] ).

cnf(i_0_1756,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_874]),
    [final] ).

cnf(i_0_1757,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_894]),
    [final] ).

cnf(i_0_1758,plain,
    ( c_Arrow__Order__Mirabelle_Odictator(X1,X2)
    | hAPP(X1,esk27_2(X2,X1)) != hAPP(esk27_2(X2,X1),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_661]),
    [final] ).

cnf(i_0_1759,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_990]),
    [final] ).

cnf(i_0_1760,plain,
    hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2)),
    inference(split_conjunct,[status(thm)],[i_0_991]),
    [final] ).

cnf(i_0_1761,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_992]),
    [final] ).

cnf(i_0_1762,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_993]),
    [final] ).

cnf(i_0_1763,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_994]),
    [final] ).

cnf(i_0_1764,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_954]),
    [final] ).

cnf(i_0_1765,plain,
    ( X1 = X2
    | hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_995]),
    [final] ).

cnf(i_0_1766,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_996]),
    [final] ).

cnf(i_0_1767,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP(hAPP(c_fequal,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_997]),
    [final] ).

cnf(i_0_1768,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_993]),
    [final] ).

cnf(i_0_1769,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_993]),
    [final] ).

cnf(i_0_1770,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_994]),
    [final] ).

cnf(i_0_1771,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_994]),
    [final] ).

cnf(i_0_1772,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_998]),
    [final] ).

cnf(i_0_1773,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_999]),
    [final] ).

cnf(i_0_1774,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_1000]),
    [final] ).

cnf(i_0_1775,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_1001]),
    [final] ).

cnf(i_0_1776,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_963]),
    [final] ).

cnf(i_0_1777,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_993]),
    [final] ).

cnf(i_0_1778,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_994]),
    [final] ).

cnf(i_0_1779,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_1002]),
    [final] ).

cnf(i_0_1780,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_1003]),
    [final] ).

cnf(i_0_1781,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_1004]),
    [final] ).

cnf(i_0_1782,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_1005]),
    [final] ).

cnf(i_0_1783,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_993]),
    [final] ).

cnf(i_0_1784,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_993]),
    [final] ).

cnf(i_0_1785,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_994]),
    [final] ).

cnf(i_0_1786,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_994]),
    [final] ).

cnf(i_0_1787,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_899]),
    [final] ).

cnf(i_0_1788,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_899]),
    [final] ).

cnf(i_0_1789,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_1006]),
    [final] ).

cnf(i_0_1790,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_907]),
    [final] ).

cnf(i_0_1791,plain,
    hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
    inference(split_conjunct,[status(thm)],[i_0_1007]),
    [final] ).

cnf(i_0_1792,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_1008]),
    [final] ).

cnf(i_0_1793,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X2))
    | ~ class_Orderings_Opreorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1009]),
    [final] ).

cnf(i_0_1794,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_1010]),
    [final] ).

cnf(i_0_1795,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_1011]),
    [final] ).

cnf(i_0_1796,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_992]),
    [final] ).

cnf(i_0_1797,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_1012]),
    [final] ).

cnf(i_0_1798,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_1013]),
    [final] ).

cnf(i_0_1799,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_1013]),
    [final] ).

cnf(i_0_1800,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_929]),
    [final] ).

cnf(i_0_1801,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_931]),
    [final] ).

cnf(i_0_1802,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_1014]),
    [final] ).

cnf(i_0_1803,plain,
    ( hBOOL(hAPP(hAPP(c_fequal,X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_1015]),
    [final] ).

cnf(i_0_1804,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_1016]),
    [final] ).

cnf(i_0_1805,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_1017]),
    [final] ).

cnf(i_0_1806,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_1018]),
    [final] ).

cnf(i_0_1807,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_1019]),
    [final] ).

cnf(i_0_1808,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_1020]),
    [final] ).

cnf(i_0_1809,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_1021]),
    [final] ).

cnf(i_0_1810,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_1003]),
    [final] ).

cnf(i_0_1811,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_1004]),
    [final] ).

cnf(i_0_1812,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_1005]),
    [final] ).

cnf(i_0_1813,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_1022]),
    [final] ).

cnf(i_0_1814,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_1023]),
    [final] ).

cnf(i_0_1815,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_1024]),
    [final] ).

cnf(i_0_1816,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_1025]),
    [final] ).

cnf(i_0_1817,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_1026]),
    [final] ).

cnf(i_0_1818,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_1819,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_1013]),
    [final] ).

cnf(i_0_1820,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_1821,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_1027]),
    [final] ).

cnf(i_0_1822,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_1028]),
    [final] ).

cnf(i_0_1823,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_1029]),
    [final] ).

cnf(i_0_1824,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_1030]),
    [final] ).

cnf(i_0_1825,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_1031]),
    [final] ).

cnf(i_0_1826,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_1032]),
    [final] ).

cnf(i_0_1827,plain,
    ( X1 = X2
    | hAPP(c_Nat_OSuc,X1) != hAPP(c_Nat_OSuc,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1033]),
    [final] ).

cnf(i_0_1828,plain,
    ( X1 = X2
    | hAPP(c_Nat_OSuc,X1) != hAPP(c_Nat_OSuc,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1034]),
    [final] ).

cnf(i_0_1829,plain,
    ( class_Orderings_Oorder(tc_fun(X2,X1))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1035]),
    [final] ).

cnf(i_0_1830,plain,
    ( class_Orderings_Otop(tc_fun(X2,X1))
    | ~ class_Orderings_Otop(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1036]),
    [final] ).

cnf(i_0_1831,plain,
    ( class_Orderings_Oord(tc_fun(X2,X1))
    | ~ class_Orderings_Oord(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1037]),
    [final] ).

cnf(i_0_1832,plain,
    ( class_Orderings_Opreorder(tc_fun(X2,X1))
    | ~ class_Orderings_Opreorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1038]),
    [final] ).

cnf(i_0_1833,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_622]),
    [final] ).

cnf(i_0_1834,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_1039]),
    [final] ).

cnf(i_0_1835,plain,
    hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_1040]),
    [final] ).

cnf(i_0_1836,plain,
    hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_1041]),
    [final] ).

cnf(i_0_1837,plain,
    hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_1042]),
    [final] ).

cnf(i_0_1838,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
    inference(split_conjunct,[status(thm)],[i_0_1043]),
    [final] ).

cnf(i_0_1839,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
    inference(split_conjunct,[status(thm)],[i_0_1044]),
    [final] ).

cnf(i_0_1840,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
    inference(split_conjunct,[status(thm)],[i_0_1045]),
    [final] ).

cnf(i_0_1841,plain,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ class_Finite__Set_Ofinite(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1046]),
    [final] ).

cnf(i_0_1842,plain,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ class_Finite__Set_Ofinite(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1047]),
    [final] ).

cnf(i_0_1843,plain,
    hAPP(c_Nat_OSuc,X1) != X1,
    inference(split_conjunct,[status(thm)],[i_0_1048]),
    [final] ).

cnf(i_0_1844,plain,
    X1 != hAPP(c_Nat_OSuc,X1),
    inference(split_conjunct,[status(thm)],[i_0_1049]),
    [final] ).

cnf(i_0_1845,plain,
    hAPP(c_COMBI(X1),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_1050]),
    [final] ).

cnf(i_0_1846,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_1051]),
    [final] ).

cnf(i_0_1847,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_1052]),
    [final] ).

cnf(i_0_1848,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_1849,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_1850,plain,
    ( class_Finite__Set_Ofinite(tc_Option_Ooption(X1))
    | ~ class_Finite__Set_Ofinite(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1053]),
    [final] ).

cnf(i_0_1851,plain,
    c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
    inference(split_conjunct,[status(thm)],[i_0_1054]),
    [final] ).

cnf(i_0_1852,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_1853,plain,
    ~ hBOOL(c_fFalse),
    inference(split_conjunct,[status(thm)],[i_0_1055]),
    [final] ).

cnf(i_0_1854,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_1855,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_1856,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_1857,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_1858,plain,
    class_Groups_Omonoid__add(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__add]),
    [final] ).

cnf(i_0_1859,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_1860,plain,
    class_Groups_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ozero]),
    [final] ).

cnf(i_0_1861,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_1862,plain,
    class_Finite__Set_Ofinite(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Finite__Set_Ofinite]),
    [final] ).

cnf(i_0_1863,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_1864,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_1865,plain,
    class_Groups_Oone(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oone]),
    [final] ).

cnf(i_0_1866,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_1867,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_1868,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_1869,plain,
    class_Orderings_Oorder(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]),
    [final] ).

cnf(i_0_1870,plain,
    class_Orderings_Oorder(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]),
    [final] ).

cnf(i_0_1871,plain,
    class_Orderings_Olinorder(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]),
    [final] ).

cnf(i_0_1872,plain,
    class_Orderings_Otop(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Otop]),
    [final] ).

cnf(i_0_1873,plain,
    class_Orderings_Oord(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oord]),
    [final] ).

cnf(i_0_1874,plain,
    class_Orderings_Oord(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oord]),
    [final] ).

cnf(i_0_1875,plain,
    class_Orderings_Opreorder(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]),
    [final] ).

cnf(i_0_1876,plain,
    class_Orderings_Opreorder(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]),
    [final] ).

cnf(i_0_1877,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_1878,plain,
    class_Rings_Olinordered__semidom(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semidom]),
    [final] ).

cnf(i_0_1879,plain,
    c_Arrow__Order__Mirabelle_Ounanimity(v_F),
    inference(split_conjunct,[status(thm)],[fact_u]),
    [final] ).

cnf(i_0_1880,plain,
    c_Arrow__Order__Mirabelle_OIIA(v_F),
    inference(split_conjunct,[status(thm)],[fact_assms_I3_J]),
    [final] ).

cnf(i_0_1881,plain,
    v_c____ != v_d____,
    inference(split_conjunct,[status(thm)],[fact__096c_A_126_061_Ad_096]),
    [final] ).

cnf(i_0_1882,plain,
    v_a____ != v_b____,
    inference(split_conjunct,[status(thm)],[fact__096a_A_126_061_Ab_096]),
    [final] ).

cnf(i_0_1883,axiom,
    X1 = X1 ).

cnf(i_0_1884,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_1885,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_1886,axiom,
    ( X1 != X2
    | hAPP(X1,X3) = hAPP(X2,X3) ) ).

cnf(i_0_1887,axiom,
    ( X1 != X2
    | hAPP(X3,X1) = hAPP(X3,X2) ) ).

cnf(i_0_1888,axiom,
    ( X1 != X2
    | c_Groups_Oone__class_Oone(X1) = c_Groups_Oone__class_Oone(X2) ) ).

cnf(i_0_1889,axiom,
    ( X1 != X2
    | c_Orderings_Oord__class_Oless__eq(X1,X3) = c_Orderings_Oord__class_Oless__eq(X2,X3) ) ).

cnf(i_0_1890,axiom,
    ( X1 != X2
    | c_Orderings_Oord__class_Oless__eq(X3,X1) = c_Orderings_Oord__class_Oless__eq(X3,X2) ) ).

cnf(i_0_1891,axiom,
    ( X1 != X2
    | c_FuncSet_OPi(X1,X3,X4,X5) = c_FuncSet_OPi(X2,X3,X4,X5) ) ).

cnf(i_0_1892,axiom,
    ( X1 != X2
    | c_FuncSet_OPi(X3,X1,X4,X5) = c_FuncSet_OPi(X3,X2,X4,X5) ) ).

cnf(i_0_1893,axiom,
    ( X1 != X2
    | c_FuncSet_OPi(X3,X4,X1,X5) = c_FuncSet_OPi(X3,X4,X2,X5) ) ).

cnf(i_0_1894,axiom,
    ( X1 != X2
    | c_FuncSet_OPi(X3,X4,X5,X1) = c_FuncSet_OPi(X3,X4,X5,X2) ) ).

cnf(i_0_1895,axiom,
    ( X1 != X2
    | esk23_2(X1,X3) = esk23_2(X2,X3) ) ).

cnf(i_0_1896,axiom,
    ( X1 != X2
    | esk23_2(X3,X1) = esk23_2(X3,X2) ) ).

cnf(i_0_1897,axiom,
    ( X1 != X2
    | esk24_2(X1,X3) = esk24_2(X2,X3) ) ).

cnf(i_0_1898,axiom,
    ( X1 != X2
    | esk24_2(X3,X1) = esk24_2(X3,X2) ) ).

cnf(i_0_1899,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_1900,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_1901,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_1902,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_1903,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_1904,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_1905,axiom,
    ( X1 != X2
    | c_Set_Oimage(X1,X3,X4,X5) = c_Set_Oimage(X2,X3,X4,X5) ) ).

cnf(i_0_1906,axiom,
    ( X1 != X2
    | c_Set_Oimage(X3,X1,X4,X5) = c_Set_Oimage(X3,X2,X4,X5) ) ).

cnf(i_0_1907,axiom,
    ( X1 != X2
    | c_Set_Oimage(X3,X4,X1,X5) = c_Set_Oimage(X3,X4,X2,X5) ) ).

cnf(i_0_1908,axiom,
    ( X1 != X2
    | c_Set_Oimage(X3,X4,X5,X1) = c_Set_Oimage(X3,X4,X5,X2) ) ).

cnf(i_0_1909,axiom,
    ( X1 != X2
    | c_Set_Oinsert(X1,X3,X4) = c_Set_Oinsert(X2,X3,X4) ) ).

cnf(i_0_1910,axiom,
    ( X1 != X2
    | c_Set_Oinsert(X3,X1,X4) = c_Set_Oinsert(X3,X2,X4) ) ).

cnf(i_0_1911,axiom,
    ( X1 != X2
    | c_Set_Oinsert(X3,X4,X1) = c_Set_Oinsert(X3,X4,X2) ) ).

cnf(i_0_1912,axiom,
    ( X1 != X2
    | c_Finite__Set_Ocard(X1,X3) = c_Finite__Set_Ocard(X2,X3) ) ).

cnf(i_0_1913,axiom,
    ( X1 != X2
    | c_Finite__Set_Ocard(X3,X1) = c_Finite__Set_Ocard(X3,X2) ) ).

cnf(i_0_1914,axiom,
    ( X1 != X2
    | c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).

cnf(i_0_1915,axiom,
    ( X1 != X2
    | c_Orderings_Otop__class_Otop(X1) = c_Orderings_Otop__class_Otop(X2) ) ).

cnf(i_0_1916,axiom,
    ( X1 != X2
    | esk37_5(X1,X3,X4,X5,X6) = esk37_5(X2,X3,X4,X5,X6) ) ).

cnf(i_0_1917,axiom,
    ( X1 != X2
    | esk37_5(X3,X1,X4,X5,X6) = esk37_5(X3,X2,X4,X5,X6) ) ).

cnf(i_0_1918,axiom,
    ( X1 != X2
    | esk37_5(X3,X4,X1,X5,X6) = esk37_5(X3,X4,X2,X5,X6) ) ).

cnf(i_0_1919,axiom,
    ( X1 != X2
    | esk37_5(X3,X4,X5,X1,X6) = esk37_5(X3,X4,X5,X2,X6) ) ).

cnf(i_0_1920,axiom,
    ( X1 != X2
    | esk37_5(X3,X4,X5,X6,X1) = esk37_5(X3,X4,X5,X6,X2) ) ).

cnf(i_0_1921,axiom,
    ( X1 != X2
    | esk36_4(X1,X3,X4,X5) = esk36_4(X2,X3,X4,X5) ) ).

cnf(i_0_1922,axiom,
    ( X1 != X2
    | esk36_4(X3,X1,X4,X5) = esk36_4(X3,X2,X4,X5) ) ).

cnf(i_0_1923,axiom,
    ( X1 != X2
    | esk36_4(X3,X4,X1,X5) = esk36_4(X3,X4,X2,X5) ) ).

cnf(i_0_1924,axiom,
    ( X1 != X2
    | esk36_4(X3,X4,X5,X1) = esk36_4(X3,X4,X5,X2) ) ).

cnf(i_0_1925,axiom,
    ( X1 != X2
    | esk34_3(X1,X3,X4) = esk34_3(X2,X3,X4) ) ).

cnf(i_0_1926,axiom,
    ( X1 != X2
    | esk34_3(X3,X1,X4) = esk34_3(X3,X2,X4) ) ).

cnf(i_0_1927,axiom,
    ( X1 != X2
    | esk34_3(X3,X4,X1) = esk34_3(X3,X4,X2) ) ).

cnf(i_0_1928,axiom,
    ( X1 != X2
    | esk26_4(X1,X3,X4,X5) = esk26_4(X2,X3,X4,X5) ) ).

cnf(i_0_1929,axiom,
    ( X1 != X2
    | esk26_4(X3,X1,X4,X5) = esk26_4(X3,X2,X4,X5) ) ).

cnf(i_0_1930,axiom,
    ( X1 != X2
    | esk26_4(X3,X4,X1,X5) = esk26_4(X3,X4,X2,X5) ) ).

cnf(i_0_1931,axiom,
    ( X1 != X2
    | esk26_4(X3,X4,X5,X1) = esk26_4(X3,X4,X5,X2) ) ).

cnf(i_0_1932,axiom,
    ( X1 != X2
    | esk25_4(X1,X3,X4,X5) = esk25_4(X2,X3,X4,X5) ) ).

cnf(i_0_1933,axiom,
    ( X1 != X2
    | esk25_4(X3,X1,X4,X5) = esk25_4(X3,X2,X4,X5) ) ).

cnf(i_0_1934,axiom,
    ( X1 != X2
    | esk25_4(X3,X4,X1,X5) = esk25_4(X3,X4,X2,X5) ) ).

cnf(i_0_1935,axiom,
    ( X1 != X2
    | esk25_4(X3,X4,X5,X1) = esk25_4(X3,X4,X5,X2) ) ).

cnf(i_0_1936,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastLessThan(X1,X3,X4) = c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X4) ) ).

cnf(i_0_1937,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastLessThan(X3,X1,X4) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X2,X4) ) ).

cnf(i_0_1938,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X2) ) ).

cnf(i_0_1939,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__case(X1,X3,X4,X5) = c_Nat_Onat_Onat__case(X2,X3,X4,X5) ) ).

cnf(i_0_1940,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__case(X3,X1,X4,X5) = c_Nat_Onat_Onat__case(X3,X2,X4,X5) ) ).

cnf(i_0_1941,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__case(X3,X4,X1,X5) = c_Nat_Onat_Onat__case(X3,X4,X2,X5) ) ).

cnf(i_0_1942,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__case(X3,X4,X5,X1) = c_Nat_Onat_Onat__case(X3,X4,X5,X2) ) ).

cnf(i_0_1943,axiom,
    ( X1 != X2
    | c_Sum__Type_OPlus(X1,X3,X4,X5) = c_Sum__Type_OPlus(X2,X3,X4,X5) ) ).

cnf(i_0_1944,axiom,
    ( X1 != X2
    | c_Sum__Type_OPlus(X3,X1,X4,X5) = c_Sum__Type_OPlus(X3,X2,X4,X5) ) ).

cnf(i_0_1945,axiom,
    ( X1 != X2
    | c_Sum__Type_OPlus(X3,X4,X1,X5) = c_Sum__Type_OPlus(X3,X4,X2,X5) ) ).

cnf(i_0_1946,axiom,
    ( X1 != X2
    | c_Sum__Type_OPlus(X3,X4,X5,X1) = c_Sum__Type_OPlus(X3,X4,X5,X2) ) ).

cnf(i_0_1947,axiom,
    ( X1 != X2
    | c_Nat_Osize__class_Osize(X1,X3) = c_Nat_Osize__class_Osize(X2,X3) ) ).

cnf(i_0_1948,axiom,
    ( X1 != X2
    | c_Nat_Osize__class_Osize(X3,X1) = c_Nat_Osize__class_Osize(X3,X2) ) ).

cnf(i_0_1949,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__size(X1) = c_Nat_Onat_Onat__size(X2) ) ).

cnf(i_0_1950,axiom,
    ( X1 != X2
    | ~ c_Arrow__Order__Mirabelle_Ounanimity(X1)
    | c_Arrow__Order__Mirabelle_Ounanimity(X2) ) ).

cnf(i_0_1951,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__idom(X1)
    | class_Rings_Olinordered__idom(X2) ) ).

cnf(i_0_1952,axiom,
    ( X1 != X2
    | ~ c_FunDef_Oin__rel(X1,X3,X4,X5,X6)
    | c_FunDef_Oin__rel(X2,X3,X4,X5,X6) ) ).

cnf(i_0_1953,axiom,
    ( X1 != X2
    | ~ c_FunDef_Oin__rel(X3,X1,X4,X5,X6)
    | c_FunDef_Oin__rel(X3,X2,X4,X5,X6) ) ).

cnf(i_0_1954,axiom,
    ( X1 != X2
    | ~ c_FunDef_Oin__rel(X3,X4,X1,X5,X6)
    | c_FunDef_Oin__rel(X3,X4,X2,X5,X6) ) ).

cnf(i_0_1955,axiom,
    ( X1 != X2
    | ~ c_FunDef_Oin__rel(X3,X4,X5,X1,X6)
    | c_FunDef_Oin__rel(X3,X4,X5,X2,X6) ) ).

cnf(i_0_1956,axiom,
    ( X1 != X2
    | ~ c_FunDef_Oin__rel(X3,X4,X5,X6,X1)
    | c_FunDef_Oin__rel(X3,X4,X5,X6,X2) ) ).

cnf(i_0_1957,axiom,
    ( X1 != X2
    | ~ class_Orderings_Olinorder(X1)
    | class_Orderings_Olinorder(X2) ) ).

cnf(i_0_1958,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | class_Groups_Oordered__ab__semigroup__add__imp__le(X2) ) ).

cnf(i_0_1959,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
    | class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).

cnf(i_0_1960,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__semigroup__add(X1)
    | class_Groups_Oordered__ab__semigroup__add(X2) ) ).

cnf(i_0_1961,axiom,
    ( X1 != X2
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | class_Groups_Olinordered__ab__group__add(X2) ) ).

cnf(i_0_1962,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | class_Groups_Oordered__comm__monoid__add(X2) ) ).

cnf(i_0_1963,axiom,
    ( X1 != X2
    | ~ class_Rings_Oring__1(X1)
    | class_Rings_Oring__1(X2) ) ).

cnf(i_0_1964,axiom,
    ( X1 != X2
    | ~ hBOOL(X1)
    | hBOOL(X2) ) ).

cnf(i_0_1965,axiom,
    ( X1 != X2
    | ~ class_Rings_Ocomm__semiring__1(X1)
    | class_Rings_Ocomm__semiring__1(X2) ) ).

cnf(i_0_1966,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semidom(X1)
    | class_Rings_Olinordered__semidom(X2) ) ).

cnf(i_0_1967,axiom,
    ( X1 != X2
    | ~ class_Int_Oring__char__0(X1)
    | class_Int_Oring__char__0(X2) ) ).

cnf(i_0_1968,axiom,
    ( X1 != X2
    | ~ class_Orderings_Opreorder(X1)
    | class_Orderings_Opreorder(X2) ) ).

cnf(i_0_1969,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oorder(X1)
    | class_Orderings_Oorder(X2) ) ).

cnf(i_0_1970,axiom,
    ( X1 != X2
    | ~ class_Groups_Oab__semigroup__add(X1)
    | class_Groups_Oab__semigroup__add(X2) ) ).

cnf(i_0_1971,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocancel__semigroup__add(X1)
    | class_Groups_Ocancel__semigroup__add(X2) ) ).

cnf(i_0_1972,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocancel__ab__semigroup__add(X1)
    | class_Groups_Ocancel__ab__semigroup__add(X2) ) ).

cnf(i_0_1973,axiom,
    ( X1 != X2
    | ~ class_Orderings_Otop(X1)
    | class_Orderings_Otop(X2) ) ).

cnf(i_0_1974,axiom,
    ( X1 != X2
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ).

cnf(i_0_1975,axiom,
    ( X1 != X2
    | ~ c_Arrow__Order__Mirabelle_OIIA(X1)
    | c_Arrow__Order__Mirabelle_OIIA(X2) ) ).

cnf(i_0_1976,axiom,
    ( X1 != X2
    | ~ class_Finite__Set_Ofinite(X1)
    | class_Finite__Set_Ofinite(X2) ) ).

cnf(i_0_1977,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | class_Groups_Ocomm__monoid__add(X2) ) ).

cnf(i_0_1978,axiom,
    ( X1 != X2
    | ~ class_Groups_Omonoid__add(X1)
    | class_Groups_Omonoid__add(X2) ) ).

cnf(i_0_1979,axiom,
    ( X1 != X2
    | ~ class_Rings_Ozero__neq__one(X1)
    | class_Rings_Ozero__neq__one(X2) ) ).

cnf(i_0_1980,axiom,
    ( X1 != X2
    | ~ class_Groups_Ozero(X1)
    | class_Groups_Ozero(X2) ) ).

cnf(i_0_1981,axiom,
    ( X1 != X2
    | ~ class_Groups_Oone(X1)
    | class_Groups_Oone(X2) ) ).

cnf(i_0_1982,axiom,
    ( X1 != X2
    | ~ c_Arrow__Order__Mirabelle_Odictator(X1,X3)
    | c_Arrow__Order__Mirabelle_Odictator(X2,X3) ) ).

cnf(i_0_1983,axiom,
    ( X1 != X2
    | ~ c_Arrow__Order__Mirabelle_Odictator(X3,X1)
    | c_Arrow__Order__Mirabelle_Odictator(X3,X2) ) ).

cnf(i_0_1984,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_1985,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_1986,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_1987,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_1988,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_1989,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_1990,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofinite(X1,X3)
    | c_Finite__Set_Ofinite(X2,X3) ) ).

cnf(i_0_1991,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofinite(X3,X1)
    | c_Finite__Set_Ofinite(X3,X2) ) ).

cnf(i_0_1992,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oord(X1)
    | class_Orderings_Oord(X2) ) ).

cnf(i_0_1993,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image__simple__idem(X1,X3,X4,X5,X6,X7)
    | c_Finite__Set_Ofolding__image__simple__idem(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_1994,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image__simple__idem(X3,X1,X4,X5,X6,X7)
    | c_Finite__Set_Ofolding__image__simple__idem(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_1995,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X1,X5,X6,X7)
    | c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_1996,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X5,X1,X6,X7)
    | c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_1997,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X5,X6,X1,X7)
    | c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_1998,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X5,X6,X7,X1)
    | c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_1999,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X1,X3,X4,X5)
    | c_Fun_Oinj__on(X2,X3,X4,X5) ) ).

cnf(i_0_2000,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X1,X4,X5)
    | c_Fun_Oinj__on(X3,X2,X4,X5) ) ).

cnf(i_0_2001,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X4,X1,X5)
    | c_Fun_Oinj__on(X3,X4,X2,X5) ) ).

cnf(i_0_2002,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X4,X5,X1)
    | c_Fun_Oinj__on(X3,X4,X5,X2) ) ).

cnf(i_0_1883_001,axiom,
    X1 = X1 ).

cnf(i_0_1884_002,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_1885_003,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_1886_004,axiom,
    ( X1 != X2
    | hAPP(X1,X3) = hAPP(X2,X3) ) ).

cnf(i_0_1887_005,axiom,
    ( X1 != X2
    | hAPP(X3,X1) = hAPP(X3,X2) ) ).

cnf(i_0_1888_006,axiom,
    ( X1 != X2
    | c_Groups_Oone__class_Oone(X1) = c_Groups_Oone__class_Oone(X2) ) ).

cnf(i_0_1889_007,axiom,
    ( X1 != X2
    | c_Orderings_Oord__class_Oless__eq(X1,X3) = c_Orderings_Oord__class_Oless__eq(X2,X3) ) ).

cnf(i_0_1890_008,axiom,
    ( X1 != X2
    | c_Orderings_Oord__class_Oless__eq(X3,X1) = c_Orderings_Oord__class_Oless__eq(X3,X2) ) ).

cnf(i_0_1891_009,axiom,
    ( X1 != X2
    | c_FuncSet_OPi(X1,X3,X4,X5) = c_FuncSet_OPi(X2,X3,X4,X5) ) ).

cnf(i_0_1892_010,axiom,
    ( X1 != X2
    | c_FuncSet_OPi(X3,X1,X4,X5) = c_FuncSet_OPi(X3,X2,X4,X5) ) ).

cnf(i_0_1893_011,axiom,
    ( X1 != X2
    | c_FuncSet_OPi(X3,X4,X1,X5) = c_FuncSet_OPi(X3,X4,X2,X5) ) ).

cnf(i_0_1894_012,axiom,
    ( X1 != X2
    | c_FuncSet_OPi(X3,X4,X5,X1) = c_FuncSet_OPi(X3,X4,X5,X2) ) ).

cnf(i_0_1895_013,axiom,
    ( X1 != X2
    | esk23_2(X1,X3) = esk23_2(X2,X3) ) ).

cnf(i_0_1896_014,axiom,
    ( X1 != X2
    | esk23_2(X3,X1) = esk23_2(X3,X2) ) ).

cnf(i_0_1897_015,axiom,
    ( X1 != X2
    | esk24_2(X1,X3) = esk24_2(X2,X3) ) ).

cnf(i_0_1898_016,axiom,
    ( X1 != X2
    | esk24_2(X3,X1) = esk24_2(X3,X2) ) ).

cnf(i_0_1899_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_1900_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_1901_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_1902_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_1903_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_1904_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_1905_023,axiom,
    ( X1 != X2
    | c_Set_Oimage(X1,X3,X4,X5) = c_Set_Oimage(X2,X3,X4,X5) ) ).

cnf(i_0_1906_024,axiom,
    ( X1 != X2
    | c_Set_Oimage(X3,X1,X4,X5) = c_Set_Oimage(X3,X2,X4,X5) ) ).

cnf(i_0_1907_025,axiom,
    ( X1 != X2
    | c_Set_Oimage(X3,X4,X1,X5) = c_Set_Oimage(X3,X4,X2,X5) ) ).

cnf(i_0_1908_026,axiom,
    ( X1 != X2
    | c_Set_Oimage(X3,X4,X5,X1) = c_Set_Oimage(X3,X4,X5,X2) ) ).

cnf(i_0_1909_027,axiom,
    ( X1 != X2
    | c_Set_Oinsert(X1,X3,X4) = c_Set_Oinsert(X2,X3,X4) ) ).

cnf(i_0_1910_028,axiom,
    ( X1 != X2
    | c_Set_Oinsert(X3,X1,X4) = c_Set_Oinsert(X3,X2,X4) ) ).

cnf(i_0_1911_029,axiom,
    ( X1 != X2
    | c_Set_Oinsert(X3,X4,X1) = c_Set_Oinsert(X3,X4,X2) ) ).

cnf(i_0_1912_030,axiom,
    ( X1 != X2
    | c_Finite__Set_Ocard(X1,X3) = c_Finite__Set_Ocard(X2,X3) ) ).

cnf(i_0_1913_031,axiom,
    ( X1 != X2
    | c_Finite__Set_Ocard(X3,X1) = c_Finite__Set_Ocard(X3,X2) ) ).

cnf(i_0_1914_032,axiom,
    ( X1 != X2
    | c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).

cnf(i_0_1915_033,axiom,
    ( X1 != X2
    | c_Orderings_Otop__class_Otop(X1) = c_Orderings_Otop__class_Otop(X2) ) ).

cnf(i_0_1916_034,axiom,
    ( X1 != X2
    | esk37_5(X1,X3,X4,X5,X6) = esk37_5(X2,X3,X4,X5,X6) ) ).

cnf(i_0_1917_035,axiom,
    ( X1 != X2
    | esk37_5(X3,X1,X4,X5,X6) = esk37_5(X3,X2,X4,X5,X6) ) ).

cnf(i_0_1918_036,axiom,
    ( X1 != X2
    | esk37_5(X3,X4,X1,X5,X6) = esk37_5(X3,X4,X2,X5,X6) ) ).

cnf(i_0_1919_037,axiom,
    ( X1 != X2
    | esk37_5(X3,X4,X5,X1,X6) = esk37_5(X3,X4,X5,X2,X6) ) ).

cnf(i_0_1920_038,axiom,
    ( X1 != X2
    | esk37_5(X3,X4,X5,X6,X1) = esk37_5(X3,X4,X5,X6,X2) ) ).

cnf(i_0_1921_039,axiom,
    ( X1 != X2
    | esk36_4(X1,X3,X4,X5) = esk36_4(X2,X3,X4,X5) ) ).

cnf(i_0_1922_040,axiom,
    ( X1 != X2
    | esk36_4(X3,X1,X4,X5) = esk36_4(X3,X2,X4,X5) ) ).

cnf(i_0_1923_041,axiom,
    ( X1 != X2
    | esk36_4(X3,X4,X1,X5) = esk36_4(X3,X4,X2,X5) ) ).

cnf(i_0_1924_042,axiom,
    ( X1 != X2
    | esk36_4(X3,X4,X5,X1) = esk36_4(X3,X4,X5,X2) ) ).

cnf(i_0_1925_043,axiom,
    ( X1 != X2
    | esk34_3(X1,X3,X4) = esk34_3(X2,X3,X4) ) ).

cnf(i_0_1926_044,axiom,
    ( X1 != X2
    | esk34_3(X3,X1,X4) = esk34_3(X3,X2,X4) ) ).

cnf(i_0_1927_045,axiom,
    ( X1 != X2
    | esk34_3(X3,X4,X1) = esk34_3(X3,X4,X2) ) ).

cnf(i_0_1928_046,axiom,
    ( X1 != X2
    | esk26_4(X1,X3,X4,X5) = esk26_4(X2,X3,X4,X5) ) ).

cnf(i_0_1929_047,axiom,
    ( X1 != X2
    | esk26_4(X3,X1,X4,X5) = esk26_4(X3,X2,X4,X5) ) ).

cnf(i_0_1930_048,axiom,
    ( X1 != X2
    | esk26_4(X3,X4,X1,X5) = esk26_4(X3,X4,X2,X5) ) ).

cnf(i_0_1931_049,axiom,
    ( X1 != X2
    | esk26_4(X3,X4,X5,X1) = esk26_4(X3,X4,X5,X2) ) ).

cnf(i_0_1932_050,axiom,
    ( X1 != X2
    | esk25_4(X1,X3,X4,X5) = esk25_4(X2,X3,X4,X5) ) ).

cnf(i_0_1933_051,axiom,
    ( X1 != X2
    | esk25_4(X3,X1,X4,X5) = esk25_4(X3,X2,X4,X5) ) ).

cnf(i_0_1934_052,axiom,
    ( X1 != X2
    | esk25_4(X3,X4,X1,X5) = esk25_4(X3,X4,X2,X5) ) ).

cnf(i_0_1935_053,axiom,
    ( X1 != X2
    | esk25_4(X3,X4,X5,X1) = esk25_4(X3,X4,X5,X2) ) ).

cnf(i_0_1936_054,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastLessThan(X1,X3,X4) = c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X4) ) ).

cnf(i_0_1937_055,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastLessThan(X3,X1,X4) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X2,X4) ) ).

cnf(i_0_1938_056,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X2) ) ).

cnf(i_0_1939_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_1940_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_1941_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_1942_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_1943_061,axiom,
    ( X1 != X2
    | c_Sum__Type_OPlus(X1,X3,X4,X5) = c_Sum__Type_OPlus(X2,X3,X4,X5) ) ).

cnf(i_0_1944_062,axiom,
    ( X1 != X2
    | c_Sum__Type_OPlus(X3,X1,X4,X5) = c_Sum__Type_OPlus(X3,X2,X4,X5) ) ).

cnf(i_0_1945_063,axiom,
    ( X1 != X2
    | c_Sum__Type_OPlus(X3,X4,X1,X5) = c_Sum__Type_OPlus(X3,X4,X2,X5) ) ).

cnf(i_0_1946_064,axiom,
    ( X1 != X2
    | c_Sum__Type_OPlus(X3,X4,X5,X1) = c_Sum__Type_OPlus(X3,X4,X5,X2) ) ).

cnf(i_0_1947_065,axiom,
    ( X1 != X2
    | c_Nat_Osize__class_Osize(X1,X3) = c_Nat_Osize__class_Osize(X2,X3) ) ).

cnf(i_0_1948_066,axiom,
    ( X1 != X2
    | c_Nat_Osize__class_Osize(X3,X1) = c_Nat_Osize__class_Osize(X3,X2) ) ).

cnf(i_0_1949_067,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__size(X1) = c_Nat_Onat_Onat__size(X2) ) ).

cnf(i_0_1950_068,axiom,
    ( X1 != X2
    | ~ c_Arrow__Order__Mirabelle_Ounanimity(X1)
    | c_Arrow__Order__Mirabelle_Ounanimity(X2) ) ).

cnf(i_0_1951_069,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__idom(X1)
    | class_Rings_Olinordered__idom(X2) ) ).

cnf(i_0_1952_070,axiom,
    ( X1 != X2
    | ~ c_FunDef_Oin__rel(X1,X3,X4,X5,X6)
    | c_FunDef_Oin__rel(X2,X3,X4,X5,X6) ) ).

cnf(i_0_1953_071,axiom,
    ( X1 != X2
    | ~ c_FunDef_Oin__rel(X3,X1,X4,X5,X6)
    | c_FunDef_Oin__rel(X3,X2,X4,X5,X6) ) ).

cnf(i_0_1954_072,axiom,
    ( X1 != X2
    | ~ c_FunDef_Oin__rel(X3,X4,X1,X5,X6)
    | c_FunDef_Oin__rel(X3,X4,X2,X5,X6) ) ).

cnf(i_0_1955_073,axiom,
    ( X1 != X2
    | ~ c_FunDef_Oin__rel(X3,X4,X5,X1,X6)
    | c_FunDef_Oin__rel(X3,X4,X5,X2,X6) ) ).

cnf(i_0_1956_074,axiom,
    ( X1 != X2
    | ~ c_FunDef_Oin__rel(X3,X4,X5,X6,X1)
    | c_FunDef_Oin__rel(X3,X4,X5,X6,X2) ) ).

cnf(i_0_1957_075,axiom,
    ( X1 != X2
    | ~ class_Orderings_Olinorder(X1)
    | class_Orderings_Olinorder(X2) ) ).

cnf(i_0_1958_076,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | class_Groups_Oordered__ab__semigroup__add__imp__le(X2) ) ).

cnf(i_0_1959_077,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
    | class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).

cnf(i_0_1960_078,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__semigroup__add(X1)
    | class_Groups_Oordered__ab__semigroup__add(X2) ) ).

cnf(i_0_1961_079,axiom,
    ( X1 != X2
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | class_Groups_Olinordered__ab__group__add(X2) ) ).

cnf(i_0_1962_080,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | class_Groups_Oordered__comm__monoid__add(X2) ) ).

cnf(i_0_1963_081,axiom,
    ( X1 != X2
    | ~ class_Rings_Oring__1(X1)
    | class_Rings_Oring__1(X2) ) ).

cnf(i_0_1964_082,axiom,
    ( X1 != X2
    | ~ hBOOL(X1)
    | hBOOL(X2) ) ).

cnf(i_0_1965_083,axiom,
    ( X1 != X2
    | ~ class_Rings_Ocomm__semiring__1(X1)
    | class_Rings_Ocomm__semiring__1(X2) ) ).

cnf(i_0_1966_084,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semidom(X1)
    | class_Rings_Olinordered__semidom(X2) ) ).

cnf(i_0_1967_085,axiom,
    ( X1 != X2
    | ~ class_Int_Oring__char__0(X1)
    | class_Int_Oring__char__0(X2) ) ).

cnf(i_0_1968_086,axiom,
    ( X1 != X2
    | ~ class_Orderings_Opreorder(X1)
    | class_Orderings_Opreorder(X2) ) ).

cnf(i_0_1969_087,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oorder(X1)
    | class_Orderings_Oorder(X2) ) ).

cnf(i_0_1970_088,axiom,
    ( X1 != X2
    | ~ class_Groups_Oab__semigroup__add(X1)
    | class_Groups_Oab__semigroup__add(X2) ) ).

cnf(i_0_1971_089,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocancel__semigroup__add(X1)
    | class_Groups_Ocancel__semigroup__add(X2) ) ).

cnf(i_0_1972_090,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocancel__ab__semigroup__add(X1)
    | class_Groups_Ocancel__ab__semigroup__add(X2) ) ).

cnf(i_0_1973_091,axiom,
    ( X1 != X2
    | ~ class_Orderings_Otop(X1)
    | class_Orderings_Otop(X2) ) ).

cnf(i_0_1974_092,axiom,
    ( X1 != X2
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ).

cnf(i_0_1975_093,axiom,
    ( X1 != X2
    | ~ c_Arrow__Order__Mirabelle_OIIA(X1)
    | c_Arrow__Order__Mirabelle_OIIA(X2) ) ).

cnf(i_0_1976_094,axiom,
    ( X1 != X2
    | ~ class_Finite__Set_Ofinite(X1)
    | class_Finite__Set_Ofinite(X2) ) ).

cnf(i_0_1977_095,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | class_Groups_Ocomm__monoid__add(X2) ) ).

cnf(i_0_1978_096,axiom,
    ( X1 != X2
    | ~ class_Groups_Omonoid__add(X1)
    | class_Groups_Omonoid__add(X2) ) ).

cnf(i_0_1979_097,axiom,
    ( X1 != X2
    | ~ class_Rings_Ozero__neq__one(X1)
    | class_Rings_Ozero__neq__one(X2) ) ).

cnf(i_0_1980_098,axiom,
    ( X1 != X2
    | ~ class_Groups_Ozero(X1)
    | class_Groups_Ozero(X2) ) ).

cnf(i_0_1981_099,axiom,
    ( X1 != X2
    | ~ class_Groups_Oone(X1)
    | class_Groups_Oone(X2) ) ).

cnf(i_0_1982_100,axiom,
    ( X1 != X2
    | ~ c_Arrow__Order__Mirabelle_Odictator(X1,X3)
    | c_Arrow__Order__Mirabelle_Odictator(X2,X3) ) ).

cnf(i_0_1983_101,axiom,
    ( X1 != X2
    | ~ c_Arrow__Order__Mirabelle_Odictator(X3,X1)
    | c_Arrow__Order__Mirabelle_Odictator(X3,X2) ) ).

cnf(i_0_1984_102,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_1985_103,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_1986_104,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_1987_105,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_1988_106,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_1989_107,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_1990_108,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofinite(X1,X3)
    | c_Finite__Set_Ofinite(X2,X3) ) ).

cnf(i_0_1991_109,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofinite(X3,X1)
    | c_Finite__Set_Ofinite(X3,X2) ) ).

cnf(i_0_1992_110,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oord(X1)
    | class_Orderings_Oord(X2) ) ).

cnf(i_0_1993_111,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image__simple__idem(X1,X3,X4,X5,X6,X7)
    | c_Finite__Set_Ofolding__image__simple__idem(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_1994_112,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image__simple__idem(X3,X1,X4,X5,X6,X7)
    | c_Finite__Set_Ofolding__image__simple__idem(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_1995_113,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X1,X5,X6,X7)
    | c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_1996_114,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X5,X1,X6,X7)
    | c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_1997_115,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X5,X6,X1,X7)
    | c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_1998_116,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X5,X6,X7,X1)
    | c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_1999_117,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X1,X3,X4,X5)
    | c_Fun_Oinj__on(X2,X3,X4,X5) ) ).

cnf(i_0_2000_118,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X1,X4,X5)
    | c_Fun_Oinj__on(X3,X2,X4,X5) ) ).

cnf(i_0_2001_119,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X4,X1,X5)
    | c_Fun_Oinj__on(X3,X4,X2,X5) ) ).

cnf(i_0_2002_120,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X4,X5,X1)
    | c_Fun_Oinj__on(X3,X4,X5,X2) ) ).

cnf(i_0_2003,plain,
    X1 = X1,
    inference(equality_inference,[],[1130]) ).

cnf(i_0_2004,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,[],[1162]) ).

cnf(i_0_2005,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,[],[1196]) ).

cnf(i_0_2006,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,[],[1197]) ).

cnf(i_0_2007,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,[],[1198]) ).

cnf(i_0_2008,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,[],[1202]) ).

cnf(i_0_2009,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,[],[1203]) ).

cnf(i_0_2010,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,[],[1223]) ).

cnf(i_0_2011,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,[],[1225]) ).

cnf(i_0_2012,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,[],[1234]) ).

cnf(i_0_2013,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,[],[1235]) ).

cnf(i_0_2014,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,[],[1237]) ).

cnf(i_0_2015,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,[],[1238]) ).

cnf(i_0_2016,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,[],[1241]) ).

cnf(i_0_2017,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,[],[1249]) ).

cnf(i_0_2018,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,[],[1250]) ).

cnf(i_0_2019,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,[],[1252]) ).

cnf(i_0_2020,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,[],[1268]) ).

cnf(i_0_2021,plain,
    ( X1 = esk36_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,[],[1274]) ).

cnf(i_0_2022,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,[],[1277]) ).

cnf(i_0_2023,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,[],[1291]) ).

cnf(i_0_2024,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,[],[1312]) ).

cnf(i_0_2025,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,[],[1321]) ).

cnf(i_0_2026,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,[],[1322]) ).

cnf(i_0_2027,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,[],[1334]) ).

cnf(i_0_2028,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,[],[1340]) ).

cnf(i_0_2029,plain,
    ( X1 = X1
    | ~ c_Fun_Oinj__on(X2,X3,X4,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
    inference(equality_inference,[],[1343]) ).

cnf(i_0_2030,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,[],[1358]) ).

cnf(i_0_2031,plain,
    X1 = X1,
    inference(equality_inference,[],[1359]) ).

cnf(i_0_2032,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,[],[1362]) ).

cnf(i_0_2033,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,[],[1370]) ).

cnf(i_0_2034,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,[],[1371]) ).

cnf(i_0_2035,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,[],[1428]) ).

cnf(i_0_2036,plain,
    ( X1 = X1
    | ~ c_Fun_Oinj__on(X2,X3,X4,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
    inference(equality_inference,[],[1496]) ).

cnf(i_0_2037,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,[],[1499]) ).

cnf(i_0_2038,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,[],[1500]) ).

cnf(i_0_2039,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X2)),
    inference(equality_inference,[],[1512]) ).

cnf(i_0_2040,plain,
    ( X1 = X1
    | hBOOL(hAPP(hAPP(c_member(X2),X3),X1))
    | hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) ),
    inference(equality_inference,[],[1544]) ).

cnf(i_0_2041,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X2,X3))),
    inference(equality_inference,[],[1582]) ).

cnf(i_0_2042,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,[],[1597]) ).

cnf(i_0_2043,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,[],[1634]) ).

cnf(i_0_2044,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,[],[1635]) ).

cnf(i_0_2045,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,[],[1636]) ).

cnf(i_0_2046,plain,
    hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X2)),
    inference(equality_inference,[],[1647]) ).

cnf(i_0_2047,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,[],[1691]) ).

cnf(i_0_2048,plain,
    ( ~ class_Orderings_Oorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
    inference(equality_inference,[],[1706]) ).

cnf(i_0_2049,plain,
    ( ~ class_Orderings_Oorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
    inference(equality_inference,[],[1708]) ).

cnf(i_0_2050,plain,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
    inference(equality_inference,[],[1709]) ).

cnf(i_0_2051,plain,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
    inference(equality_inference,[],[1710]) ).

cnf(i_0_2052,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
    inference(equality_inference,[],[1716]) ).

cnf(i_0_2053,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
    inference(equality_inference,[],[1717]) ).

cnf(i_0_2054,plain,
    ( ~ class_Groups_Ocancel__semigroup__add(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[1722]) ).

cnf(i_0_2055,plain,
    ( X1 = X1
    | ~ class_Groups_Ocancel__ab__semigroup__add(X2) ),
    inference(equality_inference,[],[1723]) ).

cnf(i_0_2056,plain,
    ( ~ class_Groups_Ocancel__semigroup__add(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[1725]) ).

cnf(i_0_2057,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))),
    inference(equality_inference,[],[1735]) ).

cnf(i_0_2058,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(equality_inference,[],[1737]) ).

cnf(i_0_2059,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
    inference(equality_inference,[],[1742]) ).

cnf(i_0_2060,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
    inference(equality_inference,[],[1744]) ).

cnf(i_0_2061,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,[],[1745]) ).

cnf(i_0_2062,plain,
    X1 = X1,
    inference(equality_inference,[],[1751]) ).

cnf(i_0_2063,plain,
    X1 = X1,
    inference(equality_inference,[],[1752]) ).

cnf(i_0_2064,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,[],[1753]) ).

cnf(i_0_2065,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
    inference(equality_inference,[],[1756]) ).

cnf(i_0_2066,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,[],[1764]) ).

cnf(i_0_2067,plain,
    X1 = X1,
    inference(equality_inference,[],[1765]) ).

cnf(i_0_2068,plain,
    ( ~ class_Orderings_Oorder(X1)
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X2)) ),
    inference(equality_inference,[],[1788]) ).

cnf(i_0_2069,plain,
    ( ~ class_Orderings_Opreorder(X1)
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X2)) ),
    inference(equality_inference,[],[1789]) ).

cnf(i_0_2070,plain,
    ( ~ class_Orderings_Oorder(X1)
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X2)) ),
    inference(equality_inference,[],[1790]) ).

cnf(i_0_2071,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
    inference(equality_inference,[],[1802]) ).

cnf(i_0_2072,plain,
    hBOOL(hAPP(hAPP(c_fequal,X1),X1)),
    inference(equality_inference,[],[1803]) ).

cnf(i_0_2073,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,[],[1810]) ).

cnf(i_0_2074,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,[],[1811]) ).

cnf(i_0_2075,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,[],[1812]) ).

cnf(i_0_2076,plain,
    X1 = X1,
    inference(equality_inference,[],[1828]) ).

cnf(i_0_2077,plain,
    ( v_c____ = v_e____
    | epred1_0 ),
    inference(scs_inference,[],[i_0_1882,i_0_1115,i_0_1119,i_0_1056]) ).

cnf(i_0_2078,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(scs_inference,[],[i_0_1118,i_0_1057]) ).

cnf(i_0_2079,plain,
    ( hAPP(v_h____,esk45_0) != v_n____
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_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_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(scs_inference,[],[i_0_1118,i_0_1407,i_0_1092]) ).

cnf(i_0_2080,plain,
    ( hAPP(v_h____,esk45_0) != v_n____
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_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_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(scs_inference,[],[i_0_1118,i_0_1407,i_0_1100]) ).

cnf(i_0_2081,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_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_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(scs_inference,[],[i_0_1118,i_0_1407,i_0_1102]) ).

cnf(i_0_2082,plain,
    ( hAPP(v_h____,esk45_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_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_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_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(scs_inference,[],[i_0_1333,i_0_1118,i_0_1107]) ).

cnf(i_0_2083,plain,
    ( hAPP(v_h____,esk45_0) = v_n____
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),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____,esk45_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_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(scs_inference,[],[i_0_1333,i_0_2026,i_0_1118,i_0_1111]) ).

cnf(i_0_2084,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_1333,i_0_1189]) ).

cnf(i_0_2085,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_1333,i_0_1221]) ).

cnf(i_0_2086,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_1407,i_0_1231]) ).

cnf(i_0_2087,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_1407,i_0_1255]) ).

cnf(i_0_2088,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_1407,i_0_1257]) ).

cnf(i_0_2089,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_2025,i_0_1267]) ).

cnf(i_0_2090,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_1267]) ).

cnf(i_0_2091,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X3,c_Set_Oinsert(X1,X2,X4)))),
    inference(scs_inference,[],[i_0_2025,i_0_1543,i_0_1267,i_0_1369]) ).

cnf(i_0_2092,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_1543]) ).

cnf(i_0_2093,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_1369]) ).

cnf(i_0_2094,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_2025,i_0_1543,i_0_1329,i_0_1267,i_0_1369,i_0_1692]) ).

cnf(i_0_2095,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hBOOL(hAPP(X3,X2)) ),
    inference(rename_variables,[],[i_0_1692]) ).

cnf(i_0_2096,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_2025,i_0_1543,i_0_1329,i_0_1267,i_0_1369,i_0_1692,i_0_1736]) ).

cnf(i_0_2097,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(rename_variables,[],[i_0_1736]) ).

cnf(i_0_2098,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_2039,i_0_2025,i_0_1543,i_0_1329,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190]) ).

cnf(i_0_2099,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_1190]) ).

cnf(i_0_2100,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_2039,i_0_2025,i_0_1543,i_0_1329,i_0_1303,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192]) ).

cnf(i_0_2101,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_1192]) ).

cnf(i_0_2102,plain,
    c_Set_Oimage(X1,X2,X3,X4) = c_Set_Oimage(X1,X2,X3,esk35_5(X4,X3,X1,c_Set_Oimage(X1,X2,X3,X4),X2)),
    inference(scs_inference,[],[i_0_2039,i_0_2025,i_0_1543,i_0_1719,i_0_1329,i_0_1303,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208]) ).

cnf(i_0_2103,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
    inference(rename_variables,[],[i_0_1719]) ).

cnf(i_0_2104,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,esk35_5(X5,X4,X3,X2,X1)) ),
    inference(rename_variables,[],[i_0_1208]) ).

cnf(i_0_2105,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_2039,i_0_2025,i_0_1543,i_0_2092,i_0_1719,i_0_1329,i_0_1303,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232]) ).

cnf(i_0_2106,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_1232]) ).

cnf(i_0_2107,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_2039,i_0_2025,i_0_1543,i_0_2092,i_0_1719,i_0_1329,i_0_1303,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254]) ).

cnf(i_0_2108,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_1254]) ).

cnf(i_0_2109,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_2039,i_0_2025,i_0_2057,i_0_1543,i_0_2092,i_0_1719,i_0_1329,i_0_1303,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272]) ).

cnf(i_0_2110,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))),
    inference(rename_variables,[],[i_0_2057]) ).

cnf(i_0_2111,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_1272]) ).

cnf(i_0_2112,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_2039,i_0_2025,i_0_2057,i_0_1543,i_0_2092,i_0_1719,i_0_1329,i_0_1303,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275]) ).

cnf(i_0_2113,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_1275]) ).

cnf(i_0_2114,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_2039,i_0_2025,i_0_2057,i_0_1543,i_0_2092,i_0_1719,i_0_2103,i_0_1329,i_0_1303,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279]) ).

cnf(i_0_2115,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
    inference(rename_variables,[],[i_0_1719]) ).

cnf(i_0_2116,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_1279]) ).

cnf(i_0_2117,plain,
    hAPP(X1,X2) = hAPP(X1,esk38_4(c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)),X1,X3,hAPP(X1,X2))),
    inference(scs_inference,[],[i_0_2039,i_0_2025,i_0_2057,i_0_1543,i_0_2092,i_0_1719,i_0_2103,i_0_1329,i_0_1303,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296]) ).

cnf(i_0_2118,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oimage(X3,X1,X4,X5)))
    | X2 = hAPP(X4,esk38_4(X5,X4,X3,X2)) ),
    inference(rename_variables,[],[i_0_1296]) ).

cnf(i_0_2119,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_2039,i_0_2025,i_0_2057,i_0_1543,i_0_2092,i_0_1719,i_0_2103,i_0_1750,i_0_1329,i_0_1303,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306]) ).

cnf(i_0_2120,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
    inference(rename_variables,[],[i_0_1750]) ).

cnf(i_0_2121,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_1306]) ).

cnf(i_0_2122,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_2039,i_0_2025,i_0_2057,i_0_1543,i_0_2092,i_0_1719,i_0_2103,i_0_1750,i_0_1329,i_0_1303,i_0_1469,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309]) ).

cnf(i_0_2123,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_1309]) ).

cnf(i_0_2124,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_2039,i_0_2025,i_0_2057,i_0_1543,i_0_2092,i_0_1719,i_0_2103,i_0_1750,i_0_1329,i_0_1303,i_0_1469,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310]) ).

cnf(i_0_2125,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_1310]) ).

cnf(i_0_2126,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_2039,i_0_2025,i_0_2057,i_0_1543,i_0_2092,i_0_1719,i_0_2103,i_0_1750,i_0_1329,i_0_1303,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317]) ).

cnf(i_0_2127,plain,
    hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(rename_variables,[],[i_0_1837]) ).

cnf(i_0_2128,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_1317]) ).

cnf(i_0_2129,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_2039,i_0_2025,i_0_2057,i_0_1543,i_0_2092,i_0_1759,i_0_1719,i_0_2103,i_0_1750,i_0_1329,i_0_1303,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318]) ).

cnf(i_0_2130,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
    inference(rename_variables,[],[i_0_1759]) ).

cnf(i_0_2131,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_1318]) ).

cnf(i_0_2132,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_2039,i_0_2025,i_0_2057,i_0_1543,i_0_2092,i_0_1759,i_0_2130,i_0_1719,i_0_2103,i_0_1750,i_0_1329,i_0_1303,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324]) ).

cnf(i_0_2133,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
    inference(rename_variables,[],[i_0_1759]) ).

cnf(i_0_2134,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_1324]) ).

cnf(i_0_2135,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_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1543,i_0_2092,i_0_1759,i_0_2130,i_0_1719,i_0_2103,i_0_1750,i_0_1329,i_0_1303,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331]) ).

cnf(i_0_2136,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_1331]) ).

cnf(i_0_2137,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_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1543,i_0_2092,i_0_1759,i_0_2130,i_0_1719,i_0_2103,i_0_1750,i_0_1329,i_0_1303,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359]) ).

cnf(i_0_2138,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_1359]) ).

cnf(i_0_2139,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_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1543,i_0_2092,i_0_1759,i_0_2130,i_0_1719,i_0_2103,i_0_1750,i_0_1329,i_0_1303,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365]) ).

cnf(i_0_2140,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_1365]) ).

cnf(i_0_2141,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_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1543,i_0_2092,i_0_1759,i_0_2130,i_0_1719,i_0_2103,i_0_1750,i_0_1631,i_0_1329,i_0_1303,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380]) ).

cnf(i_0_2142,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_1380]) ).

cnf(i_0_2143,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_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1543,i_0_2092,i_0_1759,i_0_2130,i_0_1719,i_0_2103,i_0_1750,i_0_1631,i_0_1329,i_0_1303,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381]) ).

cnf(i_0_2144,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_1381]) ).

cnf(i_0_2145,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_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1543,i_0_2092,i_0_1759,i_0_2130,i_0_1719,i_0_2103,i_0_1750,i_0_1631,i_0_1329,i_0_1303,i_0_1503,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416]) ).

cnf(i_0_2146,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_1503]) ).

cnf(i_0_2147,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_1416]) ).

cnf(i_0_2148,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_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1543,i_0_2092,i_0_1805,i_0_1759,i_0_2130,i_0_1719,i_0_2103,i_0_1750,i_0_1631,i_0_1329,i_0_1303,i_0_1503,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418]) ).

cnf(i_0_2149,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
    inference(rename_variables,[],[i_0_1805]) ).

cnf(i_0_2150,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_1418]) ).

cnf(i_0_2151,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_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1543,i_0_2092,i_0_1805,i_0_1759,i_0_2130,i_0_1719,i_0_2103,i_0_1750,i_0_1631,i_0_1329,i_0_1642,i_0_1303,i_0_1503,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432]) ).

cnf(i_0_2152,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_1642]) ).

cnf(i_0_2153,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_1432]) ).

cnf(i_0_2154,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_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1543,i_0_2092,i_0_1805,i_0_1759,i_0_2130,i_0_1719,i_0_2103,i_0_1750,i_0_1631,i_0_1329,i_0_1642,i_0_2152,i_0_1303,i_0_1503,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433]) ).

cnf(i_0_2155,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_1642]) ).

cnf(i_0_2156,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_1433]) ).

cnf(i_0_2157,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_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1543,i_0_2092,i_0_1805,i_0_1759,i_0_2130,i_0_1719,i_0_2103,i_0_1750,i_0_1631,i_0_1329,i_0_1642,i_0_2152,i_0_1303,i_0_1503,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457]) ).

cnf(i_0_2158,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_1457]) ).

cnf(i_0_2159,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X3,hAPP(c_fequal,X2)))),
    inference(scs_inference,[],[i_0_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1543,i_0_2092,i_0_1805,i_0_1759,i_0_2130,i_0_1719,i_0_2103,i_0_1750,i_0_1631,i_0_1329,i_0_1642,i_0_2152,i_0_1303,i_0_1503,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506]) ).

cnf(i_0_2160,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_1506]) ).

cnf(i_0_2161,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_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1543,i_0_2092,i_0_1805,i_0_1759,i_0_2130,i_0_1733,i_0_1719,i_0_2103,i_0_1750,i_0_1631,i_0_1329,i_0_1642,i_0_2152,i_0_1303,i_0_1503,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514]) ).

cnf(i_0_2162,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_1514]) ).

cnf(i_0_2163,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_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1543,i_0_2092,i_0_1805,i_0_1759,i_0_2130,i_0_1733,i_0_1719,i_0_2103,i_0_1750,i_0_1631,i_0_1329,i_0_1642,i_0_2152,i_0_1303,i_0_1447,i_0_1503,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525]) ).

cnf(i_0_2164,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_1447]) ).

cnf(i_0_2165,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_1525]) ).

cnf(i_0_2166,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_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1543,i_0_2092,i_0_1805,i_0_1759,i_0_2130,i_0_1733,i_0_1719,i_0_2103,i_0_1750,i_0_1631,i_0_1329,i_0_1642,i_0_2152,i_0_1303,i_0_1447,i_0_2164,i_0_1503,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527]) ).

cnf(i_0_2167,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_1447]) ).

cnf(i_0_2168,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_1527]) ).

cnf(i_0_2169,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_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1543,i_0_2092,i_0_1805,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_1750,i_0_1631,i_0_1329,i_0_1642,i_0_2152,i_0_1303,i_0_1447,i_0_2164,i_0_1503,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545]) ).

cnf(i_0_2170,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
    inference(rename_variables,[],[i_0_1759]) ).

cnf(i_0_2171,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_1545]) ).

cnf(i_0_2172,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_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1543,i_0_2092,i_0_1805,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_1750,i_0_1631,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_1303,i_0_1447,i_0_2164,i_0_1503,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546]) ).

cnf(i_0_2173,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_1642]) ).

cnf(i_0_2174,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_1546]) ).

cnf(i_0_2175,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_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1543,i_0_2092,i_0_1805,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_1750,i_0_1631,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_1303,i_0_1447,i_0_2164,i_0_1503,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548]) ).

cnf(i_0_2176,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_1548]) ).

cnf(i_0_2177,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_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1543,i_0_2092,i_0_1805,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_1750,i_0_1631,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_1303,i_0_1447,i_0_2164,i_0_1503,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550]) ).

cnf(i_0_2178,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
    inference(rename_variables,[],[i_0_1631]) ).

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),X2),X3)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
    inference(rename_variables,[],[i_0_1550]) ).

cnf(i_0_2180,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_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1543,i_0_2092,i_0_1805,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_1750,i_0_1631,i_0_2178,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_1303,i_0_1447,i_0_2164,i_0_1503,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552]) ).

cnf(i_0_2181,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
    inference(rename_variables,[],[i_0_1631]) ).

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),X2),X3)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3)) ),
    inference(rename_variables,[],[i_0_1552]) ).

cnf(i_0_2183,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_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1543,i_0_2092,i_0_1805,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_1750,i_0_1631,i_0_2178,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_1591,i_0_1303,i_0_1447,i_0_2164,i_0_1503,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556]) ).

cnf(i_0_2184,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_1556]) ).

cnf(i_0_2185,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_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1543,i_0_2092,i_0_1805,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_1750,i_0_1631,i_0_2178,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1447,i_0_2164,i_0_1503,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560]) ).

cnf(i_0_2186,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_1642]) ).

cnf(i_0_2187,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_1560]) ).

cnf(i_0_2188,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X1))),
    inference(scs_inference,[],[i_0_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1543,i_0_2092,i_0_1805,i_0_2149,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_1750,i_0_1631,i_0_2178,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1447,i_0_2164,i_0_1503,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574]) ).

cnf(i_0_2189,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
    inference(rename_variables,[],[i_0_1805]) ).

cnf(i_0_2190,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_1574]) ).

cnf(i_0_2191,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_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1543,i_0_2092,i_0_1805,i_0_2149,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_1750,i_0_1631,i_0_2178,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1447,i_0_2164,i_0_1503,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576]) ).

cnf(i_0_2192,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_1576]) ).

cnf(i_0_2193,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_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1543,i_0_2092,i_0_1805,i_0_2149,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_1750,i_0_1631,i_0_2178,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1447,i_0_2164,i_0_1503,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605]) ).

cnf(i_0_2194,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_1605]) ).

cnf(i_0_2195,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_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1543,i_0_2092,i_0_1805,i_0_2149,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_1750,i_0_1631,i_0_2178,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1447,i_0_2164,i_0_1503,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606]) ).

cnf(i_0_2196,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_1606]) ).

cnf(i_0_2197,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_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1543,i_0_2092,i_0_1805,i_0_2149,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_1750,i_0_1631,i_0_2178,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1447,i_0_2164,i_0_1503,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614]) ).

cnf(i_0_2198,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_1614]) ).

cnf(i_0_2199,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_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1543,i_0_2092,i_0_1805,i_0_2149,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_1750,i_0_1631,i_0_2178,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1447,i_0_2164,i_0_1503,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633]) ).

cnf(i_0_2200,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_1633]) ).

cnf(i_0_2201,plain,
    X1 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),
    inference(scs_inference,[],[i_0_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1543,i_0_2092,i_0_1805,i_0_2149,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_1750,i_0_2120,i_0_1631,i_0_2178,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1447,i_0_2164,i_0_1503,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636]) ).

cnf(i_0_2202,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_1636]) ).

cnf(i_0_2203,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_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1543,i_0_2092,i_0_1805,i_0_2149,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_1750,i_0_2120,i_0_1631,i_0_2178,i_0_2181,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1447,i_0_2164,i_0_1503,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663]) ).

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_1631]) ).

cnf(i_0_2205,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_1663]) ).

cnf(i_0_2206,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_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1543,i_0_2092,i_0_1805,i_0_2149,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_1750,i_0_2120,i_0_1631,i_0_2178,i_0_2181,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1447,i_0_2164,i_0_1503,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665]) ).

cnf(i_0_2207,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_1665]) ).

cnf(i_0_2208,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_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1543,i_0_2092,i_0_1805,i_0_2149,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_1750,i_0_2120,i_0_1631,i_0_2178,i_0_2181,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1447,i_0_2164,i_0_1503,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671]) ).

cnf(i_0_2209,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_1671]) ).

cnf(i_0_2210,plain,
    c_Set_Oinsert(X1,X2,hAPP(c_fequal,X2)) = hAPP(c_fequal,X2),
    inference(scs_inference,[],[i_0_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1543,i_0_2092,i_0_1805,i_0_2149,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_1750,i_0_2120,i_0_1631,i_0_2178,i_0_2181,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1447,i_0_2164,i_0_1503,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672]) ).

cnf(i_0_2211,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | c_Set_Oinsert(X1,X2,X3) = X3 ),
    inference(rename_variables,[],[i_0_1672]) ).

cnf(i_0_2212,plain,
    X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk2_2(X1,X1)),
    inference(scs_inference,[],[i_0_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1543,i_0_2092,i_0_1805,i_0_2149,i_0_2189,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_1750,i_0_2120,i_0_1631,i_0_2178,i_0_2181,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1447,i_0_2164,i_0_1503,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700]) ).

cnf(i_0_2213,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),esk2_2(X2,X1)) ),
    inference(rename_variables,[],[i_0_1700]) ).

cnf(i_0_2214,plain,
    hAPP(c_Nat_OSuc,X1) = hAPP(c_Nat_OSuc,esk31_1(hAPP(c_Nat_OSuc,X1))),
    inference(scs_inference,[],[i_0_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1543,i_0_2092,i_0_1805,i_0_2149,i_0_2189,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_1750,i_0_2120,i_0_1631,i_0_2178,i_0_2181,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1447,i_0_2164,i_0_1503,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703]) ).

cnf(i_0_2215,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,esk31_1(X1)) ),
    inference(rename_variables,[],[i_0_1703]) ).

cnf(i_0_2216,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_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1543,i_0_2092,i_0_1805,i_0_2149,i_0_2189,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_1750,i_0_2120,i_0_1631,i_0_2178,i_0_2181,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1447,i_0_2164,i_0_1503,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737]) ).

cnf(i_0_2217,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_1737]) ).

cnf(i_0_2218,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_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1543,i_0_2092,i_0_1805,i_0_2149,i_0_2189,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_1750,i_0_2120,i_0_1631,i_0_2178,i_0_2181,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1447,i_0_2164,i_0_1503,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738]) ).

cnf(i_0_2219,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_1738]) ).

cnf(i_0_2220,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_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1543,i_0_2092,i_0_1805,i_0_2149,i_0_2189,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_1750,i_0_2120,i_0_1631,i_0_2178,i_0_2181,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1447,i_0_2164,i_0_1503,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742]) ).

cnf(i_0_2221,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X2 != X1 ),
    inference(rename_variables,[],[i_0_1742]) ).

cnf(i_0_2222,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_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1543,i_0_2092,i_0_1805,i_0_2149,i_0_2189,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_1750,i_0_2120,i_0_1631,i_0_2178,i_0_2181,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1447,i_0_2164,i_0_1503,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744]) ).

cnf(i_0_2223,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X1 != X2 ),
    inference(rename_variables,[],[i_0_1744]) ).

cnf(i_0_2224,plain,
    X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2),
    inference(scs_inference,[],[i_0_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1543,i_0_2092,i_0_1805,i_0_2149,i_0_2189,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_1750,i_0_2120,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1447,i_0_2164,i_0_1503,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745]) ).

cnf(i_0_2225,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_1745]) ).

cnf(i_0_2226,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_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1543,i_0_2092,i_0_1805,i_0_2149,i_0_2189,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_1750,i_0_2120,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1446,i_0_1447,i_0_2164,i_0_1503,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753]) ).

cnf(i_0_2227,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_1446]) ).

cnf(i_0_2228,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_1753]) ).

cnf(i_0_2229,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2) != X1,
    inference(scs_inference,[],[i_0_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1543,i_0_2092,i_0_1805,i_0_2149,i_0_2189,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_1750,i_0_2120,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1446,i_0_2227,i_0_1447,i_0_2164,i_0_1503,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756]) ).

cnf(i_0_2230,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_1446]) ).

cnf(i_0_2231,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_1756]) ).

cnf(i_0_2232,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_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1816,i_0_1543,i_0_2092,i_0_1805,i_0_2149,i_0_2189,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_1750,i_0_2120,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1446,i_0_2227,i_0_1447,i_0_2164,i_0_1503,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765]) ).

cnf(i_0_2233,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_1816]) ).

cnf(i_0_2234,plain,
    ( hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1))
    | X1 = X2 ),
    inference(rename_variables,[],[i_0_1765]) ).

cnf(i_0_2235,plain,
    ~ class_Orderings_Otop(tc_Nat_Onat),
    inference(scs_inference,[],[i_0_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1816,i_0_1543,i_0_2092,i_0_1805,i_0_2149,i_0_2189,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_1750,i_0_2120,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1446,i_0_2227,i_0_1447,i_0_2164,i_0_1503,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779]) ).

cnf(i_0_2236,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
    inference(rename_variables,[],[i_0_1631]) ).

cnf(i_0_2237,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_1779]) ).

cnf(i_0_2238,plain,
    hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)) != X1,
    inference(scs_inference,[],[i_0_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1816,i_0_1543,i_0_2092,i_0_1805,i_0_2149,i_0_2189,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_1750,i_0_2120,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1446,i_0_2227,i_0_1447,i_0_2164,i_0_1503,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802]) ).

cnf(i_0_2239,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
    | X1 != X2 ),
    inference(rename_variables,[],[i_0_1802]) ).

cnf(i_0_2240,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_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1816,i_0_1543,i_0_2092,i_0_1805,i_0_2149,i_0_2189,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_1750,i_0_2120,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1446,i_0_2227,i_0_1447,i_0_2164,i_0_1503,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828]) ).

cnf(i_0_2241,plain,
    ( hAPP(c_Nat_OSuc,X1) != hAPP(c_Nat_OSuc,X2)
    | X1 = X2 ),
    inference(rename_variables,[],[i_0_1828]) ).

cnf(i_0_2242,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_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1816,i_0_1543,i_0_2092,i_0_1805,i_0_2149,i_0_2189,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_1750,i_0_2120,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1446,i_0_2227,i_0_1447,i_0_2164,i_0_1503,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023]) ).

cnf(i_0_2243,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
    inference(rename_variables,[],[i_0_1719]) ).

cnf(i_0_2244,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_2023]) ).

cnf(i_0_2245,plain,
    X1 = c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),
    inference(scs_inference,[],[i_0_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1851,i_0_1816,i_0_1543,i_0_2092,i_0_1805,i_0_2149,i_0_2189,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_1750,i_0_2120,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1446,i_0_2227,i_0_1447,i_0_2164,i_0_1503,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884]) ).

cnf(i_0_2246,plain,
    hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(X1,X2))) != X1,
    inference(scs_inference,[],[i_0_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1851,i_0_1816,i_0_1543,i_0_2092,i_0_1805,i_0_2149,i_0_2189,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_1750,i_0_2120,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1446,i_0_2227,i_0_1447,i_0_2164,i_0_1503,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886]) ).

cnf(i_0_2247,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_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1851,i_0_1644,i_0_1816,i_0_1543,i_0_2092,i_0_1805,i_0_2149,i_0_2189,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_1750,i_0_2120,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1446,i_0_2227,i_0_1447,i_0_2164,i_0_1503,i_0_1469,i_0_1837,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327]) ).

cnf(i_0_2248,plain,
    c_Set_Oimage(X1,X1,c_COMBI(X1),X2) = X2,
    inference(rename_variables,[],[i_0_1644]) ).

cnf(i_0_2249,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_1327]) ).

cnf(i_0_2250,plain,
    c_Finite__Set_Ofinite(tc_Product__Type_Ounit,X1),
    inference(scs_inference,[],[i_0_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1851,i_0_1644,i_0_1816,i_0_1543,i_0_2092,i_0_1805,i_0_2149,i_0_2189,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_1750,i_0_2120,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1446,i_0_2227,i_0_1447,i_0_2164,i_0_1503,i_0_1469,i_0_1837,i_0_1861,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842]) ).

cnf(i_0_2251,plain,
    ( ~ class_Finite__Set_Ofinite(X1)
    | c_Finite__Set_Ofinite(X1,X2) ),
    inference(rename_variables,[],[i_0_1842]) ).

cnf(i_0_2252,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_2046,i_0_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1851,i_0_1644,i_0_1816,i_0_1543,i_0_2092,i_0_1805,i_0_2149,i_0_2189,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_1750,i_0_2120,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1446,i_0_2227,i_0_1447,i_0_2164,i_0_1503,i_0_1469,i_0_1837,i_0_1861,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964]) ).

cnf(i_0_2253,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_2046,i_0_2039,i_0_2025,i_0_2057,i_0_2110,i_0_1851,i_0_1644,i_0_1816,i_0_1543,i_0_2092,i_0_1805,i_0_2149,i_0_2189,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_1750,i_0_2120,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1446,i_0_2227,i_0_1447,i_0_2164,i_0_1503,i_0_1469,i_0_1843,i_0_1837,i_0_1861,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280]) ).

cnf(i_0_2254,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_2025]) ).

cnf(i_0_2255,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_1280]) ).

cnf(i_0_2256,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2057,i_0_2110,i_0_1851,i_0_1644,i_0_1816,i_0_1543,i_0_2092,i_0_1805,i_0_2149,i_0_2189,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_1750,i_0_2120,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1446,i_0_2227,i_0_1447,i_0_2164,i_0_1503,i_0_1469,i_0_1843,i_0_1837,i_0_1861,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281]) ).

cnf(i_0_2257,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_2025]) ).

cnf(i_0_2258,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_1281]) ).

cnf(i_0_2259,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_1851,i_0_1644,i_0_1816,i_0_1543,i_0_2092,i_0_1805,i_0_2149,i_0_2189,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_1750,i_0_2120,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1446,i_0_2227,i_0_1447,i_0_2164,i_0_1503,i_0_1469,i_0_1645,i_0_1843,i_0_1837,i_0_1861,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285]) ).

cnf(i_0_2260,plain,
    c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
    inference(rename_variables,[],[i_0_1645]) ).

cnf(i_0_2261,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_1285]) ).

cnf(i_0_2262,plain,
    hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_COMBI(X1),X2)),hAPP(c_fequal,X2))),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_1851,i_0_1644,i_0_1816,i_0_1543,i_0_2092,i_0_1805,i_0_2149,i_0_2189,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_1750,i_0_2120,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1446,i_0_2227,i_0_1447,i_0_2164,i_0_1503,i_0_1469,i_0_1645,i_0_1843,i_0_1837,i_0_1861,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488]) ).

cnf(i_0_2263,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_1488]) ).

cnf(i_0_2264,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_1851,i_0_1644,i_0_1816,i_0_1543,i_0_2092,i_0_1805,i_0_2149,i_0_2189,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_1750,i_0_2120,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1446,i_0_2227,i_0_1447,i_0_2164,i_0_1503,i_0_1469,i_0_1645,i_0_1843,i_0_1837,i_0_1861,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562]) ).

cnf(i_0_2265,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_1562]) ).

cnf(i_0_2266,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_Nat_Onat),X2),X2)),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_1851,i_0_1644,i_0_1816,i_0_1543,i_0_2092,i_0_1805,i_0_2149,i_0_2189,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_1750,i_0_2120,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1446,i_0_2227,i_0_1447,i_0_2164,i_0_1503,i_0_1469,i_0_1645,i_0_1843,i_0_1837,i_0_1861,i_0_1874,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164]) ).

cnf(i_0_2267,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
    inference(rename_variables,[],[i_0_1805]) ).

cnf(i_0_2268,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_1164]) ).

cnf(i_0_2269,plain,
    ~ c_Finite__Set_Ofolding__image__simple__idem(X1,tc_Nat_Onat,c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool)),X3,c_Set_Oinsert(X4,c_Set_Oinsert(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X5,X6),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X5,X6)),X7),c_Set_Oinsert(X4,c_Set_Oinsert(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X5,X6),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X5,X6)),X7)),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_1851,i_0_1644,i_0_1816,i_0_1543,i_0_2092,i_0_1805,i_0_2149,i_0_2189,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_1750,i_0_2120,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1446,i_0_2227,i_0_1447,i_0_2164,i_0_1503,i_0_1469,i_0_1645,i_0_1843,i_0_1837,i_0_1861,i_0_1874,i_0_1772,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168]) ).

cnf(i_0_2270,plain,
    ( hAPP(X1,c_Set_Oinsert(X2,X3,X4)) = hAPP(hAPP(X5,hAPP(X6,X3)),hAPP(X1,X4))
    | ~ c_Finite__Set_Ofinite(X2,X4)
    | ~ c_Finite__Set_Ofolding__image__simple__idem(X7,X2,X5,X8,X6,X1) ),
    inference(rename_variables,[],[i_0_1168]) ).

cnf(i_0_2271,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_1851,i_0_1644,i_0_1816,i_0_1543,i_0_2092,i_0_1805,i_0_2149,i_0_2189,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_1750,i_0_2120,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1446,i_0_2227,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1645,i_0_1843,i_0_1837,i_0_1861,i_0_1874,i_0_1772,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227]) ).

cnf(i_0_2272,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_1227]) ).

cnf(i_0_2273,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_1851,i_0_1644,i_0_1816,i_0_1543,i_0_2092,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_1750,i_0_2120,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1446,i_0_2227,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1645,i_0_1843,i_0_1837,i_0_1861,i_0_1874,i_0_1772,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259]) ).

cnf(i_0_2274,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))),
    inference(rename_variables,[],[i_0_2057]) ).

cnf(i_0_2275,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
    inference(rename_variables,[],[i_0_1805]) ).

cnf(i_0_2276,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_1259]) ).

cnf(i_0_2277,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_1851,i_0_1644,i_0_1816,i_0_1543,i_0_2092,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_1750,i_0_2120,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1446,i_0_2227,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1645,i_0_1843,i_0_1837,i_0_1861,i_0_1874,i_0_1772,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284]) ).

cnf(i_0_2278,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))),
    inference(rename_variables,[],[i_0_2057]) ).

cnf(i_0_2279,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_2025]) ).

cnf(i_0_2280,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_1284]) ).

cnf(i_0_2281,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_1851,i_0_1644,i_0_2248,i_0_1816,i_0_1543,i_0_2092,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_1750,i_0_2120,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1446,i_0_2227,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1645,i_0_1843,i_0_1837,i_0_1861,i_0_1874,i_0_1772,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291]) ).

cnf(i_0_2282,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_1543]) ).

cnf(i_0_2283,plain,
    c_Set_Oimage(X1,X1,c_COMBI(X1),X2) = X2,
    inference(rename_variables,[],[i_0_1644]) ).

cnf(i_0_2284,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_1291]) ).

cnf(i_0_2285,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_1851,i_0_1644,i_0_2248,i_0_1816,i_0_1543,i_0_2092,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_1750,i_0_2120,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1446,i_0_2227,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_1843,i_0_1837,i_0_1861,i_0_1874,i_0_1772,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300]) ).

cnf(i_0_2286,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_1300]) ).

cnf(i_0_2287,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_1851,i_0_1644,i_0_2248,i_0_1816,i_0_1543,i_0_2092,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_1750,i_0_2120,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1446,i_0_2227,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_1843,i_0_1837,i_0_1861,i_0_1874,i_0_1772,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305]) ).

cnf(i_0_2288,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_1305]) ).

cnf(i_0_2289,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_1851,i_0_1644,i_0_2248,i_0_1816,i_0_1543,i_0_2092,i_0_2282,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_1750,i_0_2120,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1446,i_0_2227,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_1843,i_0_1837,i_0_1861,i_0_1874,i_0_1772,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307]) ).

cnf(i_0_2290,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_1543]) ).

cnf(i_0_2291,plain,
    c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
    inference(rename_variables,[],[i_0_1645]) ).

cnf(i_0_2292,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_1307]) ).

cnf(i_0_2293,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_1851,i_0_1644,i_0_2248,i_0_1816,i_0_1543,i_0_2092,i_0_2282,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1446,i_0_2227,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_1843,i_0_1837,i_0_1861,i_0_1874,i_0_1772,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308]) ).

cnf(i_0_2294,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
    inference(rename_variables,[],[i_0_1719]) ).

cnf(i_0_2295,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_1308]) ).

cnf(i_0_2296,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_1851,i_0_1644,i_0_2248,i_0_1816,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1446,i_0_2227,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_1843,i_0_1837,i_0_1861,i_0_1874,i_0_1772,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312]) ).

cnf(i_0_2297,plain,
    c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
    inference(rename_variables,[],[i_0_1851]) ).

cnf(i_0_2298,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_1312]) ).

cnf(i_0_2299,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_1644,i_0_2248,i_0_1816,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1446,i_0_2227,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_1843,i_0_1837,i_0_1861,i_0_1874,i_0_1772,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340]) ).

cnf(i_0_2300,plain,
    c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
    inference(rename_variables,[],[i_0_1851]) ).

cnf(i_0_2301,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_1340]) ).

cnf(i_0_2302,plain,
    X1 = esk35_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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_1644,i_0_2248,i_0_1816,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1446,i_0_2227,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_1843,i_0_1659,i_0_1837,i_0_1861,i_0_1874,i_0_1772,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343]) ).

cnf(i_0_2303,plain,
    c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1),
    inference(rename_variables,[],[i_0_1659]) ).

cnf(i_0_2304,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_1343]) ).

cnf(i_0_2305,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_1644,i_0_2248,i_0_1816,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1446,i_0_2227,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_1843,i_0_1659,i_0_1837,i_0_1861,i_0_1864,i_0_1874,i_0_1772,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351]) ).

cnf(i_0_2306,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_1351]) ).

cnf(i_0_2307,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_1644,i_0_2248,i_0_1816,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1446,i_0_2227,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_1843,i_0_1844,i_0_1659,i_0_1837,i_0_1861,i_0_1864,i_0_1874,i_0_1772,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358]) ).

cnf(i_0_2308,plain,
    X1 != hAPP(c_Nat_OSuc,X1),
    inference(rename_variables,[],[i_0_1844]) ).

cnf(i_0_2309,plain,
    c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
    inference(rename_variables,[],[i_0_1645]) ).

cnf(i_0_2310,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_1358]) ).

cnf(i_0_2311,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_1644,i_0_2248,i_0_1816,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1446,i_0_2227,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_1844,i_0_1659,i_0_1837,i_0_1861,i_0_1864,i_0_1874,i_0_1772,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361]) ).

cnf(i_0_2312,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))),
    inference(rename_variables,[],[i_0_2057]) ).

cnf(i_0_2313,plain,
    c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
    inference(rename_variables,[],[i_0_1645]) ).

cnf(i_0_2314,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_1361]) ).

cnf(i_0_2315,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_1644,i_0_2248,i_0_1816,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1446,i_0_2227,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_1844,i_0_1659,i_0_1837,i_0_1861,i_0_1864,i_0_1874,i_0_1772,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394]) ).

cnf(i_0_2316,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_1394]) ).

cnf(i_0_2317,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_1644,i_0_2248,i_0_1816,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_1620,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1446,i_0_2227,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_1844,i_0_1659,i_0_1837,i_0_1861,i_0_1864,i_0_1874,i_0_1772,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484]) ).

cnf(i_0_2318,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_1543]) ).

cnf(i_0_2319,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_1620]) ).

cnf(i_0_2320,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_1484]) ).

cnf(i_0_2321,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_1644,i_0_2248,i_0_1816,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_1620,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1446,i_0_2227,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_1844,i_0_1659,i_0_1837,i_0_1861,i_0_1864,i_0_1873,i_0_1874,i_0_1772,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491]) ).

cnf(i_0_2322,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_1491]) ).

cnf(i_0_2323,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(tc_Product__Type_Ounit,X1)),c_Finite__Set_Ocard(tc_Product__Type_Ounit,c_Set_Oinsert(tc_Product__Type_Ounit,X2,X1)))),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_1644,i_0_2248,i_0_1816,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_1620,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1446,i_0_2227,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_1844,i_0_1659,i_0_1837,i_0_1861,i_0_1864,i_0_1873,i_0_1874,i_0_1772,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493]) ).

cnf(i_0_2324,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_1543]) ).

cnf(i_0_2325,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_1493]) ).

cnf(i_0_2326,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_1644,i_0_2248,i_0_1816,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_1620,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1446,i_0_2227,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_1844,i_0_1659,i_0_1837,i_0_1861,i_0_1864,i_0_1873,i_0_1874,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496]) ).

cnf(i_0_2327,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_1439]) ).

cnf(i_0_2328,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_1496]) ).

cnf(i_0_2329,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_1644,i_0_2248,i_0_1816,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_1620,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1446,i_0_2227,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_1844,i_0_1659,i_0_1837,i_0_1861,i_0_1864,i_0_1873,i_0_1874,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542]) ).

cnf(i_0_2330,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_1542]) ).

cnf(i_0_2331,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X1)),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_1644,i_0_2248,i_0_1816,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_1620,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1446,i_0_2227,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_1844,i_0_1659,i_0_1837,i_0_1861,i_0_1864,i_0_1870,i_0_1873,i_0_1874,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566]) ).

cnf(i_0_2332,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_1566]) ).

cnf(i_0_2333,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_1644,i_0_2248,i_0_1816,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_1620,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1303,i_0_1446,i_0_2227,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_1844,i_0_1659,i_0_1837,i_0_1861,i_0_1864,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567]) ).

cnf(i_0_2334,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_1567]) ).

cnf(i_0_2335,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_1644,i_0_2248,i_0_1816,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_1620,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1303,i_0_1446,i_0_2227,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_1844,i_0_1659,i_0_1837,i_0_1861,i_0_1864,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571]) ).

cnf(i_0_2336,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_1571]) ).

cnf(i_0_2337,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_1644,i_0_2248,i_0_1816,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_1620,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1303,i_0_1446,i_0_2227,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_1844,i_0_1659,i_0_1837,i_0_1861,i_0_1864,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573]) ).

cnf(i_0_2338,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_1573]) ).

cnf(i_0_2339,plain,
    c_Finite__Set_Ocard(tc_Product__Type_Ounit,c_Set_Oinsert(tc_Product__Type_Ounit,X1,c_Set_Oinsert(tc_Product__Type_Ounit,X1,X2))) = c_Finite__Set_Ocard(tc_Product__Type_Ounit,c_Set_Oinsert(tc_Product__Type_Ounit,X1,X2)),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_1620,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1303,i_0_1446,i_0_2227,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_1844,i_0_1659,i_0_1837,i_0_1861,i_0_1864,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579]) ).

cnf(i_0_2340,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X2,X3))),
    inference(rename_variables,[],[i_0_1584]) ).

cnf(i_0_2341,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_1579]) ).

cnf(i_0_2342,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_1620,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_1844,i_0_1659,i_0_1837,i_0_1861,i_0_1864,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588]) ).

cnf(i_0_2343,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_1446]) ).

cnf(i_0_2344,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_1588]) ).

cnf(i_0_2345,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_1620,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_1844,i_0_1659,i_0_1837,i_0_1861,i_0_1864,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596]) ).

cnf(i_0_2346,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
    inference(rename_variables,[],[i_0_1631]) ).

cnf(i_0_2347,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_1596]) ).

cnf(i_0_2348,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_1620,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_1844,i_0_1659,i_0_1837,i_0_1861,i_0_1864,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597]) ).

cnf(i_0_2349,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
    inference(rename_variables,[],[i_0_1750]) ).

cnf(i_0_2350,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_1597]) ).

cnf(i_0_2351,plain,
    c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,X1),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_1620,i_0_2319,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_1844,i_0_1659,i_0_1837,i_0_1861,i_0_1864,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599]) ).

cnf(i_0_2352,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_1620]) ).

cnf(i_0_2353,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_1599]) ).

cnf(i_0_2354,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_1620,i_0_2319,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_1844,i_0_1659,i_0_1837,i_0_1861,i_0_1864,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603]) ).

cnf(i_0_2355,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_1603]) ).

cnf(i_0_2356,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)))),esk12_0)),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_1620,i_0_2319,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_1844,i_0_1659,i_0_1837,i_0_1861,i_0_1864,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604]) ).

cnf(i_0_2357,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_1604]) ).

cnf(i_0_2358,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_1844,i_0_1659,i_0_1837,i_0_1861,i_0_1864,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621]) ).

cnf(i_0_2359,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
    inference(rename_variables,[],[i_0_1688]) ).

cnf(i_0_2360,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
    inference(rename_variables,[],[i_0_1750]) ).

cnf(i_0_2361,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_1621]) ).

cnf(i_0_2362,plain,
    hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_OSuc,esk30_2(hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_1844,i_0_1659,i_0_1837,i_0_1861,i_0_1864,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628]) ).

cnf(i_0_2363,plain,
    hAPP(c_Nat_OSuc,X1) != X1,
    inference(rename_variables,[],[i_0_1843]) ).

cnf(i_0_2364,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
    | X1 = hAPP(c_Nat_OSuc,esk30_2(X2,X1))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(rename_variables,[],[i_0_1628]) ).

cnf(i_0_2365,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_1844,i_0_1659,i_0_1837,i_0_1861,i_0_1864,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639]) ).

cnf(i_0_2366,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_1639]) ).

cnf(i_0_2367,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk12_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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_1844,i_0_1659,i_0_1837,i_0_1861,i_0_1864,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641]) ).

cnf(i_0_2368,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_1641]) ).

cnf(i_0_2369,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_1844,i_0_1659,i_0_1837,i_0_1861,i_0_1864,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683]) ).

cnf(i_0_2370,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_1446]) ).

cnf(i_0_2371,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_1683]) ).

cnf(i_0_2372,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_1844,i_0_1659,i_0_1837,i_0_1861,i_0_1864,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697]) ).

cnf(i_0_2373,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_1697]) ).

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),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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_1844,i_0_1659,i_0_1837,i_0_1861,i_0_1864,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702]) ).

cnf(i_0_2375,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_1446]) ).

cnf(i_0_2376,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_1702]) ).

cnf(i_0_2377,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_1844,i_0_1659,i_0_1837,i_0_1861,i_0_1864,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706]) ).

cnf(i_0_2378,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | X3 != X2
    | ~ class_Orderings_Oorder(X1) ),
    inference(rename_variables,[],[i_0_1706]) ).

cnf(i_0_2379,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_1844,i_0_1659,i_0_1837,i_0_1861,i_0_1864,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708]) ).

cnf(i_0_2380,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | X2 != X3
    | ~ class_Orderings_Oorder(X1) ),
    inference(rename_variables,[],[i_0_1708]) ).

cnf(i_0_2381,plain,
    esk12_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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_1844,i_0_1659,i_0_1837,i_0_1861,i_0_1864,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709]) ).

cnf(i_0_2382,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | X2 != X3
    | ~ class_Orderings_Olinorder(X1) ),
    inference(rename_variables,[],[i_0_1709]) ).

cnf(i_0_2383,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))) != esk12_0,
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_1844,i_0_1659,i_0_1837,i_0_1861,i_0_1864,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710]) ).

cnf(i_0_2384,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | X3 != X2
    | ~ class_Orderings_Olinorder(X1) ),
    inference(rename_variables,[],[i_0_1710]) ).

cnf(i_0_2385,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_1844,i_0_1659,i_0_1837,i_0_1861,i_0_1864,i_0_1866,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723]) ).

cnf(i_0_2386,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_1723]) ).

cnf(i_0_2387,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_1844,i_0_1659,i_0_1837,i_0_1861,i_0_1864,i_0_1866,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727]) ).

cnf(i_0_2388,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_1727]) ).

cnf(i_0_2389,plain,
    esk2_2(hAPP(X1,esk9_4(X1,X1,X2,tc_Nat_Onat)),hAPP(X1,esk9_4(X1,X1,X2,tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_1844,i_0_1659,i_0_1837,i_0_1854,i_0_1861,i_0_1864,i_0_1866,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782]) ).

cnf(i_0_2390,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_1782]) ).

cnf(i_0_2391,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_1844,i_0_1659,i_0_1837,i_0_1854,i_0_1861,i_0_1864,i_0_1866,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788]) ).

cnf(i_0_2392,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | X3 != X2
    | ~ class_Orderings_Oorder(X1) ),
    inference(rename_variables,[],[i_0_1788]) ).

cnf(i_0_2393,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_1844,i_0_1659,i_0_1837,i_0_1854,i_0_1861,i_0_1864,i_0_1866,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789]) ).

cnf(i_0_2394,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | ~ class_Orderings_Opreorder(X1)
    | X2 != X3 ),
    inference(rename_variables,[],[i_0_1789]) ).

cnf(i_0_2395,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)) != X2,
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_1844,i_0_1659,i_0_1837,i_0_1854,i_0_1861,i_0_1864,i_0_1866,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790]) ).

cnf(i_0_2396,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | X2 != X3
    | ~ class_Orderings_Oorder(X1) ),
    inference(rename_variables,[],[i_0_1790]) ).

cnf(i_0_2397,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_2363,i_0_1844,i_0_1659,i_0_1837,i_0_1854,i_0_1861,i_0_1864,i_0_1866,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020]) ).

cnf(i_0_2398,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_2020]) ).

cnf(i_0_2399,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_2363,i_0_1844,i_0_1659,i_0_1837,i_0_1854,i_0_1861,i_0_1864,i_0_1866,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022]) ).

cnf(i_0_2400,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_2022]) ).

cnf(i_0_2401,plain,
    hAPP(c_Nat_OSuc,X1) != c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_2363,i_0_1844,i_0_1659,i_0_1837,i_0_1854,i_0_1861,i_0_1864,i_0_1866,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885]) ).

cnf(i_0_2402,plain,
    c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
    inference(rename_variables,[],[i_0_1851]) ).

cnf(i_0_2403,plain,
    class_Finite__Set_Ofinite(esk35_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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_2363,i_0_1844,i_0_1659,i_0_1837,i_0_1854,i_0_1861,i_0_1864,i_0_1866,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976]) ).

cnf(i_0_2404,plain,
    class_Groups_Ocomm__monoid__add(esk32_2(hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_2363,i_0_1844,i_0_1659,i_0_1837,i_0_1854,i_0_1857,i_0_1861,i_0_1864,i_0_1866,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977]) ).

cnf(i_0_2405,plain,
    class_Groups_Omonoid__add(esk32_2(hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_2363,i_0_1844,i_0_1659,i_0_1837,i_0_1854,i_0_1857,i_0_1858,i_0_1861,i_0_1864,i_0_1866,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978]) ).

cnf(i_0_2406,plain,
    class_Rings_Ozero__neq__one(esk32_2(hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_2363,i_0_1844,i_0_1659,i_0_1837,i_0_1854,i_0_1857,i_0_1858,i_0_1859,i_0_1861,i_0_1864,i_0_1866,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979]) ).

cnf(i_0_2407,plain,
    class_Groups_Ozero(esk32_2(hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_2363,i_0_1844,i_0_1659,i_0_1837,i_0_1854,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1864,i_0_1866,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980]) ).

cnf(i_0_2408,plain,
    class_Groups_Oone(esk32_2(hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_2363,i_0_1844,i_0_1659,i_0_1837,i_0_1854,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1864,i_0_1865,i_0_1866,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981]) ).

cnf(i_0_2409,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_2363,i_0_1844,i_0_1659,i_0_1837,i_0_1854,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1864,i_0_1865,i_0_1866,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982]) ).

cnf(i_0_2410,plain,
    c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
    inference(rename_variables,[],[i_0_1851]) ).

cnf(i_0_2411,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_2363,i_0_1844,i_0_1659,i_0_1837,i_0_1854,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1864,i_0_1865,i_0_1866,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983]) ).

cnf(i_0_2412,plain,
    c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
    inference(rename_variables,[],[i_0_1851]) ).

cnf(i_0_2413,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_2363,i_0_1844,i_0_1659,i_0_1837,i_0_1854,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1864,i_0_1865,i_0_1866,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990]) ).

cnf(i_0_2414,plain,
    c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
    inference(rename_variables,[],[i_0_1851]) ).

cnf(i_0_2415,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_2363,i_0_1844,i_0_1659,i_0_1837,i_0_1854,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1864,i_0_1865,i_0_1866,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991]) ).

cnf(i_0_2416,plain,
    c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
    inference(rename_variables,[],[i_0_1851]) ).

cnf(i_0_2417,plain,
    class_Orderings_Oord(esk32_2(hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_2363,i_0_1844,i_0_1659,i_0_1837,i_0_1854,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1864,i_0_1865,i_0_1866,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992]) ).

cnf(i_0_2418,plain,
    ~ c_Finite__Set_Ofolding__image__simple__idem(X1,c_Nat_Osize__class_Osize(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool)),X3,c_Set_Oinsert(X4,c_Set_Oinsert(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X5,X6),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X5,X6)),X7),c_Set_Oinsert(X4,c_Set_Oinsert(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X5,X6),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X5,X6)),X7)),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_2363,i_0_1844,i_0_1659,i_0_1837,i_0_1854,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1864,i_0_1865,i_0_1866,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994]) ).

cnf(i_0_2419,plain,
    c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
    inference(rename_variables,[],[i_0_1851]) ).

cnf(i_0_2420,plain,
    ~ c_Finite__Set_Ofolding__image__simple__idem(X1,tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool))),X3,c_Set_Oinsert(X4,c_Set_Oinsert(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X5,X6),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X5,X6)),X7),c_Set_Oinsert(X4,c_Set_Oinsert(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X5,X6),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X5,X6)),X7)),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_2363,i_0_1844,i_0_1659,i_0_1837,i_0_1854,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1864,i_0_1865,i_0_1866,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995]) ).

cnf(i_0_2421,plain,
    c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
    inference(rename_variables,[],[i_0_1851]) ).

cnf(i_0_2422,plain,
    ~ c_Finite__Set_Ofolding__image__simple__idem(X1,tc_Nat_Onat,c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool)),X3,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Set_Oinsert(X4,c_Set_Oinsert(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X5,X6),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X5,X6)),X7)),c_Set_Oinsert(X4,c_Set_Oinsert(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X5,X6),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X5,X6)),X7)),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_2363,i_0_1844,i_0_1659,i_0_1837,i_0_1854,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1864,i_0_1865,i_0_1866,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997]) ).

cnf(i_0_2423,plain,
    c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
    inference(rename_variables,[],[i_0_1851]) ).

cnf(i_0_2424,plain,
    ~ c_Finite__Set_Ofolding__image__simple__idem(X1,tc_Nat_Onat,c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool)),X3,c_Set_Oinsert(X4,c_Set_Oinsert(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X5,X6),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X5,X6)),X7),c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Set_Oinsert(X4,c_Set_Oinsert(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X5,X6),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X5,X6)),X7))),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_2363,i_0_1844,i_0_1659,i_0_1837,i_0_1854,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1864,i_0_1865,i_0_1866,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998]) ).

cnf(i_0_2425,plain,
    c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
    inference(rename_variables,[],[i_0_1851]) ).

cnf(i_0_2426,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_2363,i_0_1844,i_0_1659,i_0_1837,i_0_1854,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1864,i_0_1865,i_0_1866,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999]) ).

cnf(i_0_2427,plain,
    c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
    inference(rename_variables,[],[i_0_1851]) ).

cnf(i_0_2428,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_2363,i_0_1844,i_0_1659,i_0_1837,i_0_1854,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1864,i_0_1865,i_0_1866,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000]) ).

cnf(i_0_2429,plain,
    c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
    inference(rename_variables,[],[i_0_1851]) ).

cnf(i_0_2430,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_2363,i_0_1844,i_0_1659,i_0_1837,i_0_1854,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1864,i_0_1865,i_0_1866,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001]) ).

cnf(i_0_2431,plain,
    c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
    inference(rename_variables,[],[i_0_1851]) ).

cnf(i_0_2432,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_2363,i_0_1844,i_0_1659,i_0_1837,i_0_1854,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1864,i_0_1865,i_0_1866,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002]) ).

cnf(i_0_2433,plain,
    c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
    inference(rename_variables,[],[i_0_1851]) ).

cnf(i_0_2434,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_2363,i_0_1844,i_0_1659,i_0_1837,i_0_1854,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1864,i_0_1865,i_0_1866,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952]) ).

cnf(i_0_2435,plain,
    c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
    inference(rename_variables,[],[i_0_1851]) ).

cnf(i_0_2436,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_2363,i_0_1844,i_0_1659,i_0_1837,i_0_1854,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1864,i_0_1865,i_0_1866,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953]) ).

cnf(i_0_2437,plain,
    c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
    inference(rename_variables,[],[i_0_1851]) ).

cnf(i_0_2438,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_2363,i_0_1844,i_0_1659,i_0_1837,i_0_1854,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1864,i_0_1865,i_0_1866,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954]) ).

cnf(i_0_2439,plain,
    c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
    inference(rename_variables,[],[i_0_1851]) ).

cnf(i_0_2440,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_2363,i_0_1844,i_0_1659,i_0_1837,i_0_1854,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1864,i_0_1865,i_0_1866,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955]) ).

cnf(i_0_2441,plain,
    c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
    inference(rename_variables,[],[i_0_1851]) ).

cnf(i_0_2442,plain,
    class_Orderings_Olinorder(esk32_2(hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_2363,i_0_1844,i_0_1659,i_0_1837,i_0_1854,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1864,i_0_1865,i_0_1866,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957]) ).

cnf(i_0_2443,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(esk32_2(hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_2363,i_0_1844,i_0_1659,i_0_1837,i_0_1854,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1864,i_0_1865,i_0_1866,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958]) ).

cnf(i_0_2444,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(esk32_2(hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_2363,i_0_1844,i_0_1659,i_0_1837,i_0_1854,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1864,i_0_1865,i_0_1866,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959]) ).

cnf(i_0_2445,plain,
    class_Groups_Oordered__ab__semigroup__add(esk32_2(hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_2363,i_0_1844,i_0_1659,i_0_1837,i_0_1854,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960]) ).

cnf(i_0_2446,plain,
    class_Groups_Oordered__comm__monoid__add(esk32_2(hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_2363,i_0_1844,i_0_1659,i_0_1837,i_0_1854,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962]) ).

cnf(i_0_2447,plain,
    class_Rings_Ocomm__semiring__1(esk32_2(hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_2363,i_0_1844,i_0_1659,i_0_1837,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965]) ).

cnf(i_0_2448,plain,
    class_Rings_Olinordered__semidom(esk32_2(hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_2363,i_0_1844,i_0_1659,i_0_1837,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966]) ).

cnf(i_0_2449,plain,
    class_Orderings_Opreorder(esk32_2(hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_2363,i_0_1844,i_0_1659,i_0_1837,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968]) ).

cnf(i_0_2450,plain,
    class_Orderings_Oorder(esk32_2(hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_2363,i_0_1844,i_0_1659,i_0_1837,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969]) ).

cnf(i_0_2451,plain,
    class_Groups_Oab__semigroup__add(esk32_2(hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_2363,i_0_1844,i_0_1659,i_0_1837,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1868,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970]) ).

cnf(i_0_2452,plain,
    class_Groups_Ocancel__semigroup__add(esk32_2(hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_2363,i_0_1844,i_0_1659,i_0_1837,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971]) ).

cnf(i_0_2453,plain,
    class_Groups_Ocancel__ab__semigroup__add(esk32_2(hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_2363,i_0_1844,i_0_1659,i_0_1837,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972]) ).

cnf(i_0_2454,plain,
    tc_HOL_Obool != tc_Nat_Onat,
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_2363,i_0_1844,i_0_1659,i_0_1837,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973]) ).

cnf(i_0_2455,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(esk32_2(hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_2363,i_0_1844,i_0_1659,i_0_1837,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974]) ).

cnf(i_0_2456,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_2363,i_0_1844,i_0_2308,i_0_1659,i_0_1837,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011]) ).

cnf(i_0_2457,plain,
    X1 != hAPP(c_Nat_OSuc,X1),
    inference(rename_variables,[],[i_0_1844]) ).

cnf(i_0_2458,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_2011]) ).

cnf(i_0_2459,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_1843,i_0_2363,i_0_1844,i_0_2308,i_0_1659,i_0_1837,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016]) ).

cnf(i_0_2460,plain,
    hAPP(c_Nat_OSuc,X1) != X1,
    inference(rename_variables,[],[i_0_1843]) ).

cnf(i_0_2461,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_2016]) ).

cnf(i_0_2462,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(tc_Product__Type_Ounit,X1)),c_Finite__Set_Ocard(tc_Product__Type_Ounit,c_Set_Oinsert(tc_Product__Type_Ounit,X2,c_Set_Oimage(tc_Product__Type_Ounit,tc_Product__Type_Ounit,c_COMBI(tc_Product__Type_Ounit),X1))))),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_1843,i_0_2363,i_0_1844,i_0_2308,i_0_1659,i_0_1837,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219]) ).

cnf(i_0_2463,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_1543]) ).

cnf(i_0_2464,plain,
    c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
    inference(rename_variables,[],[i_0_1645]) ).

cnf(i_0_2465,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_1219]) ).

cnf(i_0_2466,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_1843,i_0_2363,i_0_2460,i_0_1844,i_0_2308,i_0_1659,i_0_1837,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268]) ).

cnf(i_0_2467,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_1268]) ).

cnf(i_0_2468,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_1843,i_0_2363,i_0_2460,i_0_1844,i_0_2308,i_0_1659,i_0_1837,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277]) ).

cnf(i_0_2469,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_1277]) ).

cnf(i_0_2470,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_1644,i_0_2248,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_1843,i_0_2363,i_0_2460,i_0_1844,i_0_2308,i_0_1659,i_0_1837,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354]) ).

cnf(i_0_2471,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
    inference(rename_variables,[],[i_0_1805]) ).

cnf(i_0_2472,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_1354]) ).

cnf(i_0_2473,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_1644,i_0_2248,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_2359,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_1843,i_0_2363,i_0_2460,i_0_1844,i_0_2308,i_0_2457,i_0_1659,i_0_1837,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362]) ).

cnf(i_0_2474,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
    inference(rename_variables,[],[i_0_1688]) ).

cnf(i_0_2475,plain,
    X1 != hAPP(c_Nat_OSuc,X1),
    inference(rename_variables,[],[i_0_1844]) ).

cnf(i_0_2476,plain,
    hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
    inference(rename_variables,[],[i_0_1791]) ).

cnf(i_0_2477,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_1362]) ).

cnf(i_0_2478,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_1644,i_0_2248,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_2359,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_1843,i_0_2363,i_0_2460,i_0_1844,i_0_2308,i_0_2457,i_0_1659,i_0_1837,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417]) ).

cnf(i_0_2479,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
    inference(rename_variables,[],[i_0_1805]) ).

cnf(i_0_2480,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_1417]) ).

cnf(i_0_2481,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_1644,i_0_2248,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_2359,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_1843,i_0_2363,i_0_2460,i_0_1844,i_0_2308,i_0_2457,i_0_1659,i_0_1837,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459]) ).

cnf(i_0_2482,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
    inference(rename_variables,[],[i_0_1805]) ).

cnf(i_0_2483,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(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(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(rename_variables,[],[i_0_1459]) ).

cnf(i_0_2484,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_1644,i_0_2248,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_2359,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_1843,i_0_2363,i_0_2460,i_0_1844,i_0_2308,i_0_2457,i_0_1659,i_0_1837,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473]) ).

cnf(i_0_2485,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
    inference(rename_variables,[],[i_0_1805]) ).

cnf(i_0_2486,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_1473]) ).

cnf(i_0_2487,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_1644,i_0_2248,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_2485,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_1620,i_0_2319,i_0_1688,i_0_2359,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_1843,i_0_2363,i_0_2460,i_0_1844,i_0_2308,i_0_2457,i_0_1659,i_0_1837,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473,i_0_1474]) ).

cnf(i_0_2488,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
    inference(rename_variables,[],[i_0_1805]) ).

cnf(i_0_2489,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_1474]) ).

cnf(i_0_2490,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)))),esk12_0)),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_1644,i_0_2248,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_2485,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_2360,i_0_1620,i_0_2319,i_0_1688,i_0_2359,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_1843,i_0_2363,i_0_2460,i_0_1844,i_0_2308,i_0_2457,i_0_1659,i_0_1837,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473,i_0_1474,i_0_1518]) ).

cnf(i_0_2491,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
    inference(rename_variables,[],[i_0_1750]) ).

cnf(i_0_2492,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_1518]) ).

cnf(i_0_2493,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_1644,i_0_2248,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_2485,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_2360,i_0_2491,i_0_1620,i_0_2319,i_0_1688,i_0_2359,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_1843,i_0_2363,i_0_2460,i_0_1844,i_0_2308,i_0_2457,i_0_1659,i_0_1837,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473,i_0_1474,i_0_1518,i_0_1519]) ).

cnf(i_0_2494,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
    inference(rename_variables,[],[i_0_1750]) ).

cnf(i_0_2495,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_1519]) ).

cnf(i_0_2496,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)),tc_Nat_Onat)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_1644,i_0_2248,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_2485,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_2360,i_0_2491,i_0_2494,i_0_1620,i_0_2319,i_0_1688,i_0_2359,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_1843,i_0_2363,i_0_2460,i_0_1844,i_0_2308,i_0_2457,i_0_1659,i_0_1837,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473,i_0_1474,i_0_1518,i_0_1519,i_0_1536]) ).

cnf(i_0_2497,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
    inference(rename_variables,[],[i_0_1750]) ).

cnf(i_0_2498,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_1536]) ).

cnf(i_0_2499,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),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))),X2)),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_1644,i_0_2248,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_2485,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_2360,i_0_2491,i_0_2494,i_0_1620,i_0_2319,i_0_1688,i_0_2359,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_1843,i_0_2363,i_0_2460,i_0_1844,i_0_2308,i_0_2457,i_0_1659,i_0_1837,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473,i_0_1474,i_0_1518,i_0_1519,i_0_1536,i_0_1537]) ).

cnf(i_0_2500,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
    inference(rename_variables,[],[i_0_1759]) ).

cnf(i_0_2501,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_1537]) ).

cnf(i_0_2502,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_1644,i_0_2248,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_2485,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_2360,i_0_2491,i_0_2494,i_0_2497,i_0_1620,i_0_2319,i_0_1688,i_0_2359,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_1843,i_0_2363,i_0_2460,i_0_1844,i_0_2308,i_0_2457,i_0_1659,i_0_1837,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473,i_0_1474,i_0_1518,i_0_1519,i_0_1536,i_0_1537,i_0_1538]) ).

cnf(i_0_2503,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
    inference(rename_variables,[],[i_0_1750]) ).

cnf(i_0_2504,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_1538]) ).

cnf(i_0_2505,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_1644,i_0_2248,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_2485,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_2360,i_0_2491,i_0_2494,i_0_2497,i_0_1620,i_0_2319,i_0_1688,i_0_2359,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_2346,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_1843,i_0_2363,i_0_2460,i_0_1844,i_0_2308,i_0_2457,i_0_1659,i_0_1837,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473,i_0_1474,i_0_1518,i_0_1519,i_0_1536,i_0_1537,i_0_1538,i_0_1563]) ).

cnf(i_0_2506,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
    inference(rename_variables,[],[i_0_1631]) ).

cnf(i_0_2507,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_1563]) ).

cnf(i_0_2508,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_1644,i_0_2248,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_2485,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_2360,i_0_2491,i_0_2494,i_0_2497,i_0_1620,i_0_2319,i_0_1688,i_0_2359,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_2346,i_0_2506,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_1843,i_0_2363,i_0_2460,i_0_1844,i_0_2308,i_0_2457,i_0_1659,i_0_1837,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473,i_0_1474,i_0_1518,i_0_1519,i_0_1536,i_0_1537,i_0_1538,i_0_1563,i_0_1564]) ).

cnf(i_0_2509,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_1564]) ).

cnf(i_0_2510,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)),tc_Nat_Onat)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_1644,i_0_2248,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_2485,i_0_2488,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_2360,i_0_2491,i_0_2494,i_0_2497,i_0_2503,i_0_1620,i_0_2319,i_0_1688,i_0_2359,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_2346,i_0_2506,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_1843,i_0_2363,i_0_2460,i_0_1844,i_0_2308,i_0_2457,i_0_1659,i_0_1837,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473,i_0_1474,i_0_1518,i_0_1519,i_0_1536,i_0_1537,i_0_1538,i_0_1563,i_0_1564,i_0_1575]) ).

cnf(i_0_2511,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
    inference(rename_variables,[],[i_0_1750]) ).

cnf(i_0_2512,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
    inference(rename_variables,[],[i_0_1805]) ).

cnf(i_0_2513,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_1739]) ).

cnf(i_0_2514,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_1575]) ).

cnf(i_0_2515,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)),tc_Nat_Onat)),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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_1644,i_0_2248,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_2485,i_0_2488,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_2360,i_0_2491,i_0_2494,i_0_2497,i_0_2503,i_0_1620,i_0_2319,i_0_1688,i_0_2359,i_0_1795,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_2346,i_0_2506,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_1843,i_0_2363,i_0_2460,i_0_1844,i_0_2308,i_0_2457,i_0_1659,i_0_1837,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473,i_0_1474,i_0_1518,i_0_1519,i_0_1536,i_0_1537,i_0_1538,i_0_1563,i_0_1564,i_0_1575,i_0_1578]) ).

cnf(i_0_2516,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_1795]) ).

cnf(i_0_2517,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_1578]) ).

cnf(i_0_2518,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),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_1644,i_0_2248,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_2485,i_0_2488,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_2360,i_0_2491,i_0_2494,i_0_2497,i_0_2503,i_0_1620,i_0_2319,i_0_1688,i_0_2359,i_0_1795,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_2346,i_0_2506,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_1843,i_0_2363,i_0_2460,i_0_1844,i_0_2308,i_0_2457,i_0_1659,i_0_1837,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473,i_0_1474,i_0_1518,i_0_1519,i_0_1536,i_0_1537,i_0_1538,i_0_1563,i_0_1564,i_0_1575,i_0_1578,i_0_1627]) ).

cnf(i_0_2519,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_1627]) ).

cnf(i_0_2520,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)),tc_Nat_Onat)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_1644,i_0_2248,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_2485,i_0_2488,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_2360,i_0_2491,i_0_2494,i_0_2497,i_0_2503,i_0_1620,i_0_2319,i_0_1688,i_0_2359,i_0_1795,i_0_2516,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_2346,i_0_2506,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_1843,i_0_2363,i_0_2460,i_0_1844,i_0_2308,i_0_2457,i_0_1659,i_0_1837,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473,i_0_1474,i_0_1518,i_0_1519,i_0_1536,i_0_1537,i_0_1538,i_0_1563,i_0_1564,i_0_1575,i_0_1578,i_0_1627,i_0_1653]) ).

cnf(i_0_2521,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_1795]) ).

cnf(i_0_2522,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_1653]) ).

cnf(i_0_2523,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_1644,i_0_2248,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_2485,i_0_2488,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_2360,i_0_2491,i_0_2494,i_0_2497,i_0_2503,i_0_1620,i_0_2319,i_0_1688,i_0_2359,i_0_1795,i_0_2516,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_2346,i_0_2506,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_1843,i_0_2363,i_0_2460,i_0_1844,i_0_2308,i_0_2457,i_0_1659,i_0_1837,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473,i_0_1474,i_0_1518,i_0_1519,i_0_1536,i_0_1537,i_0_1538,i_0_1563,i_0_1564,i_0_1575,i_0_1578,i_0_1627,i_0_1653,i_0_1656]) ).

cnf(i_0_2524,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_1733]) ).

cnf(i_0_2525,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_1656]) ).

cnf(i_0_2526,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)),tc_Nat_Onat)),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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_1644,i_0_2248,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_2485,i_0_2488,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_2524,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_2360,i_0_2491,i_0_2494,i_0_2497,i_0_2503,i_0_1620,i_0_2319,i_0_1688,i_0_2359,i_0_1795,i_0_2516,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_2346,i_0_2506,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_1843,i_0_2363,i_0_2460,i_0_1844,i_0_2308,i_0_2457,i_0_1659,i_0_1837,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473,i_0_1474,i_0_1518,i_0_1519,i_0_1536,i_0_1537,i_0_1538,i_0_1563,i_0_1564,i_0_1575,i_0_1578,i_0_1627,i_0_1653,i_0_1656,i_0_1678]) ).

cnf(i_0_2527,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_1733]) ).

cnf(i_0_2528,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_1678]) ).

cnf(i_0_2529,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))),X2) != X2,
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_1644,i_0_2248,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_2485,i_0_2488,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_2524,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_2360,i_0_2491,i_0_2494,i_0_2497,i_0_2503,i_0_1620,i_0_2319,i_0_1688,i_0_2359,i_0_1795,i_0_2516,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_2346,i_0_2506,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_2167,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_1843,i_0_2363,i_0_2460,i_0_1844,i_0_2308,i_0_2457,i_0_1659,i_0_1837,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473,i_0_1474,i_0_1518,i_0_1519,i_0_1536,i_0_1537,i_0_1538,i_0_1563,i_0_1564,i_0_1575,i_0_1578,i_0_1627,i_0_1653,i_0_1656,i_0_1678,i_0_1691]) ).

cnf(i_0_2530,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_1447]) ).

cnf(i_0_2531,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_1691]) ).

cnf(i_0_2532,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_1644,i_0_2248,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_2485,i_0_2488,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_2524,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_2360,i_0_2491,i_0_2494,i_0_2497,i_0_2503,i_0_1620,i_0_2319,i_0_1688,i_0_2359,i_0_1795,i_0_2516,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_2346,i_0_2506,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_2167,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_1843,i_0_2363,i_0_2460,i_0_1844,i_0_2308,i_0_2457,i_0_2475,i_0_1659,i_0_1837,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473,i_0_1474,i_0_1518,i_0_1519,i_0_1536,i_0_1537,i_0_1538,i_0_1563,i_0_1564,i_0_1575,i_0_1578,i_0_1627,i_0_1653,i_0_1656,i_0_1678,i_0_1691,i_0_1225]) ).

cnf(i_0_2533,plain,
    X1 != hAPP(c_Nat_OSuc,X1),
    inference(rename_variables,[],[i_0_1844]) ).

cnf(i_0_2534,plain,
    c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
    inference(rename_variables,[],[i_0_1851]) ).

cnf(i_0_2535,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_1225]) ).

cnf(i_0_2536,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_2534,i_0_1644,i_0_2248,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_2485,i_0_2488,i_0_1739,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_1733,i_0_2524,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_2360,i_0_2491,i_0_2494,i_0_2497,i_0_2503,i_0_1620,i_0_2319,i_0_1688,i_0_2359,i_0_1795,i_0_2516,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_2346,i_0_2506,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_2167,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_1843,i_0_2363,i_0_2460,i_0_1844,i_0_2308,i_0_2457,i_0_2475,i_0_1659,i_0_1837,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473,i_0_1474,i_0_1518,i_0_1519,i_0_1536,i_0_1537,i_0_1538,i_0_1563,i_0_1564,i_0_1575,i_0_1578,i_0_1627,i_0_1653,i_0_1656,i_0_1678,i_0_1691,i_0_1225,i_0_1241]) ).

cnf(i_0_2537,plain,
    hAPP(c_Nat_OSuc,X1) != X1,
    inference(rename_variables,[],[i_0_1843]) ).

cnf(i_0_2538,plain,
    c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
    inference(rename_variables,[],[i_0_1851]) ).

cnf(i_0_2539,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_1241]) ).

cnf(i_0_2540,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_2534,i_0_1644,i_0_2248,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_2485,i_0_2488,i_0_1739,i_0_2513,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_2500,i_0_1733,i_0_2524,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_2360,i_0_2491,i_0_2494,i_0_2497,i_0_2503,i_0_1620,i_0_2319,i_0_1688,i_0_2359,i_0_1795,i_0_2516,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_2346,i_0_2506,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_2167,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_1843,i_0_2363,i_0_2460,i_0_2537,i_0_1844,i_0_2308,i_0_2457,i_0_2475,i_0_1659,i_0_1837,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473,i_0_1474,i_0_1518,i_0_1519,i_0_1536,i_0_1537,i_0_1538,i_0_1563,i_0_1564,i_0_1575,i_0_1578,i_0_1627,i_0_1653,i_0_1656,i_0_1678,i_0_1691,i_0_1225,i_0_1241,i_0_1499]) ).

cnf(i_0_2541,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
    inference(rename_variables,[],[i_0_1759]) ).

cnf(i_0_2542,plain,
    hAPP(c_Nat_OSuc,X1) != X1,
    inference(rename_variables,[],[i_0_1843]) ).

cnf(i_0_2543,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_1499]) ).

cnf(i_0_2544,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_2534,i_0_1644,i_0_2248,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_2485,i_0_2488,i_0_1739,i_0_2513,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_2500,i_0_2541,i_0_1733,i_0_2524,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_2360,i_0_2491,i_0_2494,i_0_2497,i_0_2503,i_0_1620,i_0_2319,i_0_1688,i_0_2359,i_0_1795,i_0_2516,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_2346,i_0_2506,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_2167,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_1843,i_0_2363,i_0_2460,i_0_2537,i_0_2542,i_0_1844,i_0_2308,i_0_2457,i_0_2475,i_0_1659,i_0_1837,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473,i_0_1474,i_0_1518,i_0_1519,i_0_1536,i_0_1537,i_0_1538,i_0_1563,i_0_1564,i_0_1575,i_0_1578,i_0_1627,i_0_1653,i_0_1656,i_0_1678,i_0_1691,i_0_1225,i_0_1241,i_0_1499,i_0_1500]) ).

cnf(i_0_2545,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
    inference(rename_variables,[],[i_0_1759]) ).

cnf(i_0_2546,plain,
    hAPP(c_Nat_OSuc,X1) != X1,
    inference(rename_variables,[],[i_0_1843]) ).

cnf(i_0_2547,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_1500]) ).

cnf(i_0_2548,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(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,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),X1),hAPP(c_Nat_OSuc,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_2534,i_0_1644,i_0_2248,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_2485,i_0_2488,i_0_1739,i_0_2513,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_2500,i_0_2541,i_0_1733,i_0_2524,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_2360,i_0_2491,i_0_2494,i_0_2497,i_0_2503,i_0_1620,i_0_2319,i_0_1688,i_0_2359,i_0_1795,i_0_2516,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_2346,i_0_2506,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1643,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_2167,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_1843,i_0_2363,i_0_2460,i_0_2537,i_0_2542,i_0_1844,i_0_2308,i_0_2457,i_0_2475,i_0_1659,i_0_1837,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473,i_0_1474,i_0_1518,i_0_1519,i_0_1536,i_0_1537,i_0_1538,i_0_1563,i_0_1564,i_0_1575,i_0_1578,i_0_1627,i_0_1653,i_0_1656,i_0_1678,i_0_1691,i_0_1225,i_0_1241,i_0_1499,i_0_1500,i_0_1521]) ).

cnf(i_0_2549,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_1643]) ).

cnf(i_0_2550,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_1521]) ).

cnf(i_0_2551,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2026,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_2534,i_0_1644,i_0_2248,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_2485,i_0_2488,i_0_1739,i_0_2513,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_2500,i_0_2541,i_0_1733,i_0_2524,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_2360,i_0_2491,i_0_2494,i_0_2497,i_0_2503,i_0_1620,i_0_2319,i_0_1688,i_0_2359,i_0_1795,i_0_2516,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_2346,i_0_2506,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1643,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_2167,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_1843,i_0_2363,i_0_2460,i_0_2537,i_0_2542,i_0_2546,i_0_1844,i_0_2308,i_0_2457,i_0_2475,i_0_1659,i_0_1837,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473,i_0_1474,i_0_1518,i_0_1519,i_0_1536,i_0_1537,i_0_1538,i_0_1563,i_0_1564,i_0_1575,i_0_1578,i_0_1627,i_0_1653,i_0_1656,i_0_1678,i_0_1691,i_0_1225,i_0_1241,i_0_1499,i_0_1500,i_0_1521,i_0_1224]) ).

cnf(i_0_2552,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_2026]) ).

cnf(i_0_2553,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_1224]) ).

cnf(i_0_2554,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2026,i_0_2552,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_2534,i_0_1644,i_0_2248,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_2485,i_0_2488,i_0_1739,i_0_2513,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_2500,i_0_2541,i_0_1733,i_0_2524,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_2360,i_0_2491,i_0_2494,i_0_2497,i_0_2503,i_0_1620,i_0_2319,i_0_1688,i_0_2359,i_0_1795,i_0_2516,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_2346,i_0_2506,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1643,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_2167,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_1843,i_0_2363,i_0_2460,i_0_2537,i_0_2542,i_0_2546,i_0_1844,i_0_2308,i_0_2457,i_0_2475,i_0_2533,i_0_1659,i_0_1837,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473,i_0_1474,i_0_1518,i_0_1519,i_0_1536,i_0_1537,i_0_1538,i_0_1563,i_0_1564,i_0_1575,i_0_1578,i_0_1627,i_0_1653,i_0_1656,i_0_1678,i_0_1691,i_0_1225,i_0_1241,i_0_1499,i_0_1500,i_0_1521,i_0_1224,i_0_1240]) ).

cnf(i_0_2555,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_2026]) ).

cnf(i_0_2556,plain,
    hAPP(c_Nat_OSuc,X1) != X1,
    inference(rename_variables,[],[i_0_1843]) ).

cnf(i_0_2557,plain,
    hAPP(c_Nat_OSuc,X1) != X1,
    inference(rename_variables,[],[i_0_1843]) ).

cnf(i_0_2558,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_1240]) ).

cnf(i_0_2559,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_Omkbot,esk11_0),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)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2026,i_0_2552,i_0_2555,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_2534,i_0_1644,i_0_2248,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_2485,i_0_2488,i_0_1739,i_0_2513,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_2500,i_0_2541,i_0_1733,i_0_2524,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_2360,i_0_2491,i_0_2494,i_0_2497,i_0_2503,i_0_1620,i_0_2319,i_0_1688,i_0_2359,i_0_1795,i_0_2516,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_2346,i_0_2506,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_1643,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_2167,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_1843,i_0_2363,i_0_2460,i_0_2537,i_0_2542,i_0_2546,i_0_2557,i_0_2556,i_0_1844,i_0_2308,i_0_2457,i_0_2475,i_0_2533,i_0_1659,i_0_1837,i_0_2127,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473,i_0_1474,i_0_1518,i_0_1519,i_0_1536,i_0_1537,i_0_1538,i_0_1563,i_0_1564,i_0_1575,i_0_1578,i_0_1627,i_0_1653,i_0_1656,i_0_1678,i_0_1691,i_0_1225,i_0_1241,i_0_1499,i_0_1500,i_0_1521,i_0_1224,i_0_1240,i_0_2015]) ).

cnf(i_0_2560,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_2026]) ).

cnf(i_0_2561,plain,
    hAPP(c_Nat_OSuc,X1) != X1,
    inference(rename_variables,[],[i_0_1843]) ).

cnf(i_0_2562,plain,
    hAPP(c_Nat_OSuc,X1) != X1,
    inference(rename_variables,[],[i_0_1843]) ).

cnf(i_0_2563,plain,
    hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(rename_variables,[],[i_0_1837]) ).

cnf(i_0_2564,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_2015]) ).

cnf(i_0_2565,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2026,i_0_2552,i_0_2555,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_2534,i_0_1644,i_0_2248,i_0_1823,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_2485,i_0_2488,i_0_1739,i_0_2513,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_2500,i_0_2541,i_0_1733,i_0_2524,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_2360,i_0_2491,i_0_2494,i_0_2497,i_0_2503,i_0_1620,i_0_2319,i_0_1688,i_0_2359,i_0_1795,i_0_2516,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_2346,i_0_2506,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_2186,i_0_1643,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_2167,i_0_1503,i_0_1404,i_0_1469,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_1843,i_0_2363,i_0_2460,i_0_2537,i_0_2542,i_0_2546,i_0_2557,i_0_2556,i_0_1844,i_0_2308,i_0_2457,i_0_2475,i_0_2533,i_0_1659,i_0_1837,i_0_2127,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473,i_0_1474,i_0_1518,i_0_1519,i_0_1536,i_0_1537,i_0_1538,i_0_1563,i_0_1564,i_0_1575,i_0_1578,i_0_1627,i_0_1653,i_0_1656,i_0_1678,i_0_1691,i_0_1225,i_0_1241,i_0_1499,i_0_1500,i_0_1521,i_0_1224,i_0_1240,i_0_2015,i_0_1533]) ).

cnf(i_0_2566,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_1642]) ).

cnf(i_0_2567,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_1823]) ).

cnf(i_0_2568,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_1533]) ).

cnf(i_0_2569,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____),v_b____))),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2026,i_0_2552,i_0_2555,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_2534,i_0_1644,i_0_2248,i_0_1823,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_2485,i_0_2488,i_0_1739,i_0_2513,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_2500,i_0_2541,i_0_1733,i_0_2524,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_2360,i_0_2491,i_0_2494,i_0_2497,i_0_2503,i_0_1620,i_0_2319,i_0_1688,i_0_2359,i_0_1795,i_0_2516,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_2346,i_0_2506,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_2186,i_0_1643,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_2167,i_0_1503,i_0_1406,i_0_1404,i_0_1469,i_0_1470,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_1843,i_0_2363,i_0_2460,i_0_2537,i_0_2542,i_0_2546,i_0_2557,i_0_2556,i_0_1844,i_0_2308,i_0_2457,i_0_2475,i_0_2533,i_0_1659,i_0_1837,i_0_2127,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1882,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473,i_0_1474,i_0_1518,i_0_1519,i_0_1536,i_0_1537,i_0_1538,i_0_1563,i_0_1564,i_0_1575,i_0_1578,i_0_1627,i_0_1653,i_0_1656,i_0_1678,i_0_1691,i_0_1225,i_0_1241,i_0_1499,i_0_1500,i_0_1521,i_0_1224,i_0_1240,i_0_2015,i_0_1533,i_0_2007]) ).

cnf(i_0_2570,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_2007]) ).

cnf(i_0_2571,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2026,i_0_2552,i_0_2555,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_2534,i_0_1644,i_0_2248,i_0_1823,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_2485,i_0_2488,i_0_1739,i_0_2513,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_2500,i_0_2541,i_0_1733,i_0_2524,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_2360,i_0_2491,i_0_2494,i_0_2497,i_0_2503,i_0_1620,i_0_2319,i_0_1688,i_0_2359,i_0_1795,i_0_2516,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_2346,i_0_2506,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_2186,i_0_1643,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_2167,i_0_1503,i_0_1406,i_0_1404,i_0_1469,i_0_1470,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_1843,i_0_2363,i_0_2460,i_0_2537,i_0_2542,i_0_2546,i_0_2557,i_0_2561,i_0_2556,i_0_1844,i_0_2308,i_0_2457,i_0_2475,i_0_2533,i_0_1659,i_0_1837,i_0_2127,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1882,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473,i_0_1474,i_0_1518,i_0_1519,i_0_1536,i_0_1537,i_0_1538,i_0_1563,i_0_1564,i_0_1575,i_0_1578,i_0_1627,i_0_1653,i_0_1656,i_0_1678,i_0_1691,i_0_1225,i_0_1241,i_0_1499,i_0_1500,i_0_1521,i_0_1224,i_0_1240,i_0_2015,i_0_1533,i_0_2007,i_0_2009]) ).

cnf(i_0_2572,plain,
    hAPP(c_Nat_OSuc,X1) != X1,
    inference(rename_variables,[],[i_0_1843]) ).

cnf(i_0_2573,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_2009]) ).

cnf(i_0_2574,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,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Nat_Osize__class_Osize(tc_Nat_Onat,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),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))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2279,i_0_2026,i_0_2552,i_0_2555,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_2534,i_0_2538,i_0_1644,i_0_2248,i_0_1823,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_2485,i_0_2488,i_0_1739,i_0_2513,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_2500,i_0_2541,i_0_1733,i_0_2524,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_1750,i_0_2120,i_0_2349,i_0_2360,i_0_2491,i_0_2494,i_0_2497,i_0_2503,i_0_1620,i_0_2319,i_0_1688,i_0_2359,i_0_1795,i_0_2516,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_2346,i_0_2506,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_2186,i_0_1643,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_2167,i_0_1503,i_0_1406,i_0_1404,i_0_1469,i_0_1470,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_1843,i_0_2363,i_0_2460,i_0_2537,i_0_2542,i_0_2546,i_0_2557,i_0_2561,i_0_2572,i_0_2556,i_0_2562,i_0_1844,i_0_2308,i_0_2457,i_0_2475,i_0_2533,i_0_1659,i_0_1837,i_0_2127,i_0_2563,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1882,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473,i_0_1474,i_0_1518,i_0_1519,i_0_1536,i_0_1537,i_0_1538,i_0_1563,i_0_1564,i_0_1575,i_0_1578,i_0_1627,i_0_1653,i_0_1656,i_0_1678,i_0_1691,i_0_1225,i_0_1241,i_0_1499,i_0_1500,i_0_1521,i_0_1224,i_0_1240,i_0_2015,i_0_1533,i_0_2007,i_0_2009,i_0_1223]) ).

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),X1),X2)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X3),X1))),
    inference(rename_variables,[],[i_0_2025]) ).

cnf(i_0_2576,plain,
    hAPP(c_Nat_OSuc,X1) != X1,
    inference(rename_variables,[],[i_0_1843]) ).

cnf(i_0_2577,plain,
    hAPP(c_Nat_OSuc,X1) != X1,
    inference(rename_variables,[],[i_0_1843]) ).

cnf(i_0_2578,plain,
    hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(rename_variables,[],[i_0_1837]) ).

cnf(i_0_2579,plain,
    c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
    inference(rename_variables,[],[i_0_1851]) ).

cnf(i_0_2580,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)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1),X3),X5)))
    | X3 = X5
    | X2 = X3
    | X2 = X5
    | X4 != X5 ),
    inference(rename_variables,[],[i_0_1223]) ).

cnf(i_0_2581,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_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)))),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2279,i_0_2026,i_0_2552,i_0_2555,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_2534,i_0_2538,i_0_1644,i_0_2248,i_0_1823,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_2485,i_0_2488,i_0_1739,i_0_2513,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_2500,i_0_2541,i_0_1733,i_0_2524,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_2294,i_0_1750,i_0_2120,i_0_2349,i_0_2360,i_0_2491,i_0_2494,i_0_2497,i_0_2503,i_0_1620,i_0_2319,i_0_2352,i_0_1688,i_0_2359,i_0_1795,i_0_2516,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_2346,i_0_2506,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_2186,i_0_1643,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_2167,i_0_1503,i_0_1406,i_0_1404,i_0_1469,i_0_1470,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_2464,i_0_1843,i_0_2363,i_0_2460,i_0_2537,i_0_2542,i_0_2546,i_0_2557,i_0_2561,i_0_2572,i_0_2556,i_0_2562,i_0_1844,i_0_2308,i_0_2457,i_0_2475,i_0_2533,i_0_1659,i_0_1837,i_0_2127,i_0_2563,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1882,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473,i_0_1474,i_0_1518,i_0_1519,i_0_1536,i_0_1537,i_0_1538,i_0_1563,i_0_1564,i_0_1575,i_0_1578,i_0_1627,i_0_1653,i_0_1656,i_0_1678,i_0_1691,i_0_1225,i_0_1241,i_0_1499,i_0_1500,i_0_1521,i_0_1224,i_0_1240,i_0_2015,i_0_1533,i_0_2007,i_0_2009,i_0_1223,i_0_1170]) ).

cnf(i_0_2582,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
    inference(rename_variables,[],[i_0_1719]) ).

cnf(i_0_2583,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_1620]) ).

cnf(i_0_2584,plain,
    c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
    inference(rename_variables,[],[i_0_1645]) ).

cnf(i_0_2585,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_fun(X2,tc_HOL_Obool),c_Set_Oimage(X1,X2,X6,X5)),X4))
    | c_Finite__Set_Ocard(X2,X4) = c_Finite__Set_Ocard(X1,X5)
    | ~ c_Finite__Set_Ofinite(X2,X4)
    | ~ c_Finite__Set_Ofinite(X1,X5)
    | ~ c_Fun_Oinj__on(X2,X1,X3,X4)
    | ~ c_Fun_Oinj__on(X1,X2,X6,X5) ),
    inference(rename_variables,[],[i_0_1170]) ).

cnf(i_0_2586,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),esk34_3(c_Nat_OSuc,tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oindi))) != esk34_3(c_Nat_OSuc,tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oindi),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2279,i_0_2026,i_0_2552,i_0_2555,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_2534,i_0_2538,i_0_1644,i_0_2248,i_0_1823,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_2485,i_0_2488,i_0_1739,i_0_2513,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_2500,i_0_2541,i_0_1733,i_0_2524,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_2294,i_0_1750,i_0_2120,i_0_2349,i_0_2360,i_0_2491,i_0_2494,i_0_2497,i_0_2503,i_0_1620,i_0_2319,i_0_2352,i_0_1688,i_0_2359,i_0_1795,i_0_2516,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_2346,i_0_2506,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_2186,i_0_1643,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_2167,i_0_1503,i_0_1406,i_0_1404,i_0_1469,i_0_1470,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_2464,i_0_1843,i_0_2363,i_0_2460,i_0_2537,i_0_2542,i_0_2546,i_0_2557,i_0_2561,i_0_2572,i_0_2556,i_0_2562,i_0_1844,i_0_2308,i_0_2457,i_0_2475,i_0_2533,i_0_1659,i_0_1837,i_0_2127,i_0_2563,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1882,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473,i_0_1474,i_0_1518,i_0_1519,i_0_1536,i_0_1537,i_0_1538,i_0_1563,i_0_1564,i_0_1575,i_0_1578,i_0_1627,i_0_1653,i_0_1656,i_0_1678,i_0_1691,i_0_1225,i_0_1241,i_0_1499,i_0_1500,i_0_1521,i_0_1224,i_0_1240,i_0_2015,i_0_1533,i_0_2007,i_0_2009,i_0_1223,i_0_1170,i_0_1278]) ).

cnf(i_0_2587,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),esk34_3(X3,X2,X1))) != esk34_3(X3,X2,X1) ),
    inference(rename_variables,[],[i_0_1278]) ).

cnf(i_0_2588,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2279,i_0_2026,i_0_2552,i_0_2555,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_2534,i_0_2538,i_0_1644,i_0_2248,i_0_1823,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_2485,i_0_2488,i_0_1739,i_0_2513,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_2500,i_0_2541,i_0_1733,i_0_2524,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_2294,i_0_1750,i_0_2120,i_0_2349,i_0_2360,i_0_2491,i_0_2494,i_0_2497,i_0_2503,i_0_1620,i_0_2319,i_0_2352,i_0_1688,i_0_2359,i_0_1795,i_0_2516,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_2346,i_0_2506,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_2186,i_0_1643,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_2167,i_0_1503,i_0_1406,i_0_1404,i_0_1469,i_0_1470,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_2464,i_0_1843,i_0_2363,i_0_2460,i_0_2537,i_0_2542,i_0_2546,i_0_2557,i_0_2561,i_0_2572,i_0_2556,i_0_2562,i_0_1844,i_0_2308,i_0_2457,i_0_2475,i_0_2533,i_0_1659,i_0_1837,i_0_2127,i_0_2563,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1882,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473,i_0_1474,i_0_1518,i_0_1519,i_0_1536,i_0_1537,i_0_1538,i_0_1563,i_0_1564,i_0_1575,i_0_1578,i_0_1627,i_0_1653,i_0_1656,i_0_1678,i_0_1691,i_0_1225,i_0_1241,i_0_1499,i_0_1500,i_0_1521,i_0_1224,i_0_1240,i_0_2015,i_0_1533,i_0_2007,i_0_2009,i_0_1223,i_0_1170,i_0_1278,i_0_1535]) ).

cnf(i_0_2589,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_1535]) ).

cnf(i_0_2590,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2279,i_0_2026,i_0_2552,i_0_2555,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_2534,i_0_2538,i_0_1644,i_0_2248,i_0_1823,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_2485,i_0_2488,i_0_1739,i_0_2513,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_2500,i_0_2541,i_0_1733,i_0_2524,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_2294,i_0_1750,i_0_2120,i_0_2349,i_0_2360,i_0_2491,i_0_2494,i_0_2497,i_0_2503,i_0_1620,i_0_2319,i_0_2352,i_0_1688,i_0_2359,i_0_1795,i_0_2516,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_2346,i_0_2506,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_2186,i_0_1643,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_2167,i_0_1503,i_0_1406,i_0_1404,i_0_1469,i_0_1470,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_2464,i_0_1843,i_0_2363,i_0_2460,i_0_2537,i_0_2542,i_0_2546,i_0_2557,i_0_2561,i_0_2572,i_0_2556,i_0_2562,i_0_1844,i_0_2308,i_0_2457,i_0_2475,i_0_2533,i_0_1659,i_0_1837,i_0_2127,i_0_2563,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1882,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473,i_0_1474,i_0_1518,i_0_1519,i_0_1536,i_0_1537,i_0_1538,i_0_1563,i_0_1564,i_0_1575,i_0_1578,i_0_1627,i_0_1653,i_0_1656,i_0_1678,i_0_1691,i_0_1225,i_0_1241,i_0_1499,i_0_1500,i_0_1521,i_0_1224,i_0_1240,i_0_2015,i_0_1533,i_0_2007,i_0_2009,i_0_1223,i_0_1170,i_0_1278,i_0_1535,i_0_1594]) ).

cnf(i_0_2591,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_1594]) ).

cnf(i_0_2592,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2279,i_0_2026,i_0_2552,i_0_2555,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_2534,i_0_2538,i_0_1644,i_0_2248,i_0_1823,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_2485,i_0_2488,i_0_1739,i_0_2513,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_2500,i_0_2541,i_0_1733,i_0_2524,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_2294,i_0_1750,i_0_2120,i_0_2349,i_0_2360,i_0_2491,i_0_2494,i_0_2497,i_0_2503,i_0_1620,i_0_2319,i_0_2352,i_0_1688,i_0_2359,i_0_1795,i_0_2516,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_2346,i_0_2506,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_2186,i_0_1643,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_2167,i_0_1503,i_0_1406,i_0_1404,i_0_1469,i_0_1470,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_2464,i_0_1843,i_0_2363,i_0_2460,i_0_2537,i_0_2542,i_0_2546,i_0_2557,i_0_2561,i_0_2572,i_0_2556,i_0_2562,i_0_1844,i_0_2308,i_0_2457,i_0_2475,i_0_2533,i_0_1659,i_0_1837,i_0_2127,i_0_2563,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1882,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473,i_0_1474,i_0_1518,i_0_1519,i_0_1536,i_0_1537,i_0_1538,i_0_1563,i_0_1564,i_0_1575,i_0_1578,i_0_1627,i_0_1653,i_0_1656,i_0_1678,i_0_1691,i_0_1225,i_0_1241,i_0_1499,i_0_1500,i_0_1521,i_0_1224,i_0_1240,i_0_2015,i_0_1533,i_0_2007,i_0_2009,i_0_1223,i_0_1170,i_0_1278,i_0_1535,i_0_1594,i_0_1657]) ).

cnf(i_0_2593,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_1657]) ).

cnf(i_0_2594,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)),tc_Nat_Onat)),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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2279,i_0_2026,i_0_2552,i_0_2555,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_2534,i_0_2538,i_0_1644,i_0_2248,i_0_1823,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_2485,i_0_2488,i_0_1739,i_0_2513,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_2500,i_0_2541,i_0_1733,i_0_2524,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_2294,i_0_1750,i_0_2120,i_0_2349,i_0_2360,i_0_2491,i_0_2494,i_0_2497,i_0_2503,i_0_1620,i_0_2319,i_0_2352,i_0_1688,i_0_2359,i_0_1795,i_0_2516,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_2346,i_0_2506,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_2186,i_0_1643,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_2167,i_0_1503,i_0_1406,i_0_1404,i_0_1469,i_0_1470,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_2464,i_0_1843,i_0_2363,i_0_2460,i_0_2537,i_0_2542,i_0_2546,i_0_2557,i_0_2561,i_0_2572,i_0_2556,i_0_2562,i_0_1844,i_0_2308,i_0_2457,i_0_2475,i_0_2533,i_0_1659,i_0_1837,i_0_2127,i_0_2563,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1882,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473,i_0_1474,i_0_1518,i_0_1519,i_0_1536,i_0_1537,i_0_1538,i_0_1563,i_0_1564,i_0_1575,i_0_1578,i_0_1627,i_0_1653,i_0_1656,i_0_1678,i_0_1691,i_0_1225,i_0_1241,i_0_1499,i_0_1500,i_0_1521,i_0_1224,i_0_1240,i_0_2015,i_0_1533,i_0_2007,i_0_2009,i_0_1223,i_0_1170,i_0_1278,i_0_1535,i_0_1594,i_0_1657,i_0_1764]) ).

cnf(i_0_2595,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_1764]) ).

cnf(i_0_2596,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2279,i_0_2026,i_0_2552,i_0_2555,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_2534,i_0_2538,i_0_1644,i_0_2248,i_0_1823,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_2485,i_0_2488,i_0_1739,i_0_2513,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_2500,i_0_2541,i_0_1733,i_0_2524,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_2294,i_0_1750,i_0_2120,i_0_2349,i_0_2360,i_0_2491,i_0_2494,i_0_2497,i_0_2503,i_0_1620,i_0_2319,i_0_2352,i_0_1688,i_0_2359,i_0_1795,i_0_2516,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_2346,i_0_2506,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_2186,i_0_1643,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_2167,i_0_1503,i_0_1406,i_0_1404,i_0_1469,i_0_1470,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_2464,i_0_1843,i_0_2363,i_0_2460,i_0_2537,i_0_2542,i_0_2546,i_0_2557,i_0_2561,i_0_2572,i_0_2556,i_0_2562,i_0_1844,i_0_2308,i_0_2457,i_0_2475,i_0_2533,i_0_1659,i_0_1837,i_0_2127,i_0_2563,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1882,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473,i_0_1474,i_0_1518,i_0_1519,i_0_1536,i_0_1537,i_0_1538,i_0_1563,i_0_1564,i_0_1575,i_0_1578,i_0_1627,i_0_1653,i_0_1656,i_0_1678,i_0_1691,i_0_1225,i_0_1241,i_0_1499,i_0_1500,i_0_1521,i_0_1224,i_0_1240,i_0_2015,i_0_1533,i_0_2007,i_0_2009,i_0_1223,i_0_1170,i_0_1278,i_0_1535,i_0_1594,i_0_1657,i_0_1764,i_0_1887]) ).

cnf(i_0_2597,plain,
    c_Finite__Set_Ofinite(X1,c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,X1,hAPP(c_COMBB(tc_Arrow__Order__Mirabelle_Oindi,X1,tc_Arrow__Order__Mirabelle_Oindi,X2),c_COMBI(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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2279,i_0_2026,i_0_2552,i_0_2555,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_2534,i_0_2538,i_0_1644,i_0_2248,i_0_1823,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_2485,i_0_2488,i_0_1739,i_0_2513,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_2500,i_0_2541,i_0_1733,i_0_2524,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_2294,i_0_1750,i_0_2120,i_0_2349,i_0_2360,i_0_2491,i_0_2494,i_0_2497,i_0_2503,i_0_1620,i_0_2319,i_0_2352,i_0_1688,i_0_2359,i_0_1795,i_0_2516,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_2346,i_0_2506,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_2186,i_0_1643,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_2167,i_0_1503,i_0_1406,i_0_1404,i_0_1469,i_0_1470,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_2464,i_0_1843,i_0_2363,i_0_2460,i_0_2537,i_0_2542,i_0_2546,i_0_2557,i_0_2561,i_0_2572,i_0_2556,i_0_2562,i_0_1844,i_0_2308,i_0_2457,i_0_2475,i_0_2533,i_0_1659,i_0_1837,i_0_2127,i_0_2563,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1882,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473,i_0_1474,i_0_1518,i_0_1519,i_0_1536,i_0_1537,i_0_1538,i_0_1563,i_0_1564,i_0_1575,i_0_1578,i_0_1627,i_0_1653,i_0_1656,i_0_1678,i_0_1691,i_0_1225,i_0_1241,i_0_1499,i_0_1500,i_0_1521,i_0_1224,i_0_1240,i_0_2015,i_0_1533,i_0_2007,i_0_2009,i_0_1223,i_0_1170,i_0_1278,i_0_1535,i_0_1594,i_0_1657,i_0_1764,i_0_1887,i_0_1239]) ).

cnf(i_0_2598,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_1239]) ).

cnf(i_0_2599,plain,
    ( ~ c_Finite__Set_Ofinite(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1),X2))
    | c_Finite__Set_Ocard(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Set_Oinsert(tc_prod(tc_Arrow__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(c_Arrow__Order__Mirabelle_Omktop,X1),X2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Finite__Set_Ocard(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1),X2))) ),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2279,i_0_2575,i_0_2026,i_0_2552,i_0_2555,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_2534,i_0_2538,i_0_1644,i_0_2248,i_0_1823,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_2485,i_0_2488,i_0_1739,i_0_2513,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_2500,i_0_2541,i_0_1733,i_0_2524,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_2294,i_0_1750,i_0_2120,i_0_2349,i_0_2360,i_0_2491,i_0_2494,i_0_2497,i_0_2503,i_0_1620,i_0_2319,i_0_2352,i_0_1688,i_0_2359,i_0_1795,i_0_2516,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_2346,i_0_2506,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_2186,i_0_1643,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_2167,i_0_1503,i_0_1406,i_0_1404,i_0_1469,i_0_1470,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_2464,i_0_1843,i_0_2363,i_0_2460,i_0_2537,i_0_2542,i_0_2546,i_0_2557,i_0_2561,i_0_2572,i_0_2556,i_0_2562,i_0_1844,i_0_2308,i_0_2457,i_0_2475,i_0_2533,i_0_1659,i_0_1837,i_0_2127,i_0_2563,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1882,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473,i_0_1474,i_0_1518,i_0_1519,i_0_1536,i_0_1537,i_0_1538,i_0_1563,i_0_1564,i_0_1575,i_0_1578,i_0_1627,i_0_1653,i_0_1656,i_0_1678,i_0_1691,i_0_1225,i_0_1241,i_0_1499,i_0_1500,i_0_1521,i_0_1224,i_0_1240,i_0_2015,i_0_1533,i_0_2007,i_0_2009,i_0_1223,i_0_1170,i_0_1278,i_0_1535,i_0_1594,i_0_1657,i_0_1764,i_0_1887,i_0_1239,i_0_1577]) ).

cnf(i_0_2600,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | c_Finite__Set_Ocard(X1,c_Set_Oinsert(X1,X2,X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Finite__Set_Ocard(X1,X3))
    | ~ c_Finite__Set_Ofinite(X1,X3) ),
    inference(rename_variables,[],[i_0_1577]) ).

cnf(i_0_2601,plain,
    ~ 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,X1,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2279,i_0_2575,i_0_2026,i_0_2552,i_0_2555,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_2534,i_0_2538,i_0_1644,i_0_2248,i_0_1823,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_2463,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_2485,i_0_2488,i_0_1739,i_0_2513,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_2500,i_0_2541,i_0_1733,i_0_2524,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_2294,i_0_1750,i_0_2120,i_0_2349,i_0_2360,i_0_2491,i_0_2494,i_0_2497,i_0_2503,i_0_1620,i_0_2319,i_0_2352,i_0_1688,i_0_2359,i_0_1795,i_0_2516,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_2346,i_0_2506,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_2186,i_0_1643,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_2167,i_0_1503,i_0_1406,i_0_1404,i_0_1469,i_0_1470,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_2464,i_0_1843,i_0_2363,i_0_2460,i_0_2537,i_0_2542,i_0_2546,i_0_2557,i_0_2561,i_0_2572,i_0_2556,i_0_2562,i_0_1844,i_0_2308,i_0_2457,i_0_2475,i_0_2533,i_0_1659,i_0_1837,i_0_2127,i_0_2563,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1882,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473,i_0_1474,i_0_1518,i_0_1519,i_0_1536,i_0_1537,i_0_1538,i_0_1563,i_0_1564,i_0_1575,i_0_1578,i_0_1627,i_0_1653,i_0_1656,i_0_1678,i_0_1691,i_0_1225,i_0_1241,i_0_1499,i_0_1500,i_0_1521,i_0_1224,i_0_1240,i_0_2015,i_0_1533,i_0_2007,i_0_2009,i_0_1223,i_0_1170,i_0_1278,i_0_1535,i_0_1594,i_0_1657,i_0_1764,i_0_1887,i_0_1239,i_0_1577,i_0_1390]) ).

cnf(i_0_2602,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_1543]) ).

cnf(i_0_2603,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_1390]) ).

cnf(i_0_2604,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,esk8_0))),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2279,i_0_2575,i_0_2026,i_0_2552,i_0_2555,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_2534,i_0_2538,i_0_1644,i_0_2248,i_0_1823,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_2463,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_2485,i_0_2488,i_0_1739,i_0_2513,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_2500,i_0_2541,i_0_1733,i_0_2524,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_2294,i_0_1750,i_0_2120,i_0_2349,i_0_2360,i_0_2491,i_0_2494,i_0_2497,i_0_2503,i_0_1620,i_0_2319,i_0_2352,i_0_1688,i_0_2359,i_0_1795,i_0_2516,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_2346,i_0_2506,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_2186,i_0_1643,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_1447,i_0_2164,i_0_2167,i_0_1503,i_0_1406,i_0_1404,i_0_1469,i_0_1470,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_2464,i_0_1843,i_0_2363,i_0_2460,i_0_2537,i_0_2542,i_0_2546,i_0_2557,i_0_2561,i_0_2572,i_0_2556,i_0_2562,i_0_1844,i_0_2308,i_0_2457,i_0_2475,i_0_2533,i_0_1659,i_0_1837,i_0_2127,i_0_2563,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1882,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473,i_0_1474,i_0_1518,i_0_1519,i_0_1536,i_0_1537,i_0_1538,i_0_1563,i_0_1564,i_0_1575,i_0_1578,i_0_1627,i_0_1653,i_0_1656,i_0_1678,i_0_1691,i_0_1225,i_0_1241,i_0_1499,i_0_1500,i_0_1521,i_0_1224,i_0_1240,i_0_2015,i_0_1533,i_0_2007,i_0_2009,i_0_1223,i_0_1170,i_0_1278,i_0_1535,i_0_1594,i_0_1657,i_0_1764,i_0_1887,i_0_1239,i_0_1577,i_0_1390,i_0_1587]) ).

cnf(i_0_2605,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_1587]) ).

cnf(i_0_2606,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2279,i_0_2575,i_0_2026,i_0_2552,i_0_2555,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_2534,i_0_2538,i_0_1644,i_0_2248,i_0_1823,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_2463,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_2485,i_0_2488,i_0_1739,i_0_2513,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_2500,i_0_2541,i_0_1733,i_0_2524,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_2294,i_0_1750,i_0_2120,i_0_2349,i_0_2360,i_0_2491,i_0_2494,i_0_2497,i_0_2503,i_0_1620,i_0_2319,i_0_2352,i_0_1688,i_0_2359,i_0_1795,i_0_2516,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_2346,i_0_2506,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_2186,i_0_1643,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_2375,i_0_1447,i_0_2164,i_0_2167,i_0_1503,i_0_1406,i_0_1404,i_0_1469,i_0_1470,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_2464,i_0_1843,i_0_2363,i_0_2460,i_0_2537,i_0_2542,i_0_2546,i_0_2557,i_0_2561,i_0_2572,i_0_2556,i_0_2562,i_0_1844,i_0_2308,i_0_2457,i_0_2475,i_0_2533,i_0_1659,i_0_1837,i_0_2127,i_0_2563,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1882,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473,i_0_1474,i_0_1518,i_0_1519,i_0_1536,i_0_1537,i_0_1538,i_0_1563,i_0_1564,i_0_1575,i_0_1578,i_0_1627,i_0_1653,i_0_1656,i_0_1678,i_0_1691,i_0_1225,i_0_1241,i_0_1499,i_0_1500,i_0_1521,i_0_1224,i_0_1240,i_0_2015,i_0_1533,i_0_2007,i_0_2009,i_0_1223,i_0_1170,i_0_1278,i_0_1535,i_0_1594,i_0_1657,i_0_1764,i_0_1887,i_0_1239,i_0_1577,i_0_1390,i_0_1587,i_0_1375]) ).

cnf(i_0_2607,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_1446]) ).

cnf(i_0_2608,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_1375]) ).

cnf(i_0_2609,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2279,i_0_2575,i_0_2026,i_0_2552,i_0_2555,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_2534,i_0_2538,i_0_1644,i_0_2248,i_0_1823,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_2463,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_2485,i_0_2488,i_0_1739,i_0_2513,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_2500,i_0_2541,i_0_1733,i_0_2524,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_2294,i_0_1750,i_0_2120,i_0_2349,i_0_2360,i_0_2491,i_0_2494,i_0_2497,i_0_2503,i_0_1620,i_0_2319,i_0_2352,i_0_1688,i_0_2359,i_0_1795,i_0_2516,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_2346,i_0_2506,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_2186,i_0_1643,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_2375,i_0_1447,i_0_2164,i_0_2167,i_0_2530,i_0_1503,i_0_1406,i_0_1404,i_0_1469,i_0_1470,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_2464,i_0_1843,i_0_2363,i_0_2460,i_0_2537,i_0_2542,i_0_2546,i_0_2557,i_0_2561,i_0_2572,i_0_2556,i_0_2562,i_0_1844,i_0_2308,i_0_2457,i_0_2475,i_0_2533,i_0_1659,i_0_1837,i_0_2127,i_0_2563,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1882,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473,i_0_1474,i_0_1518,i_0_1519,i_0_1536,i_0_1537,i_0_1538,i_0_1563,i_0_1564,i_0_1575,i_0_1578,i_0_1627,i_0_1653,i_0_1656,i_0_1678,i_0_1691,i_0_1225,i_0_1241,i_0_1499,i_0_1500,i_0_1521,i_0_1224,i_0_1240,i_0_2015,i_0_1533,i_0_2007,i_0_2009,i_0_1223,i_0_1170,i_0_1278,i_0_1535,i_0_1594,i_0_1657,i_0_1764,i_0_1887,i_0_1239,i_0_1577,i_0_1390,i_0_1587,i_0_1375,i_0_1376]) ).

cnf(i_0_2610,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_1447]) ).

cnf(i_0_2611,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_1376]) ).

cnf(i_0_2612,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2279,i_0_2575,i_0_2026,i_0_2552,i_0_2555,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_2534,i_0_2538,i_0_1644,i_0_2248,i_0_1823,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_2463,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_2485,i_0_2488,i_0_1739,i_0_2513,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_2500,i_0_2541,i_0_1733,i_0_2524,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_2294,i_0_1750,i_0_2120,i_0_2349,i_0_2360,i_0_2491,i_0_2494,i_0_2497,i_0_2503,i_0_1620,i_0_2319,i_0_2352,i_0_1688,i_0_2359,i_0_1795,i_0_2516,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_2346,i_0_2506,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_2186,i_0_1643,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_2375,i_0_1447,i_0_2164,i_0_2167,i_0_2530,i_0_2610,i_0_1503,i_0_1406,i_0_1404,i_0_1469,i_0_1470,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_2464,i_0_1843,i_0_2363,i_0_2460,i_0_2537,i_0_2542,i_0_2546,i_0_2557,i_0_2561,i_0_2572,i_0_2556,i_0_2562,i_0_1844,i_0_2308,i_0_2457,i_0_2475,i_0_2533,i_0_1659,i_0_1837,i_0_2127,i_0_2563,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1882,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473,i_0_1474,i_0_1518,i_0_1519,i_0_1536,i_0_1537,i_0_1538,i_0_1563,i_0_1564,i_0_1575,i_0_1578,i_0_1627,i_0_1653,i_0_1656,i_0_1678,i_0_1691,i_0_1225,i_0_1241,i_0_1499,i_0_1500,i_0_1521,i_0_1224,i_0_1240,i_0_2015,i_0_1533,i_0_2007,i_0_2009,i_0_1223,i_0_1170,i_0_1278,i_0_1535,i_0_1594,i_0_1657,i_0_1764,i_0_1887,i_0_1239,i_0_1577,i_0_1390,i_0_1587,i_0_1375,i_0_1376,i_0_1460]) ).

cnf(i_0_2613,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_1447]) ).

cnf(i_0_2614,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_1460]) ).

cnf(i_0_2615,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2279,i_0_2575,i_0_2026,i_0_2552,i_0_2555,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_2534,i_0_2538,i_0_1644,i_0_2248,i_0_1823,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_2463,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_2485,i_0_2488,i_0_1739,i_0_2513,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_2500,i_0_2541,i_0_1733,i_0_2524,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_2294,i_0_1750,i_0_2120,i_0_2349,i_0_2360,i_0_2491,i_0_2494,i_0_2497,i_0_2503,i_0_1620,i_0_2319,i_0_2352,i_0_1688,i_0_2359,i_0_1795,i_0_2516,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_2346,i_0_2506,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_2186,i_0_1643,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_2375,i_0_2607,i_0_1447,i_0_2164,i_0_2167,i_0_2530,i_0_2610,i_0_1503,i_0_1406,i_0_1404,i_0_1469,i_0_1470,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_2464,i_0_1843,i_0_2363,i_0_2460,i_0_2537,i_0_2542,i_0_2546,i_0_2557,i_0_2561,i_0_2572,i_0_2556,i_0_2562,i_0_1844,i_0_2308,i_0_2457,i_0_2475,i_0_2533,i_0_1659,i_0_1837,i_0_2127,i_0_2563,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1882,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473,i_0_1474,i_0_1518,i_0_1519,i_0_1536,i_0_1537,i_0_1538,i_0_1563,i_0_1564,i_0_1575,i_0_1578,i_0_1627,i_0_1653,i_0_1656,i_0_1678,i_0_1691,i_0_1225,i_0_1241,i_0_1499,i_0_1500,i_0_1521,i_0_1224,i_0_1240,i_0_2015,i_0_1533,i_0_2007,i_0_2009,i_0_1223,i_0_1170,i_0_1278,i_0_1535,i_0_1594,i_0_1657,i_0_1764,i_0_1887,i_0_1239,i_0_1577,i_0_1390,i_0_1587,i_0_1375,i_0_1376,i_0_1460,i_0_1539]) ).

cnf(i_0_2616,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_1446]) ).

cnf(i_0_2617,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_1539]) ).

cnf(i_0_2618,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_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2279,i_0_2575,i_0_2026,i_0_2552,i_0_2555,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_2534,i_0_2538,i_0_1644,i_0_2248,i_0_1823,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_2463,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_2485,i_0_2488,i_0_1739,i_0_2513,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_2500,i_0_2541,i_0_1733,i_0_2524,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_2294,i_0_1750,i_0_2120,i_0_2349,i_0_2360,i_0_2491,i_0_2494,i_0_2497,i_0_2503,i_0_1620,i_0_2319,i_0_2352,i_0_1688,i_0_2359,i_0_1795,i_0_2516,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_2346,i_0_2506,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_2186,i_0_1643,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_2375,i_0_2607,i_0_1447,i_0_2164,i_0_2167,i_0_2530,i_0_2610,i_0_1503,i_0_1406,i_0_1404,i_0_1469,i_0_1470,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_2464,i_0_1843,i_0_2363,i_0_2460,i_0_2537,i_0_2542,i_0_2546,i_0_2557,i_0_2561,i_0_2572,i_0_2556,i_0_2562,i_0_1844,i_0_2308,i_0_2457,i_0_2475,i_0_2533,i_0_1659,i_0_1837,i_0_2127,i_0_2563,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1882,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473,i_0_1474,i_0_1518,i_0_1519,i_0_1536,i_0_1537,i_0_1538,i_0_1563,i_0_1564,i_0_1575,i_0_1578,i_0_1627,i_0_1653,i_0_1656,i_0_1678,i_0_1691,i_0_1225,i_0_1241,i_0_1499,i_0_1500,i_0_1521,i_0_1224,i_0_1240,i_0_2015,i_0_1533,i_0_2007,i_0_2009,i_0_1223,i_0_1170,i_0_1278,i_0_1535,i_0_1594,i_0_1657,i_0_1764,i_0_1887,i_0_1239,i_0_1577,i_0_1390,i_0_1587,i_0_1375,i_0_1376,i_0_1460,i_0_1539,i_0_1436]) ).

cnf(i_0_2619,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_1436]) ).

cnf(i_0_2620,plain,
    ( ~ c_Finite__Set_Ofinite(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1),X2))
    | c_Finite__Set_Ocard(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Set_Oinsert(tc_prod(tc_Arrow__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(c_Arrow__Order__Mirabelle_Omktop,X1),X2))) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1),X2))) ),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2279,i_0_2575,i_0_2026,i_0_2552,i_0_2555,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_2534,i_0_2538,i_0_1644,i_0_2248,i_0_1823,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_2463,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_2485,i_0_2488,i_0_1739,i_0_2513,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_2500,i_0_2541,i_0_1733,i_0_2524,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_2294,i_0_1750,i_0_2120,i_0_2349,i_0_2360,i_0_2491,i_0_2494,i_0_2497,i_0_2503,i_0_1620,i_0_2319,i_0_2352,i_0_1688,i_0_2359,i_0_1795,i_0_2516,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_2346,i_0_2506,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_2186,i_0_1643,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_2375,i_0_2607,i_0_1447,i_0_2164,i_0_2167,i_0_2530,i_0_2610,i_0_1503,i_0_1406,i_0_1404,i_0_1469,i_0_1470,i_0_1341,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_2464,i_0_1843,i_0_2363,i_0_2460,i_0_2537,i_0_2542,i_0_2546,i_0_2557,i_0_2561,i_0_2572,i_0_2556,i_0_2562,i_0_1844,i_0_2308,i_0_2457,i_0_2475,i_0_2533,i_0_1659,i_0_1837,i_0_2127,i_0_2563,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1882,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473,i_0_1474,i_0_1518,i_0_1519,i_0_1536,i_0_1537,i_0_1538,i_0_1563,i_0_1564,i_0_1575,i_0_1578,i_0_1627,i_0_1653,i_0_1656,i_0_1678,i_0_1691,i_0_1225,i_0_1241,i_0_1499,i_0_1500,i_0_1521,i_0_1224,i_0_1240,i_0_2015,i_0_1533,i_0_2007,i_0_2009,i_0_1223,i_0_1170,i_0_1278,i_0_1535,i_0_1594,i_0_1657,i_0_1764,i_0_1887,i_0_1239,i_0_1577,i_0_1390,i_0_1587,i_0_1375,i_0_1376,i_0_1460,i_0_1539,i_0_1436,i_0_1612]) ).

cnf(i_0_2621,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(rename_variables,[],[i_0_1612]) ).

cnf(i_0_2622,plain,
    ( c_Arrow__Order__Mirabelle_Odictator(v_F,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),esk23_2(X1,v_F)),esk24_2(X1,v_F))),hAPP(v_F,esk22_2(X1,v_F)))) ),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2279,i_0_2575,i_0_2026,i_0_2552,i_0_2555,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_2534,i_0_2538,i_0_1644,i_0_2248,i_0_1823,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_2463,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_2485,i_0_2488,i_0_1739,i_0_2513,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_2500,i_0_2541,i_0_1733,i_0_2524,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_2294,i_0_1750,i_0_2120,i_0_2349,i_0_2360,i_0_2491,i_0_2494,i_0_2497,i_0_2503,i_0_1620,i_0_2319,i_0_2352,i_0_1688,i_0_2359,i_0_1795,i_0_2516,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_2346,i_0_2506,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_2186,i_0_1643,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_2375,i_0_2607,i_0_1447,i_0_2164,i_0_2167,i_0_2530,i_0_2610,i_0_1503,i_0_1406,i_0_1404,i_0_1469,i_0_1470,i_0_1341,i_0_1161,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_2464,i_0_1843,i_0_2363,i_0_2460,i_0_2537,i_0_2542,i_0_2546,i_0_2557,i_0_2561,i_0_2572,i_0_2556,i_0_2562,i_0_1844,i_0_2308,i_0_2457,i_0_2475,i_0_2533,i_0_1659,i_0_1837,i_0_2127,i_0_2563,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1882,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473,i_0_1474,i_0_1518,i_0_1519,i_0_1536,i_0_1537,i_0_1538,i_0_1563,i_0_1564,i_0_1575,i_0_1578,i_0_1627,i_0_1653,i_0_1656,i_0_1678,i_0_1691,i_0_1225,i_0_1241,i_0_1499,i_0_1500,i_0_1521,i_0_1224,i_0_1240,i_0_2015,i_0_1533,i_0_2007,i_0_2009,i_0_1223,i_0_1170,i_0_1278,i_0_1535,i_0_1594,i_0_1657,i_0_1764,i_0_1887,i_0_1239,i_0_1577,i_0_1390,i_0_1587,i_0_1375,i_0_1376,i_0_1460,i_0_1539,i_0_1436,i_0_1612,i_0_1146]) ).

cnf(i_0_2623,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))),X1),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),esk23_2(X2,X1)),esk24_2(X2,X1))),hAPP(X1,esk22_2(X2,X1))))
    | c_Arrow__Order__Mirabelle_Odictator(X1,X2) ),
    inference(rename_variables,[],[i_0_1146]) ).

cnf(i_0_2624,plain,
    ( c_Arrow__Order__Mirabelle_Odictator(v_F,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),esk23_2(X1,v_F)),esk24_2(X1,v_F))),hAPP(esk22_2(X1,v_F),X1))) ),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2279,i_0_2575,i_0_2026,i_0_2552,i_0_2555,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_2534,i_0_2538,i_0_1644,i_0_2248,i_0_1823,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_2463,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_2485,i_0_2488,i_0_1739,i_0_2513,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_2500,i_0_2541,i_0_1733,i_0_2524,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_2294,i_0_1750,i_0_2120,i_0_2349,i_0_2360,i_0_2491,i_0_2494,i_0_2497,i_0_2503,i_0_1620,i_0_2319,i_0_2352,i_0_1688,i_0_2359,i_0_1795,i_0_2516,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_2346,i_0_2506,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_2186,i_0_1643,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_2375,i_0_2607,i_0_1447,i_0_2164,i_0_2167,i_0_2530,i_0_2610,i_0_1503,i_0_1406,i_0_1404,i_0_1469,i_0_1470,i_0_1341,i_0_1161,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_2464,i_0_1843,i_0_2363,i_0_2460,i_0_2537,i_0_2542,i_0_2546,i_0_2557,i_0_2561,i_0_2572,i_0_2556,i_0_2562,i_0_1844,i_0_2308,i_0_2457,i_0_2475,i_0_2533,i_0_1659,i_0_1837,i_0_2127,i_0_2563,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1882,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473,i_0_1474,i_0_1518,i_0_1519,i_0_1536,i_0_1537,i_0_1538,i_0_1563,i_0_1564,i_0_1575,i_0_1578,i_0_1627,i_0_1653,i_0_1656,i_0_1678,i_0_1691,i_0_1225,i_0_1241,i_0_1499,i_0_1500,i_0_1521,i_0_1224,i_0_1240,i_0_2015,i_0_1533,i_0_2007,i_0_2009,i_0_1223,i_0_1170,i_0_1278,i_0_1535,i_0_1594,i_0_1657,i_0_1764,i_0_1887,i_0_1239,i_0_1577,i_0_1390,i_0_1587,i_0_1375,i_0_1376,i_0_1460,i_0_1539,i_0_1436,i_0_1612,i_0_1146,i_0_1147]) ).

cnf(i_0_2625,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))),X1),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),esk23_2(X2,X1)),esk24_2(X2,X1))),hAPP(esk22_2(X2,X1),X2)))
    | c_Arrow__Order__Mirabelle_Odictator(X1,X2) ),
    inference(rename_variables,[],[i_0_1147]) ).

cnf(i_0_2626,plain,
    ( c_Arrow__Order__Mirabelle_Odictator(v_F,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))),esk22_2(X1,v_F)),c_Arrow__Order__Mirabelle_OProf)) ),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2279,i_0_2575,i_0_2026,i_0_2552,i_0_2555,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_2534,i_0_2538,i_0_1644,i_0_2248,i_0_1823,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_2463,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_2485,i_0_2488,i_0_1739,i_0_2513,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_2500,i_0_2541,i_0_1733,i_0_2524,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_2294,i_0_1750,i_0_2120,i_0_2349,i_0_2360,i_0_2491,i_0_2494,i_0_2497,i_0_2503,i_0_1620,i_0_2319,i_0_2352,i_0_1688,i_0_2359,i_0_1795,i_0_2516,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_2346,i_0_2506,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_2186,i_0_1643,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_2375,i_0_2607,i_0_1447,i_0_2164,i_0_2167,i_0_2530,i_0_2610,i_0_1503,i_0_1406,i_0_1404,i_0_1469,i_0_1470,i_0_1341,i_0_1161,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_2464,i_0_1843,i_0_2363,i_0_2460,i_0_2537,i_0_2542,i_0_2546,i_0_2557,i_0_2561,i_0_2572,i_0_2556,i_0_2562,i_0_1844,i_0_2308,i_0_2457,i_0_2475,i_0_2533,i_0_1659,i_0_1837,i_0_2127,i_0_2563,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1882,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473,i_0_1474,i_0_1518,i_0_1519,i_0_1536,i_0_1537,i_0_1538,i_0_1563,i_0_1564,i_0_1575,i_0_1578,i_0_1627,i_0_1653,i_0_1656,i_0_1678,i_0_1691,i_0_1225,i_0_1241,i_0_1499,i_0_1500,i_0_1521,i_0_1224,i_0_1240,i_0_2015,i_0_1533,i_0_2007,i_0_2009,i_0_1223,i_0_1170,i_0_1278,i_0_1535,i_0_1594,i_0_1657,i_0_1764,i_0_1887,i_0_1239,i_0_1577,i_0_1390,i_0_1587,i_0_1375,i_0_1376,i_0_1460,i_0_1539,i_0_1436,i_0_1612,i_0_1146,i_0_1147,i_0_1148]) ).

cnf(i_0_2627,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))),X1),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_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk22_2(X2,X1)),c_Arrow__Order__Mirabelle_OProf))
    | c_Arrow__Order__Mirabelle_Odictator(X1,X2) ),
    inference(rename_variables,[],[i_0_1148]) ).

cnf(i_0_2628,plain,
    ( c_Arrow__Order__Mirabelle_Odictator(v_F,X1)
    | esk23_2(X1,v_F) != esk24_2(X1,v_F) ),
    inference(scs_inference,[],[i_0_2046,i_0_2039,i_0_2025,i_0_2254,i_0_2257,i_0_2279,i_0_2575,i_0_2026,i_0_2552,i_0_2555,i_0_2057,i_0_2110,i_0_2274,i_0_2278,i_0_1851,i_0_2297,i_0_2300,i_0_2402,i_0_2410,i_0_2412,i_0_2414,i_0_2416,i_0_2419,i_0_2421,i_0_2423,i_0_2425,i_0_2427,i_0_2429,i_0_2431,i_0_2433,i_0_2435,i_0_2437,i_0_2439,i_0_2441,i_0_2534,i_0_2538,i_0_1644,i_0_2248,i_0_1823,i_0_1791,i_0_1816,i_0_1584,i_0_1543,i_0_2092,i_0_2282,i_0_2290,i_0_2318,i_0_2324,i_0_2463,i_0_1805,i_0_2149,i_0_2189,i_0_2267,i_0_2275,i_0_2471,i_0_2479,i_0_2482,i_0_2485,i_0_2488,i_0_1739,i_0_2513,i_0_1759,i_0_2130,i_0_2133,i_0_2170,i_0_2500,i_0_2541,i_0_1733,i_0_2524,i_0_1719,i_0_2103,i_0_2115,i_0_2243,i_0_2294,i_0_1750,i_0_2120,i_0_2349,i_0_2360,i_0_2491,i_0_2494,i_0_2497,i_0_2503,i_0_1620,i_0_2319,i_0_2352,i_0_1688,i_0_2359,i_0_1795,i_0_2516,i_0_1631,i_0_2178,i_0_2181,i_0_2204,i_0_2236,i_0_2346,i_0_2506,i_0_1329,i_0_1642,i_0_2152,i_0_2155,i_0_2173,i_0_2186,i_0_1643,i_0_1591,i_0_1590,i_0_1589,i_0_1303,i_0_1446,i_0_2227,i_0_2230,i_0_2343,i_0_2370,i_0_2375,i_0_2607,i_0_1447,i_0_2164,i_0_2167,i_0_2530,i_0_2610,i_0_1503,i_0_1406,i_0_1404,i_0_1469,i_0_1470,i_0_1341,i_0_1161,i_0_1645,i_0_2260,i_0_2291,i_0_2309,i_0_2313,i_0_2464,i_0_1843,i_0_2363,i_0_2460,i_0_2537,i_0_2542,i_0_2546,i_0_2557,i_0_2561,i_0_2572,i_0_2556,i_0_2562,i_0_1844,i_0_2308,i_0_2457,i_0_2475,i_0_2533,i_0_1659,i_0_1837,i_0_2127,i_0_2563,i_0_1854,i_0_1855,i_0_1856,i_0_1857,i_0_1858,i_0_1859,i_0_1860,i_0_1861,i_0_1863,i_0_1864,i_0_1865,i_0_1866,i_0_1867,i_0_1868,i_0_1870,i_0_1871,i_0_1872,i_0_1873,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1882,i_0_1772,i_0_1439,i_0_1820,i_0_1267,i_0_1369,i_0_1692,i_0_1736,i_0_1190,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1279,i_0_1296,i_0_1306,i_0_1309,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1416,i_0_1418,i_0_1432,i_0_1433,i_0_1457,i_0_1506,i_0_1514,i_0_1525,i_0_1527,i_0_1545,i_0_1546,i_0_1548,i_0_1550,i_0_1552,i_0_1556,i_0_1560,i_0_1574,i_0_1576,i_0_1605,i_0_1606,i_0_1614,i_0_1633,i_0_1636,i_0_1663,i_0_1665,i_0_1671,i_0_1672,i_0_1700,i_0_1703,i_0_1737,i_0_1738,i_0_1742,i_0_1744,i_0_1745,i_0_1753,i_0_1756,i_0_1765,i_0_1779,i_0_1802,i_0_1828,i_0_2023,i_0_1884,i_0_1886,i_0_1327,i_0_1842,i_0_1964,i_0_1280,i_0_1281,i_0_1285,i_0_1488,i_0_1562,i_0_1164,i_0_1168,i_0_1227,i_0_1259,i_0_1284,i_0_1291,i_0_1300,i_0_1305,i_0_1307,i_0_1308,i_0_1312,i_0_1340,i_0_1343,i_0_1351,i_0_1358,i_0_1361,i_0_1394,i_0_1484,i_0_1491,i_0_1493,i_0_1496,i_0_1542,i_0_1566,i_0_1567,i_0_1571,i_0_1573,i_0_1579,i_0_1588,i_0_1596,i_0_1597,i_0_1599,i_0_1603,i_0_1604,i_0_1621,i_0_1628,i_0_1639,i_0_1641,i_0_1683,i_0_1697,i_0_1702,i_0_1706,i_0_1708,i_0_1709,i_0_1710,i_0_1723,i_0_1727,i_0_1782,i_0_1788,i_0_1789,i_0_1790,i_0_2020,i_0_2022,i_0_1885,i_0_1976,i_0_1977,i_0_1978,i_0_1979,i_0_1980,i_0_1981,i_0_1982,i_0_1983,i_0_1990,i_0_1991,i_0_1992,i_0_1994,i_0_1995,i_0_1997,i_0_1998,i_0_1999,i_0_2000,i_0_2001,i_0_2002,i_0_1952,i_0_1953,i_0_1954,i_0_1955,i_0_1957,i_0_1958,i_0_1959,i_0_1960,i_0_1962,i_0_1965,i_0_1966,i_0_1968,i_0_1969,i_0_1970,i_0_1971,i_0_1972,i_0_1973,i_0_1974,i_0_2011,i_0_2016,i_0_1219,i_0_1268,i_0_1277,i_0_1354,i_0_1362,i_0_1417,i_0_1459,i_0_1473,i_0_1474,i_0_1518,i_0_1519,i_0_1536,i_0_1537,i_0_1538,i_0_1563,i_0_1564,i_0_1575,i_0_1578,i_0_1627,i_0_1653,i_0_1656,i_0_1678,i_0_1691,i_0_1225,i_0_1241,i_0_1499,i_0_1500,i_0_1521,i_0_1224,i_0_1240,i_0_2015,i_0_1533,i_0_2007,i_0_2009,i_0_1223,i_0_1170,i_0_1278,i_0_1535,i_0_1594,i_0_1657,i_0_1764,i_0_1887,i_0_1239,i_0_1577,i_0_1390,i_0_1587,i_0_1375,i_0_1376,i_0_1460,i_0_1539,i_0_1436,i_0_1612,i_0_1146,i_0_1147,i_0_1148,i_0_1149]) ).

cnf(i_0_2629,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))),X1),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))))
    | esk23_2(X2,X1) != esk24_2(X2,X1)
    | c_Arrow__Order__Mirabelle_Odictator(X1,X2) ),
    inference(rename_variables,[],[i_0_1149]) ).

cnf(i_0_2630,plain,
    hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),c_COMBI(X2)),c_FuncSet_OPi(X1,X2,X3,c_fequal))),
    inference(scs_inference,[],[i_0_2262,i_0_1137]) ).

cnf(i_0_2631,plain,
    hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_COMBI(X1),X2)),hAPP(c_fequal,X2))),
    inference(rename_variables,[],[i_0_2262]) ).

cnf(i_0_2632,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,esk29_5(X3,X2,X1,X4,X5))),hAPP(X3,esk29_5(X3,X2,X1,X4,X5))))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X1)),X2),c_FuncSet_OPi(X5,X1,X4,X3))) ),
    inference(rename_variables,[],[i_0_1137]) ).

cnf(i_0_2633,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_2262,i_0_2508,i_0_1137,i_0_1435]) ).

cnf(i_0_2634,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(rename_variables,[],[i_0_2508]) ).

cnf(i_0_2635,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_1435]) ).

cnf(i_0_2636,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_2262,i_0_2112,i_0_2508,i_0_1137,i_0_1435,i_0_1752]) ).

cnf(i_0_2637,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_2112]) ).

cnf(i_0_2638,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_1752]) ).

cnf(i_0_2639,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_2259,i_0_2262,i_0_2112,i_0_2508,i_0_1137,i_0_1435,i_0_1752,i_0_1736]) ).

cnf(i_0_2640,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(rename_variables,[],[i_0_1736]) ).

cnf(i_0_2641,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_2259,i_0_2262,i_0_2112,i_0_2508,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192]) ).

cnf(i_0_2642,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_1192]) ).

cnf(i_0_2643,plain,
    c_Set_Oimage(X1,X2,X3,X4) = c_Set_Oimage(X1,X2,X3,esk35_5(c_Set_Oinsert(X1,X5,X4),X3,X1,c_Set_Oimage(X1,X2,X3,X4),X2)),
    inference(scs_inference,[],[i_0_2259,i_0_2262,i_0_2112,i_0_2107,i_0_2508,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208]) ).

cnf(i_0_2644,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,esk35_5(X5,X4,X3,X2,X1)) ),
    inference(rename_variables,[],[i_0_1208]) ).

cnf(i_0_2645,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_2259,i_0_2262,i_0_2112,i_0_2105,i_0_2107,i_0_2508,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232]) ).

cnf(i_0_2646,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_1232]) ).

cnf(i_0_2647,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_2259,i_0_2262,i_0_2112,i_0_2105,i_0_2107,i_0_2508,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254]) ).

cnf(i_0_2648,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_1254]) ).

cnf(i_0_2649,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_2091,i_0_2259,i_0_2262,i_0_2112,i_0_2105,i_0_2107,i_0_2508,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272]) ).

cnf(i_0_2650,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X3,c_Set_Oinsert(X1,X2,X4)))),
    inference(rename_variables,[],[i_0_2091]) ).

cnf(i_0_2651,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_1272]) ).

cnf(i_0_2652,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_2091,i_0_2259,i_0_2262,i_0_2112,i_0_2135,i_0_2105,i_0_2107,i_0_2508,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275]) ).

cnf(i_0_2653,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_1275]) ).

cnf(i_0_2654,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),esk34_3(c_Nat_OSuc,X2,X1))) != esk34_3(c_Nat_OSuc,X2,X1),
    inference(scs_inference,[],[i_0_2091,i_0_2259,i_0_2262,i_0_2112,i_0_2135,i_0_2105,i_0_2107,i_0_2508,i_0_2126,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278]) ).

cnf(i_0_2655,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),esk34_3(X3,X2,X1))) != esk34_3(X3,X2,X1) ),
    inference(rename_variables,[],[i_0_1278]) ).

cnf(i_0_2656,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_2091,i_0_2259,i_0_2262,i_0_2112,i_0_2135,i_0_2105,i_0_2107,i_0_2508,i_0_2126,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279]) ).

cnf(i_0_2657,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_1279]) ).

cnf(i_0_2658,plain,
    hAPP(X1,X2) = hAPP(X1,esk38_4(hAPP(c_fequal,X2),X1,X3,hAPP(X1,X2))),
    inference(scs_inference,[],[i_0_2091,i_0_2259,i_0_2262,i_0_2112,i_0_2135,i_0_2105,i_0_2107,i_0_2508,i_0_2126,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296]) ).

cnf(i_0_2659,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oimage(X3,X1,X4,X5)))
    | X2 = hAPP(X4,esk38_4(X5,X4,X3,X2)) ),
    inference(rename_variables,[],[i_0_1296]) ).

cnf(i_0_2660,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_2091,i_0_2259,i_0_2262,i_0_2112,i_0_2135,i_0_2105,i_0_2107,i_0_2331,i_0_2508,i_0_2126,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306]) ).

cnf(i_0_2661,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X1)),
    inference(rename_variables,[],[i_0_2331]) ).

cnf(i_0_2662,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_1306]) ).

cnf(i_0_2663,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_2091,i_0_2259,i_0_2262,i_0_1472,i_0_2112,i_0_2135,i_0_2105,i_0_2107,i_0_2331,i_0_2508,i_0_2126,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310]) ).

cnf(i_0_2664,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_1310]) ).

cnf(i_0_2665,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_2091,i_0_2259,i_0_2262,i_0_1472,i_0_2112,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2331,i_0_2508,i_0_2126,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317]) ).

cnf(i_0_2666,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2) != X1,
    inference(rename_variables,[],[i_0_2229]) ).

cnf(i_0_2667,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_1317]) ).

cnf(i_0_2668,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_2091,i_0_2259,i_0_2262,i_0_1472,i_0_2112,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2331,i_0_2508,i_0_2169,i_0_2126,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318]) ).

cnf(i_0_2669,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_2169]) ).

cnf(i_0_2670,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_1318]) ).

cnf(i_0_2671,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_2091,i_0_2259,i_0_2262,i_0_1472,i_0_2112,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2331,i_0_2508,i_0_2169,i_0_2669,i_0_2126,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324]) ).

cnf(i_0_2672,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_2169]) ).

cnf(i_0_2673,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_1324]) ).

cnf(i_0_2674,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_2091,i_0_2650,i_0_2259,i_0_2262,i_0_1472,i_0_2112,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2331,i_0_2508,i_0_2169,i_0_2669,i_0_2126,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331]) ).

cnf(i_0_2675,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_1331]) ).

cnf(i_0_2676,plain,
    X1 = esk38_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_2091,i_0_2650,i_0_2259,i_0_2262,i_0_1472,i_0_2112,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2331,i_0_2508,i_0_2169,i_0_2669,i_0_2126,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359]) ).

cnf(i_0_2677,plain,
    hAPP(X1,X2) = hAPP(X1,esk38_4(c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)),X1,X3,hAPP(X1,X2))),
    inference(rename_variables,[],[i_0_2117]) ).

cnf(i_0_2678,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_1359]) ).

cnf(i_0_2679,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_2091,i_0_2650,i_0_2259,i_0_2262,i_0_1472,i_0_2112,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2331,i_0_2508,i_0_2169,i_0_2669,i_0_2126,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365]) ).

cnf(i_0_2680,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_1365]) ).

cnf(i_0_2681,plain,
    ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,c_Orderings_Oord__class_Oless__eq(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)),tc_Nat_Onat))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(scs_inference,[],[i_0_2091,i_0_2650,i_0_2259,i_0_2262,i_0_1472,i_0_2112,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2331,i_0_2508,i_0_2496,i_0_2169,i_0_2669,i_0_2126,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380]) ).

cnf(i_0_2682,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_1380]) ).

cnf(i_0_2683,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_2091,i_0_2650,i_0_2259,i_0_2262,i_0_1472,i_0_2112,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2331,i_0_2508,i_0_2496,i_0_2169,i_0_2669,i_0_2126,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381]) ).

cnf(i_0_2684,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_1381]) ).

cnf(i_0_2685,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_2091,i_0_2650,i_0_2259,i_0_2262,i_0_1472,i_0_2112,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2331,i_0_2508,i_0_2154,i_0_2496,i_0_2169,i_0_2669,i_0_2126,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418]) ).

cnf(i_0_2686,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_2154]) ).

cnf(i_0_2687,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_1418]) ).

cnf(i_0_2688,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_2091,i_0_2650,i_0_2259,i_0_2262,i_0_1472,i_0_2112,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2331,i_0_2508,i_0_2154,i_0_2496,i_0_2169,i_0_2669,i_0_2126,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457]) ).

cnf(i_0_2689,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_1457]) ).

cnf(i_0_2690,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_2091,i_0_2650,i_0_2259,i_0_2262,i_0_1472,i_0_2112,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2331,i_0_2508,i_0_2154,i_0_2496,i_0_2169,i_0_2669,i_0_2126,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506]) ).

cnf(i_0_2691,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_1506]) ).

cnf(i_0_2692,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)),tc_Nat_Onat)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),
    inference(scs_inference,[],[i_0_2091,i_0_2650,i_0_2259,i_0_2262,i_0_1472,i_0_2510,i_0_2112,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2331,i_0_2508,i_0_2154,i_0_2496,i_0_2169,i_0_2669,i_0_2126,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514]) ).

cnf(i_0_2693,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_1514]) ).

cnf(i_0_2694,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_2091,i_0_2650,i_0_2259,i_0_2262,i_0_1472,i_0_2510,i_0_2112,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2185,i_0_2331,i_0_2508,i_0_2154,i_0_2496,i_0_2169,i_0_2669,i_0_2126,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545]) ).

cnf(i_0_2695,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_2185]) ).

cnf(i_0_2696,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_1545]) ).

cnf(i_0_2697,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_2091,i_0_2650,i_0_2259,i_0_2262,i_0_1472,i_0_2510,i_0_2112,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2185,i_0_2331,i_0_2374,i_0_2508,i_0_2154,i_0_2496,i_0_2169,i_0_2669,i_0_2126,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548]) ).

cnf(i_0_2698,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_1548]) ).

cnf(i_0_2699,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_2091,i_0_2650,i_0_2259,i_0_2262,i_0_1472,i_0_2510,i_0_2112,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2185,i_0_2331,i_0_2374,i_0_2508,i_0_2609,i_0_2154,i_0_2496,i_0_2169,i_0_2669,i_0_2126,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550]) ).

cnf(i_0_2700,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_2609]) ).

cnf(i_0_2701,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_1550]) ).

cnf(i_0_2702,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_2091,i_0_2650,i_0_2259,i_0_2262,i_0_1472,i_0_2510,i_0_2112,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2185,i_0_2331,i_0_2374,i_0_2508,i_0_2609,i_0_2191,i_0_2154,i_0_2496,i_0_2169,i_0_2669,i_0_2126,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552]) ).

cnf(i_0_2703,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_2191]) ).

cnf(i_0_2704,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_1552]) ).

cnf(i_0_2705,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_2091,i_0_2650,i_0_2259,i_0_2262,i_0_1472,i_0_2510,i_0_2112,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2185,i_0_2331,i_0_2374,i_0_2508,i_0_2609,i_0_2191,i_0_2154,i_0_2496,i_0_2169,i_0_2669,i_0_2672,i_0_2126,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605]) ).

cnf(i_0_2706,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_1605]) ).

cnf(i_0_2707,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_2091,i_0_2650,i_0_2259,i_0_2262,i_0_1472,i_0_2510,i_0_2112,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2185,i_0_2331,i_0_2374,i_0_2508,i_0_2612,i_0_2609,i_0_2191,i_0_2154,i_0_2496,i_0_2169,i_0_2669,i_0_2672,i_0_2126,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663]) ).

cnf(i_0_2708,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_2612]) ).

cnf(i_0_2709,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_1663]) ).

cnf(i_0_2710,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_2091,i_0_2650,i_0_2259,i_0_2262,i_0_1472,i_0_2510,i_0_2112,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2185,i_0_2331,i_0_2374,i_0_2508,i_0_2612,i_0_2609,i_0_2191,i_0_2154,i_0_2496,i_0_2169,i_0_2669,i_0_2672,i_0_2126,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672]) ).

cnf(i_0_2711,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | c_Set_Oinsert(X1,X2,X3) = X3 ),
    inference(rename_variables,[],[i_0_1672]) ).

cnf(i_0_2712,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),esk2_2(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2),X1)),
    inference(scs_inference,[],[i_0_2091,i_0_2650,i_0_2259,i_0_2262,i_0_1472,i_0_2510,i_0_2112,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2185,i_0_2331,i_0_2374,i_0_2508,i_0_2612,i_0_2609,i_0_2191,i_0_2154,i_0_2218,i_0_2496,i_0_2169,i_0_2669,i_0_2672,i_0_2126,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700]) ).

cnf(i_0_2713,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),esk2_2(X2,X1)) ),
    inference(rename_variables,[],[i_0_1700]) ).

cnf(i_0_2714,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,esk31_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_2091,i_0_2650,i_0_2259,i_0_2262,i_0_1472,i_0_2510,i_0_2112,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2185,i_0_2695,i_0_2331,i_0_2374,i_0_2508,i_0_2612,i_0_2609,i_0_2191,i_0_2154,i_0_2218,i_0_2496,i_0_2169,i_0_2669,i_0_2672,i_0_2126,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703]) ).

cnf(i_0_2715,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_2185]) ).

cnf(i_0_2716,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,esk31_1(X1)) ),
    inference(rename_variables,[],[i_0_1703]) ).

cnf(i_0_2717,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_2091,i_0_2650,i_0_2259,i_0_2262,i_0_1472,i_0_2510,i_0_2112,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2185,i_0_2695,i_0_2331,i_0_2374,i_0_2508,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2218,i_0_2496,i_0_2169,i_0_2669,i_0_2672,i_0_2126,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745]) ).

cnf(i_0_2718,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_1745]) ).

cnf(i_0_2719,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_2091,i_0_2650,i_0_2259,i_0_2262,i_0_1472,i_0_2510,i_0_2112,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2185,i_0_2695,i_0_2331,i_0_2374,i_0_2508,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2218,i_0_2496,i_0_2169,i_0_2669,i_0_2672,i_0_2126,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023]) ).

cnf(i_0_2720,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_2023]) ).

cnf(i_0_2721,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_2091,i_0_2650,i_0_2259,i_0_2262,i_0_1472,i_0_2510,i_0_2112,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2185,i_0_2695,i_0_2331,i_0_2374,i_0_2508,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2218,i_0_2496,i_0_2169,i_0_2669,i_0_2672,i_0_2126,i_0_2351,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239]) ).

cnf(i_0_2722,plain,
    c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,X1),
    inference(rename_variables,[],[i_0_2351]) ).

cnf(i_0_2723,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_1239]) ).

cnf(i_0_2724,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_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1472,i_0_2510,i_0_2112,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2185,i_0_2695,i_0_2331,i_0_2374,i_0_2508,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2218,i_0_2496,i_0_2169,i_0_2669,i_0_2672,i_0_2126,i_0_2351,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267]) ).

cnf(i_0_2725,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_1267]) ).

cnf(i_0_2726,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_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1472,i_0_2510,i_0_2112,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2185,i_0_2695,i_0_2331,i_0_2374,i_0_2508,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2218,i_0_2496,i_0_2169,i_0_2669,i_0_2672,i_0_2126,i_0_2351,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309]) ).

cnf(i_0_2727,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_1309]) ).

cnf(i_0_2728,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_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1472,i_0_2510,i_0_2112,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2185,i_0_2695,i_0_2331,i_0_2374,i_0_2508,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2218,i_0_2496,i_0_2169,i_0_2669,i_0_2672,i_0_2126,i_0_2351,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416]) ).

cnf(i_0_2729,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_1416]) ).

cnf(i_0_2730,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_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1472,i_0_2510,i_0_2112,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2185,i_0_2695,i_0_2331,i_0_2374,i_0_2508,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2218,i_0_2496,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2126,i_0_2351,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432]) ).

cnf(i_0_2731,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_1432]) ).

cnf(i_0_2732,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_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1472,i_0_2510,i_0_2112,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2185,i_0_2695,i_0_2331,i_0_2374,i_0_2508,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2218,i_0_2496,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2188,i_0_2126,i_0_2351,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433]) ).

cnf(i_0_2733,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X1))),
    inference(rename_variables,[],[i_0_2188]) ).

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,X2),X3)) ),
    inference(rename_variables,[],[i_0_1433]) ).

cnf(i_0_2735,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_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1472,i_0_2510,i_0_2112,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2185,i_0_2695,i_0_2331,i_0_2374,i_0_2508,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2218,i_0_2496,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2188,i_0_2126,i_0_2351,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433,i_0_1436]) ).

cnf(i_0_2736,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_1436]) ).

cnf(i_0_2737,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_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1472,i_0_2510,i_0_2112,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2185,i_0_2695,i_0_2331,i_0_2661,i_0_2374,i_0_2508,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2218,i_0_2496,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2188,i_0_2126,i_0_2351,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433,i_0_1436,i_0_1527]) ).

cnf(i_0_2738,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X1)),
    inference(rename_variables,[],[i_0_2331]) ).

cnf(i_0_2739,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_1527]) ).

cnf(i_0_2740,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_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1472,i_0_2510,i_0_2112,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2185,i_0_2695,i_0_2331,i_0_2661,i_0_2738,i_0_2374,i_0_2508,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2218,i_0_2496,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2188,i_0_2126,i_0_2351,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433,i_0_1436,i_0_1527,i_0_1636]) ).

cnf(i_0_2741,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_1636]) ).

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_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1472,i_0_2510,i_0_2112,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2185,i_0_2695,i_0_2331,i_0_2661,i_0_2738,i_0_2374,i_0_2508,i_0_2634,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2218,i_0_2496,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2188,i_0_2126,i_0_2351,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433,i_0_1436,i_0_1527,i_0_1636,i_0_1738]) ).

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_1738]) ).

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)) != X2,
    inference(scs_inference,[],[i_0_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1472,i_0_2510,i_0_2112,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2163,i_0_2185,i_0_2695,i_0_2331,i_0_2661,i_0_2738,i_0_2374,i_0_2508,i_0_2634,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2218,i_0_2496,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2188,i_0_2126,i_0_2351,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433,i_0_1436,i_0_1527,i_0_1636,i_0_1738,i_0_1756]) ).

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_2163]) ).

cnf(i_0_2746,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_1756]) ).

cnf(i_0_2747,plain,
    c_Finite__Set_Ofinite(esk35_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_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1472,i_0_2510,i_0_2112,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2163,i_0_2185,i_0_2695,i_0_2331,i_0_2661,i_0_2738,i_0_2374,i_0_2508,i_0_2634,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2218,i_0_2496,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2188,i_0_2126,i_0_2403,i_0_2351,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433,i_0_1436,i_0_1527,i_0_1636,i_0_1738,i_0_1756,i_0_1842]) ).

cnf(i_0_2748,plain,
    ( ~ class_Finite__Set_Ofinite(X1)
    | c_Finite__Set_Ofinite(X1,X2) ),
    inference(rename_variables,[],[i_0_1842]) ).

cnf(i_0_2749,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_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1472,i_0_2510,i_0_2112,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2163,i_0_2185,i_0_2695,i_0_2331,i_0_2661,i_0_2738,i_0_2374,i_0_2508,i_0_2634,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2218,i_0_2496,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2175,i_0_2188,i_0_2126,i_0_2403,i_0_2351,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433,i_0_1436,i_0_1527,i_0_1636,i_0_1738,i_0_1756,i_0_1842,i_0_1556]) ).

cnf(i_0_2750,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_1556]) ).

cnf(i_0_2751,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_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1472,i_0_2510,i_0_2112,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2163,i_0_2185,i_0_2695,i_0_2331,i_0_2661,i_0_2738,i_0_2374,i_0_2508,i_0_2634,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2686,i_0_2218,i_0_2496,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2175,i_0_2188,i_0_2126,i_0_2403,i_0_2351,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433,i_0_1436,i_0_1527,i_0_1636,i_0_1738,i_0_1756,i_0_1842,i_0_1556,i_0_1560]) ).

cnf(i_0_2752,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_2154]) ).

cnf(i_0_2753,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_1560]) ).

cnf(i_0_2754,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_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1472,i_0_2510,i_0_2112,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2163,i_0_2185,i_0_2695,i_0_2715,i_0_2331,i_0_2661,i_0_2738,i_0_2374,i_0_2508,i_0_2634,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2686,i_0_2218,i_0_2496,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2175,i_0_2188,i_0_2126,i_0_2403,i_0_2351,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433,i_0_1436,i_0_1527,i_0_1636,i_0_1738,i_0_1756,i_0_1842,i_0_1556,i_0_1560,i_0_1614]) ).

cnf(i_0_2755,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_1614]) ).

cnf(i_0_2756,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_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1472,i_0_2510,i_0_2112,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2163,i_0_2185,i_0_2695,i_0_2715,i_0_2331,i_0_2661,i_0_2738,i_0_2374,i_0_2508,i_0_2634,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2686,i_0_2218,i_0_2496,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2175,i_0_2188,i_0_2126,i_0_2403,i_0_2351,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433,i_0_1436,i_0_1527,i_0_1636,i_0_1738,i_0_1756,i_0_1842,i_0_1556,i_0_1560,i_0_1614,i_0_1737]) ).

cnf(i_0_2757,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_1737]) ).

cnf(i_0_2758,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_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1472,i_0_2510,i_0_2112,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2163,i_0_2185,i_0_2695,i_0_2715,i_0_2331,i_0_2661,i_0_2738,i_0_2374,i_0_2508,i_0_2634,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2686,i_0_2218,i_0_2496,i_0_2145,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2175,i_0_2188,i_0_2126,i_0_2403,i_0_2351,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433,i_0_1436,i_0_1527,i_0_1636,i_0_1738,i_0_1756,i_0_1842,i_0_1556,i_0_1560,i_0_1614,i_0_1737,i_0_1742]) ).

cnf(i_0_2759,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X2 != X1 ),
    inference(rename_variables,[],[i_0_1742]) ).

cnf(i_0_2760,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_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1472,i_0_2510,i_0_2112,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2163,i_0_2185,i_0_2695,i_0_2715,i_0_2331,i_0_2661,i_0_2738,i_0_2374,i_0_2508,i_0_2634,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2686,i_0_2218,i_0_2496,i_0_2145,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2175,i_0_2188,i_0_2126,i_0_2403,i_0_2351,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433,i_0_1436,i_0_1527,i_0_1636,i_0_1738,i_0_1756,i_0_1842,i_0_1556,i_0_1560,i_0_1614,i_0_1737,i_0_1742,i_0_1744]) ).

cnf(i_0_2761,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X1 != X2 ),
    inference(rename_variables,[],[i_0_1744]) ).

cnf(i_0_2762,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_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1472,i_0_2510,i_0_2112,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2163,i_0_2745,i_0_2185,i_0_2695,i_0_2715,i_0_2331,i_0_2661,i_0_2738,i_0_2374,i_0_2508,i_0_2634,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2686,i_0_2218,i_0_2496,i_0_2145,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2175,i_0_2188,i_0_2126,i_0_2403,i_0_2351,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433,i_0_1436,i_0_1527,i_0_1636,i_0_1738,i_0_1756,i_0_1842,i_0_1556,i_0_1560,i_0_1614,i_0_1737,i_0_1742,i_0_1744,i_0_1753]) ).

cnf(i_0_2763,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_2163]) ).

cnf(i_0_2764,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_1753]) ).

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),X1),hAPP(c_Nat_OSuc,X2))),X3) != X2,
    inference(scs_inference,[],[i_0_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1472,i_0_2510,i_0_2112,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2163,i_0_2745,i_0_2185,i_0_2695,i_0_2715,i_0_2331,i_0_2661,i_0_2738,i_0_2374,i_0_2508,i_0_2634,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2686,i_0_2218,i_0_2496,i_0_2145,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2175,i_0_2188,i_0_2126,i_0_2403,i_0_2351,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433,i_0_1436,i_0_1527,i_0_1636,i_0_1738,i_0_1756,i_0_1842,i_0_1556,i_0_1560,i_0_1614,i_0_1737,i_0_1742,i_0_1744,i_0_1753,i_0_1802]) ).

cnf(i_0_2766,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
    | X1 != X2 ),
    inference(rename_variables,[],[i_0_1802]) ).

cnf(i_0_2767,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_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1472,i_0_2510,i_0_2112,i_0_2637,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2163,i_0_2745,i_0_2185,i_0_2695,i_0_2715,i_0_2331,i_0_2661,i_0_2738,i_0_2374,i_0_2508,i_0_2634,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2686,i_0_2218,i_0_2496,i_0_2145,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2175,i_0_2188,i_0_2126,i_0_2403,i_0_2351,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433,i_0_1436,i_0_1527,i_0_1636,i_0_1738,i_0_1756,i_0_1842,i_0_1556,i_0_1560,i_0_1614,i_0_1737,i_0_1742,i_0_1744,i_0_1753,i_0_1802,i_0_1828]) ).

cnf(i_0_2768,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_2112]) ).

cnf(i_0_2769,plain,
    ( hAPP(c_Nat_OSuc,X1) != hAPP(c_Nat_OSuc,X2)
    | X1 = X2 ),
    inference(rename_variables,[],[i_0_1828]) ).

cnf(i_0_2770,plain,
    hBOOL(hAPP(c_Set_Oinsert(X1,X2,c_Set_Oinsert(X1,X3,X4)),X3)),
    inference(scs_inference,[],[i_0_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1472,i_0_2510,i_0_2112,i_0_2637,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2163,i_0_2745,i_0_2185,i_0_2695,i_0_2715,i_0_2331,i_0_2661,i_0_2738,i_0_2374,i_0_2508,i_0_2634,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2686,i_0_2218,i_0_2496,i_0_2145,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2175,i_0_2188,i_0_2126,i_0_2403,i_0_2351,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433,i_0_1436,i_0_1527,i_0_1636,i_0_1738,i_0_1756,i_0_1842,i_0_1556,i_0_1560,i_0_1614,i_0_1737,i_0_1742,i_0_1744,i_0_1753,i_0_1802,i_0_1828,i_0_1692]) ).

cnf(i_0_2771,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hBOOL(hAPP(X3,X2)) ),
    inference(rename_variables,[],[i_0_1692]) ).

cnf(i_0_2772,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_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1472,i_0_2510,i_0_2112,i_0_2637,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2163,i_0_2745,i_0_2185,i_0_2695,i_0_2715,i_0_2331,i_0_2661,i_0_2738,i_0_2374,i_0_2508,i_0_2634,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2686,i_0_2195,i_0_2218,i_0_2496,i_0_2145,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2175,i_0_2188,i_0_2126,i_0_2403,i_0_2351,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433,i_0_1436,i_0_1527,i_0_1636,i_0_1738,i_0_1756,i_0_1842,i_0_1556,i_0_1560,i_0_1614,i_0_1737,i_0_1742,i_0_1744,i_0_1753,i_0_1802,i_0_1828,i_0_1692,i_0_1574]) ).

cnf(i_0_2773,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_2195]) ).

cnf(i_0_2774,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_1574]) ).

cnf(i_0_2775,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_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1472,i_0_2510,i_0_2112,i_0_2637,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2163,i_0_2745,i_0_2763,i_0_2185,i_0_2695,i_0_2715,i_0_2331,i_0_2661,i_0_2738,i_0_2374,i_0_2508,i_0_2634,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2686,i_0_2195,i_0_2218,i_0_2496,i_0_2145,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2175,i_0_2188,i_0_2126,i_0_2403,i_0_2351,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433,i_0_1436,i_0_1527,i_0_1636,i_0_1738,i_0_1756,i_0_1842,i_0_1556,i_0_1560,i_0_1614,i_0_1737,i_0_1742,i_0_1744,i_0_1753,i_0_1802,i_0_1828,i_0_1692,i_0_1574,i_0_1633]) ).

cnf(i_0_2776,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_2163]) ).

cnf(i_0_2777,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_1633]) ).

cnf(i_0_2778,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_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1472,i_0_2510,i_0_2112,i_0_2637,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2163,i_0_2745,i_0_2763,i_0_2185,i_0_2695,i_0_2715,i_0_2331,i_0_2661,i_0_2738,i_0_2374,i_0_2508,i_0_2634,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2686,i_0_2195,i_0_2218,i_0_2496,i_0_2145,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2175,i_0_2188,i_0_2126,i_0_2403,i_0_2351,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433,i_0_1436,i_0_1527,i_0_1636,i_0_1738,i_0_1756,i_0_1842,i_0_1556,i_0_1560,i_0_1614,i_0_1737,i_0_1742,i_0_1744,i_0_1753,i_0_1802,i_0_1828,i_0_1692,i_0_1574,i_0_1633,i_0_1671]) ).

cnf(i_0_2779,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_1671]) ).

cnf(i_0_2780,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_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1472,i_0_2510,i_0_2112,i_0_2637,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2163,i_0_2745,i_0_2763,i_0_2185,i_0_2695,i_0_2715,i_0_2331,i_0_2661,i_0_2738,i_0_2374,i_0_2508,i_0_2634,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2686,i_0_2195,i_0_2218,i_0_2496,i_0_2145,i_0_2206,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2175,i_0_2188,i_0_2126,i_0_2403,i_0_2351,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433,i_0_1436,i_0_1527,i_0_1636,i_0_1738,i_0_1756,i_0_1842,i_0_1556,i_0_1560,i_0_1614,i_0_1737,i_0_1742,i_0_1744,i_0_1753,i_0_1802,i_0_1828,i_0_1692,i_0_1574,i_0_1633,i_0_1671,i_0_1606]) ).

cnf(i_0_2781,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_1606]) ).

cnf(i_0_2782,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_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1472,i_0_2510,i_0_2112,i_0_2637,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2163,i_0_2745,i_0_2763,i_0_2185,i_0_2695,i_0_2715,i_0_2331,i_0_2661,i_0_2738,i_0_2374,i_0_2508,i_0_2634,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2686,i_0_2195,i_0_2218,i_0_2496,i_0_2145,i_0_2206,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2175,i_0_2188,i_0_2592,i_0_2126,i_0_2403,i_0_2351,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433,i_0_1436,i_0_1527,i_0_1636,i_0_1738,i_0_1756,i_0_1842,i_0_1556,i_0_1560,i_0_1614,i_0_1737,i_0_1742,i_0_1744,i_0_1753,i_0_1802,i_0_1828,i_0_1692,i_0_1574,i_0_1633,i_0_1671,i_0_1606,i_0_1535]) ).

cnf(i_0_2783,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_2592]) ).

cnf(i_0_2784,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_1535]) ).

cnf(i_0_2785,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_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1472,i_0_2510,i_0_2112,i_0_2637,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2163,i_0_2745,i_0_2763,i_0_2185,i_0_2695,i_0_2715,i_0_2331,i_0_2661,i_0_2738,i_0_2374,i_0_2508,i_0_2634,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2686,i_0_2195,i_0_2218,i_0_2496,i_0_2145,i_0_2206,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2175,i_0_2188,i_0_2592,i_0_2126,i_0_2403,i_0_2351,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433,i_0_1436,i_0_1527,i_0_1636,i_0_1738,i_0_1756,i_0_1842,i_0_1556,i_0_1560,i_0_1614,i_0_1737,i_0_1742,i_0_1744,i_0_1753,i_0_1802,i_0_1828,i_0_1692,i_0_1574,i_0_1633,i_0_1671,i_0_1606,i_0_1535,i_0_1546]) ).

cnf(i_0_2786,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_2218]) ).

cnf(i_0_2787,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_1546]) ).

cnf(i_0_2788,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)),tc_Nat_Onat)),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_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1472,i_0_2510,i_0_2112,i_0_2637,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2163,i_0_2745,i_0_2763,i_0_2185,i_0_2695,i_0_2715,i_0_2331,i_0_2661,i_0_2738,i_0_2374,i_0_2508,i_0_2634,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2686,i_0_2195,i_0_2218,i_0_2496,i_0_2145,i_0_2206,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2175,i_0_2188,i_0_2592,i_0_2126,i_0_2403,i_0_2351,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433,i_0_1436,i_0_1527,i_0_1636,i_0_1738,i_0_1756,i_0_1842,i_0_1556,i_0_1560,i_0_1614,i_0_1737,i_0_1742,i_0_1744,i_0_1753,i_0_1802,i_0_1828,i_0_1692,i_0_1574,i_0_1633,i_0_1671,i_0_1606,i_0_1535,i_0_1546,i_0_1665]) ).

cnf(i_0_2789,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_1665]) ).

cnf(i_0_2790,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)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))),X2)),
    inference(scs_inference,[],[i_0_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1472,i_0_2510,i_0_2112,i_0_2637,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2163,i_0_2745,i_0_2763,i_0_2185,i_0_2695,i_0_2715,i_0_2331,i_0_2661,i_0_2738,i_0_2374,i_0_2508,i_0_2634,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2686,i_0_2195,i_0_2218,i_0_2496,i_0_2499,i_0_2145,i_0_2206,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2175,i_0_2188,i_0_2592,i_0_2126,i_0_2403,i_0_2351,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433,i_0_1436,i_0_1527,i_0_1636,i_0_1738,i_0_1756,i_0_1842,i_0_1556,i_0_1560,i_0_1614,i_0_1737,i_0_1742,i_0_1744,i_0_1753,i_0_1802,i_0_1828,i_0_1692,i_0_1574,i_0_1633,i_0_1671,i_0_1606,i_0_1535,i_0_1546,i_0_1665,i_0_1576]) ).

cnf(i_0_2791,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),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))),X2)),
    inference(rename_variables,[],[i_0_2499]) ).

cnf(i_0_2792,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_1576]) ).

cnf(i_0_2793,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)),tc_Nat_Onat)))),
    inference(scs_inference,[],[i_0_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1472,i_0_2510,i_0_2112,i_0_2637,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2163,i_0_2745,i_0_2763,i_0_2185,i_0_2695,i_0_2715,i_0_2331,i_0_2661,i_0_2738,i_0_2374,i_0_2508,i_0_2634,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2686,i_0_2195,i_0_2218,i_0_2496,i_0_2499,i_0_2145,i_0_2206,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2175,i_0_2188,i_0_2592,i_0_2126,i_0_2403,i_0_2351,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433,i_0_1436,i_0_1527,i_0_1636,i_0_1738,i_0_1756,i_0_1842,i_0_1556,i_0_1560,i_0_1614,i_0_1737,i_0_1742,i_0_1744,i_0_1753,i_0_1802,i_0_1828,i_0_1692,i_0_1574,i_0_1633,i_0_1671,i_0_1606,i_0_1535,i_0_1546,i_0_1665,i_0_1576,i_0_1657]) ).

cnf(i_0_2794,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_1657]) ).

cnf(i_0_2795,plain,
    X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),
    inference(scs_inference,[],[i_0_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1821,i_0_1472,i_0_2510,i_0_2112,i_0_2637,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2163,i_0_2745,i_0_2763,i_0_2185,i_0_2695,i_0_2715,i_0_2331,i_0_2661,i_0_2738,i_0_2374,i_0_2508,i_0_2634,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2686,i_0_2195,i_0_2218,i_0_2496,i_0_2499,i_0_2145,i_0_2206,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2175,i_0_2188,i_0_2592,i_0_2126,i_0_2403,i_0_2351,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433,i_0_1436,i_0_1527,i_0_1636,i_0_1738,i_0_1756,i_0_1842,i_0_1556,i_0_1560,i_0_1614,i_0_1737,i_0_1742,i_0_1744,i_0_1753,i_0_1802,i_0_1828,i_0_1692,i_0_1574,i_0_1633,i_0_1671,i_0_1606,i_0_1535,i_0_1546,i_0_1665,i_0_1576,i_0_1657,i_0_1884]) ).

cnf(i_0_2796,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_2252,i_0_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1821,i_0_1472,i_0_2510,i_0_2112,i_0_2637,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2163,i_0_2745,i_0_2763,i_0_2185,i_0_2695,i_0_2715,i_0_2331,i_0_2661,i_0_2738,i_0_2374,i_0_2508,i_0_2634,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2686,i_0_2195,i_0_2218,i_0_2496,i_0_2499,i_0_2145,i_0_2206,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2175,i_0_2188,i_0_2592,i_0_2126,i_0_2403,i_0_2351,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433,i_0_1436,i_0_1527,i_0_1636,i_0_1738,i_0_1756,i_0_1842,i_0_1556,i_0_1560,i_0_1614,i_0_1737,i_0_1742,i_0_1744,i_0_1753,i_0_1802,i_0_1828,i_0_1692,i_0_1574,i_0_1633,i_0_1671,i_0_1606,i_0_1535,i_0_1546,i_0_1665,i_0_1576,i_0_1657,i_0_1884,i_0_1886]) ).

cnf(i_0_2797,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_2252]) ).

cnf(i_0_2798,plain,
    hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)) != X2,
    inference(scs_inference,[],[i_0_2252,i_0_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1821,i_0_1472,i_0_2510,i_0_2112,i_0_2637,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2163,i_0_2745,i_0_2763,i_0_2185,i_0_2695,i_0_2715,i_0_2395,i_0_2331,i_0_2661,i_0_2738,i_0_2374,i_0_2508,i_0_2634,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2686,i_0_2195,i_0_2218,i_0_2496,i_0_2499,i_0_2145,i_0_2206,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2175,i_0_2188,i_0_2592,i_0_2126,i_0_2403,i_0_2351,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433,i_0_1436,i_0_1527,i_0_1636,i_0_1738,i_0_1756,i_0_1842,i_0_1556,i_0_1560,i_0_1614,i_0_1737,i_0_1742,i_0_1744,i_0_1753,i_0_1802,i_0_1828,i_0_1692,i_0_1574,i_0_1633,i_0_1671,i_0_1606,i_0_1535,i_0_1546,i_0_1665,i_0_1576,i_0_1657,i_0_1884,i_0_1886,i_0_1887]) ).

cnf(i_0_2799,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)) != X2,
    inference(rename_variables,[],[i_0_2395]) ).

cnf(i_0_2800,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_2252,i_0_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1821,i_0_1472,i_0_2510,i_0_2112,i_0_2637,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2666,i_0_2163,i_0_2745,i_0_2763,i_0_2185,i_0_2695,i_0_2715,i_0_2395,i_0_2331,i_0_2661,i_0_2738,i_0_2374,i_0_2508,i_0_2634,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2686,i_0_2195,i_0_2293,i_0_2218,i_0_2496,i_0_2499,i_0_2145,i_0_2206,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2175,i_0_2188,i_0_2592,i_0_2126,i_0_2403,i_0_2351,i_0_1161,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433,i_0_1436,i_0_1527,i_0_1636,i_0_1738,i_0_1756,i_0_1842,i_0_1556,i_0_1560,i_0_1614,i_0_1737,i_0_1742,i_0_1744,i_0_1753,i_0_1802,i_0_1828,i_0_1692,i_0_1574,i_0_1633,i_0_1671,i_0_1606,i_0_1535,i_0_1546,i_0_1665,i_0_1576,i_0_1657,i_0_1884,i_0_1886,i_0_1887,i_0_1153]) ).

cnf(i_0_2801,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2) != X1,
    inference(rename_variables,[],[i_0_2229]) ).

cnf(i_0_2802,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_1153]) ).

cnf(i_0_2803,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)),esk36_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_2252,i_0_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1821,i_0_1472,i_0_2510,i_0_2112,i_0_2637,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2666,i_0_2163,i_0_2745,i_0_2763,i_0_2185,i_0_2695,i_0_2715,i_0_2395,i_0_2331,i_0_2661,i_0_2738,i_0_2374,i_0_2508,i_0_2634,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2686,i_0_2195,i_0_2293,i_0_2218,i_0_2496,i_0_2499,i_0_2145,i_0_2206,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2175,i_0_2188,i_0_2592,i_0_2126,i_0_2403,i_0_2351,i_0_1329,i_0_1161,i_0_2247,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433,i_0_1436,i_0_1527,i_0_1636,i_0_1738,i_0_1756,i_0_1842,i_0_1556,i_0_1560,i_0_1614,i_0_1737,i_0_1742,i_0_1744,i_0_1753,i_0_1802,i_0_1828,i_0_1692,i_0_1574,i_0_1633,i_0_1671,i_0_1606,i_0_1535,i_0_1546,i_0_1665,i_0_1576,i_0_1657,i_0_1884,i_0_1886,i_0_1887,i_0_1153,i_0_1264]) ).

cnf(i_0_2804,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_1329]) ).

cnf(i_0_2805,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,esk36_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_1264]) ).

cnf(i_0_2806,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_2252,i_0_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1821,i_0_1472,i_0_2510,i_0_2112,i_0_2637,i_0_2117,i_0_2135,i_0_2105,i_0_2107,i_0_2229,i_0_2666,i_0_2163,i_0_2745,i_0_2763,i_0_2185,i_0_2695,i_0_2715,i_0_2395,i_0_2331,i_0_2661,i_0_2738,i_0_2374,i_0_2508,i_0_2634,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2686,i_0_2195,i_0_2293,i_0_2218,i_0_2496,i_0_2499,i_0_2145,i_0_2206,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2175,i_0_2188,i_0_2592,i_0_2126,i_0_2403,i_0_2351,i_0_1329,i_0_1161,i_0_2247,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433,i_0_1436,i_0_1527,i_0_1636,i_0_1738,i_0_1756,i_0_1842,i_0_1556,i_0_1560,i_0_1614,i_0_1737,i_0_1742,i_0_1744,i_0_1753,i_0_1802,i_0_1828,i_0_1692,i_0_1574,i_0_1633,i_0_1671,i_0_1606,i_0_1535,i_0_1546,i_0_1665,i_0_1576,i_0_1657,i_0_1884,i_0_1886,i_0_1887,i_0_1153,i_0_1264,i_0_1455]) ).

cnf(i_0_2807,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_1455]) ).

cnf(i_0_2808,plain,
    esk2_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_2252,i_0_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1821,i_0_1472,i_0_2510,i_0_2112,i_0_2637,i_0_2117,i_0_2135,i_0_2212,i_0_2105,i_0_2107,i_0_2229,i_0_2666,i_0_2163,i_0_2745,i_0_2763,i_0_2185,i_0_2695,i_0_2715,i_0_2395,i_0_2331,i_0_2661,i_0_2738,i_0_2374,i_0_2508,i_0_2634,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2686,i_0_2195,i_0_2293,i_0_2218,i_0_2496,i_0_2499,i_0_2145,i_0_2206,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2175,i_0_2188,i_0_2592,i_0_2126,i_0_2403,i_0_2351,i_0_1329,i_0_1161,i_0_2247,i_0_1837,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433,i_0_1436,i_0_1527,i_0_1636,i_0_1738,i_0_1756,i_0_1842,i_0_1556,i_0_1560,i_0_1614,i_0_1737,i_0_1742,i_0_1744,i_0_1753,i_0_1802,i_0_1828,i_0_1692,i_0_1574,i_0_1633,i_0_1671,i_0_1606,i_0_1535,i_0_1546,i_0_1665,i_0_1576,i_0_1657,i_0_1884,i_0_1886,i_0_1887,i_0_1153,i_0_1264,i_0_1455,i_0_1778]) ).

cnf(i_0_2809,plain,
    X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk2_2(X1,X1)),
    inference(rename_variables,[],[i_0_2212]) ).

cnf(i_0_2810,plain,
    hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(rename_variables,[],[i_0_1837]) ).

cnf(i_0_2811,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_1778]) ).

cnf(i_0_2812,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_2252,i_0_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1821,i_0_1472,i_0_2510,i_0_2112,i_0_2637,i_0_2117,i_0_2135,i_0_2212,i_0_2105,i_0_2107,i_0_2229,i_0_2666,i_0_2163,i_0_2745,i_0_2763,i_0_2185,i_0_2695,i_0_2715,i_0_2395,i_0_2331,i_0_2661,i_0_2738,i_0_2374,i_0_2508,i_0_2634,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2686,i_0_2195,i_0_2293,i_0_2218,i_0_2496,i_0_2499,i_0_2145,i_0_2206,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2175,i_0_2188,i_0_2592,i_0_2126,i_0_2403,i_0_2351,i_0_1329,i_0_1161,i_0_2247,i_0_1837,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433,i_0_1436,i_0_1527,i_0_1636,i_0_1738,i_0_1756,i_0_1842,i_0_1556,i_0_1560,i_0_1614,i_0_1737,i_0_1742,i_0_1744,i_0_1753,i_0_1802,i_0_1828,i_0_1692,i_0_1574,i_0_1633,i_0_1671,i_0_1606,i_0_1535,i_0_1546,i_0_1665,i_0_1576,i_0_1657,i_0_1884,i_0_1886,i_0_1887,i_0_1153,i_0_1264,i_0_1455,i_0_1778,i_0_1783]) ).

cnf(i_0_2813,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_1821]) ).

cnf(i_0_2814,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_1783]) ).

cnf(i_0_2815,plain,
    X1 = esk36_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_2252,i_0_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1821,i_0_1472,i_0_2510,i_0_2112,i_0_2637,i_0_2117,i_0_2135,i_0_2212,i_0_2105,i_0_2107,i_0_2229,i_0_2666,i_0_2163,i_0_2745,i_0_2763,i_0_2185,i_0_2695,i_0_2715,i_0_2395,i_0_2331,i_0_2661,i_0_2738,i_0_2374,i_0_2508,i_0_2634,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2686,i_0_2195,i_0_2293,i_0_2218,i_0_2496,i_0_2499,i_0_2145,i_0_2206,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2175,i_0_2188,i_0_2592,i_0_2126,i_0_2403,i_0_2351,i_0_1329,i_0_2804,i_0_1161,i_0_2247,i_0_1837,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433,i_0_1436,i_0_1527,i_0_1636,i_0_1738,i_0_1756,i_0_1842,i_0_1556,i_0_1560,i_0_1614,i_0_1737,i_0_1742,i_0_1744,i_0_1753,i_0_1802,i_0_1828,i_0_1692,i_0_1574,i_0_1633,i_0_1671,i_0_1606,i_0_1535,i_0_1546,i_0_1665,i_0_1576,i_0_1657,i_0_1884,i_0_1886,i_0_1887,i_0_1153,i_0_1264,i_0_1455,i_0_1778,i_0_1783,i_0_2021]) ).

cnf(i_0_2816,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_2247]) ).

cnf(i_0_2817,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_1329]) ).

cnf(i_0_2818,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 = esk36_4(hAPP(X3,X4),X3,X2,X1) ),
    inference(rename_variables,[],[i_0_2021]) ).

cnf(i_0_2819,plain,
    ~ c_Finite__Set_Ofolding__image__simple(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),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_2252,i_0_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1821,i_0_2813,i_0_1472,i_0_2510,i_0_2112,i_0_2637,i_0_2117,i_0_2135,i_0_2212,i_0_2105,i_0_2107,i_0_2229,i_0_2666,i_0_2163,i_0_2745,i_0_2763,i_0_2185,i_0_2695,i_0_2715,i_0_2395,i_0_2331,i_0_2661,i_0_2738,i_0_2374,i_0_2508,i_0_2634,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2686,i_0_2195,i_0_2293,i_0_2218,i_0_2496,i_0_2499,i_0_2145,i_0_2206,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2175,i_0_2188,i_0_2592,i_0_2126,i_0_2403,i_0_2351,i_0_1329,i_0_2804,i_0_1161,i_0_2247,i_0_1837,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433,i_0_1436,i_0_1527,i_0_1636,i_0_1738,i_0_1756,i_0_1842,i_0_1556,i_0_1560,i_0_1614,i_0_1737,i_0_1742,i_0_1744,i_0_1753,i_0_1802,i_0_1828,i_0_1692,i_0_1574,i_0_1633,i_0_1671,i_0_1606,i_0_1535,i_0_1546,i_0_1665,i_0_1576,i_0_1657,i_0_1884,i_0_1886,i_0_1887,i_0_1153,i_0_1264,i_0_1455,i_0_1778,i_0_1783,i_0_2021,i_0_1984]) ).

cnf(i_0_2820,plain,
    ~ c_Finite__Set_Ofolding__image__simple(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2,X3,X4,hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Finite__Set_Ofold__image(X1,X1,X2,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_2252,i_0_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1821,i_0_2813,i_0_1472,i_0_2510,i_0_2112,i_0_2637,i_0_2117,i_0_2135,i_0_2212,i_0_2105,i_0_2107,i_0_2229,i_0_2666,i_0_2163,i_0_2745,i_0_2763,i_0_2185,i_0_2695,i_0_2715,i_0_2395,i_0_2331,i_0_2661,i_0_2738,i_0_2374,i_0_2508,i_0_2634,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2686,i_0_2195,i_0_2293,i_0_2218,i_0_2496,i_0_2499,i_0_2145,i_0_2206,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2175,i_0_2188,i_0_2592,i_0_2126,i_0_2403,i_0_2351,i_0_1329,i_0_2804,i_0_1161,i_0_2247,i_0_1837,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433,i_0_1436,i_0_1527,i_0_1636,i_0_1738,i_0_1756,i_0_1842,i_0_1556,i_0_1560,i_0_1614,i_0_1737,i_0_1742,i_0_1744,i_0_1753,i_0_1802,i_0_1828,i_0_1692,i_0_1574,i_0_1633,i_0_1671,i_0_1606,i_0_1535,i_0_1546,i_0_1665,i_0_1576,i_0_1657,i_0_1884,i_0_1886,i_0_1887,i_0_1153,i_0_1264,i_0_1455,i_0_1778,i_0_1783,i_0_2021,i_0_1984,i_0_1985]) ).

cnf(i_0_2821,plain,
    ~ c_Finite__Set_Ofolding__image__simple(X1,X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2,X3,hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Finite__Set_Ofold__image(X1,X1,X1,X3,X2,c_Set_Oimage(tc_Nat_Onat,X1,X4,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X5,X6)))))),
    inference(scs_inference,[],[i_0_2252,i_0_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1821,i_0_2813,i_0_1472,i_0_2510,i_0_2112,i_0_2637,i_0_2117,i_0_2135,i_0_2212,i_0_2105,i_0_2107,i_0_2229,i_0_2666,i_0_2163,i_0_2745,i_0_2763,i_0_2185,i_0_2695,i_0_2715,i_0_2395,i_0_2331,i_0_2661,i_0_2738,i_0_2374,i_0_2508,i_0_2634,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2686,i_0_2195,i_0_2293,i_0_2218,i_0_2496,i_0_2499,i_0_2145,i_0_2206,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2175,i_0_2188,i_0_2592,i_0_2126,i_0_2403,i_0_2351,i_0_1329,i_0_2804,i_0_1161,i_0_2247,i_0_1837,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433,i_0_1436,i_0_1527,i_0_1636,i_0_1738,i_0_1756,i_0_1842,i_0_1556,i_0_1560,i_0_1614,i_0_1737,i_0_1742,i_0_1744,i_0_1753,i_0_1802,i_0_1828,i_0_1692,i_0_1574,i_0_1633,i_0_1671,i_0_1606,i_0_1535,i_0_1546,i_0_1665,i_0_1576,i_0_1657,i_0_1884,i_0_1886,i_0_1887,i_0_1153,i_0_1264,i_0_1455,i_0_1778,i_0_1783,i_0_2021,i_0_1984,i_0_1985,i_0_1986]) ).

cnf(i_0_2822,plain,
    ~ c_Finite__Set_Ofolding__image__simple(X1,X1,X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2,hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Finite__Set_Ofold__image(X1,X1,X1,X2,X1,c_Set_Oimage(tc_Nat_Onat,X1,X3,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X4,X5)))))),
    inference(scs_inference,[],[i_0_2252,i_0_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1821,i_0_2813,i_0_1472,i_0_2510,i_0_2112,i_0_2637,i_0_2117,i_0_2135,i_0_2212,i_0_2105,i_0_2107,i_0_2229,i_0_2666,i_0_2163,i_0_2745,i_0_2763,i_0_2185,i_0_2695,i_0_2715,i_0_2395,i_0_2331,i_0_2661,i_0_2738,i_0_2374,i_0_2508,i_0_2634,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2686,i_0_2195,i_0_2293,i_0_2218,i_0_2496,i_0_2499,i_0_2145,i_0_2206,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2175,i_0_2188,i_0_2592,i_0_2126,i_0_2403,i_0_2351,i_0_1329,i_0_2804,i_0_1161,i_0_2247,i_0_1837,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433,i_0_1436,i_0_1527,i_0_1636,i_0_1738,i_0_1756,i_0_1842,i_0_1556,i_0_1560,i_0_1614,i_0_1737,i_0_1742,i_0_1744,i_0_1753,i_0_1802,i_0_1828,i_0_1692,i_0_1574,i_0_1633,i_0_1671,i_0_1606,i_0_1535,i_0_1546,i_0_1665,i_0_1576,i_0_1657,i_0_1884,i_0_1886,i_0_1887,i_0_1153,i_0_1264,i_0_1455,i_0_1778,i_0_1783,i_0_2021,i_0_1984,i_0_1985,i_0_1986,i_0_1987]) ).

cnf(i_0_2823,plain,
    ~ c_Finite__Set_Ofolding__image__simple(X1,X1,X1,X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),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,X2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3,X4)))))),
    inference(scs_inference,[],[i_0_2252,i_0_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1821,i_0_2813,i_0_1472,i_0_2510,i_0_2112,i_0_2637,i_0_2117,i_0_2135,i_0_2212,i_0_2105,i_0_2107,i_0_2229,i_0_2666,i_0_2163,i_0_2745,i_0_2763,i_0_2185,i_0_2695,i_0_2715,i_0_2395,i_0_2331,i_0_2661,i_0_2738,i_0_2374,i_0_2508,i_0_2634,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2686,i_0_2195,i_0_2293,i_0_2218,i_0_2496,i_0_2499,i_0_2145,i_0_2206,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2175,i_0_2188,i_0_2592,i_0_2126,i_0_2403,i_0_2351,i_0_1329,i_0_2804,i_0_1161,i_0_2247,i_0_1837,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433,i_0_1436,i_0_1527,i_0_1636,i_0_1738,i_0_1756,i_0_1842,i_0_1556,i_0_1560,i_0_1614,i_0_1737,i_0_1742,i_0_1744,i_0_1753,i_0_1802,i_0_1828,i_0_1692,i_0_1574,i_0_1633,i_0_1671,i_0_1606,i_0_1535,i_0_1546,i_0_1665,i_0_1576,i_0_1657,i_0_1884,i_0_1886,i_0_1887,i_0_1153,i_0_1264,i_0_1455,i_0_1778,i_0_1783,i_0_2021,i_0_1984,i_0_1985,i_0_1986,i_0_1987,i_0_1988]) ).

cnf(i_0_2824,plain,
    c_Arrow__Order__Mirabelle_Ounanimity(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_F),esk2_2(v_F,v_F))),
    inference(scs_inference,[],[i_0_2252,i_0_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1821,i_0_2813,i_0_1472,i_0_2510,i_0_2112,i_0_2637,i_0_2117,i_0_2135,i_0_2212,i_0_2809,i_0_2105,i_0_2107,i_0_2229,i_0_2666,i_0_2163,i_0_2745,i_0_2763,i_0_2185,i_0_2695,i_0_2715,i_0_2395,i_0_2331,i_0_2661,i_0_2738,i_0_2374,i_0_2508,i_0_2634,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2686,i_0_2195,i_0_2293,i_0_2218,i_0_2496,i_0_2499,i_0_2145,i_0_2206,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2175,i_0_2188,i_0_2592,i_0_2126,i_0_2403,i_0_2351,i_0_1329,i_0_2804,i_0_1161,i_0_2247,i_0_1879,i_0_1837,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433,i_0_1436,i_0_1527,i_0_1636,i_0_1738,i_0_1756,i_0_1842,i_0_1556,i_0_1560,i_0_1614,i_0_1737,i_0_1742,i_0_1744,i_0_1753,i_0_1802,i_0_1828,i_0_1692,i_0_1574,i_0_1633,i_0_1671,i_0_1606,i_0_1535,i_0_1546,i_0_1665,i_0_1576,i_0_1657,i_0_1884,i_0_1886,i_0_1887,i_0_1153,i_0_1264,i_0_1455,i_0_1778,i_0_1783,i_0_2021,i_0_1984,i_0_1985,i_0_1986,i_0_1987,i_0_1988,i_0_1950]) ).

cnf(i_0_2825,plain,
    X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk2_2(X1,X1)),
    inference(rename_variables,[],[i_0_2212]) ).

cnf(i_0_2826,plain,
    c_Arrow__Order__Mirabelle_OIIA(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_F),esk2_2(v_F,v_F))),
    inference(scs_inference,[],[i_0_2252,i_0_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1821,i_0_2813,i_0_1472,i_0_2510,i_0_2112,i_0_2637,i_0_2117,i_0_2135,i_0_2212,i_0_2809,i_0_2825,i_0_2105,i_0_2107,i_0_2229,i_0_2666,i_0_2163,i_0_2745,i_0_2763,i_0_2185,i_0_2695,i_0_2715,i_0_2395,i_0_2331,i_0_2661,i_0_2738,i_0_2374,i_0_2508,i_0_2634,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2686,i_0_2195,i_0_2293,i_0_2218,i_0_2496,i_0_2499,i_0_2145,i_0_2206,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2175,i_0_2188,i_0_2592,i_0_2126,i_0_2403,i_0_2351,i_0_1329,i_0_2804,i_0_1161,i_0_2247,i_0_1879,i_0_1880,i_0_1837,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433,i_0_1436,i_0_1527,i_0_1636,i_0_1738,i_0_1756,i_0_1842,i_0_1556,i_0_1560,i_0_1614,i_0_1737,i_0_1742,i_0_1744,i_0_1753,i_0_1802,i_0_1828,i_0_1692,i_0_1574,i_0_1633,i_0_1671,i_0_1606,i_0_1535,i_0_1546,i_0_1665,i_0_1576,i_0_1657,i_0_1884,i_0_1886,i_0_1887,i_0_1153,i_0_1264,i_0_1455,i_0_1778,i_0_1783,i_0_2021,i_0_1984,i_0_1985,i_0_1986,i_0_1987,i_0_1988,i_0_1950,i_0_1975]) ).

cnf(i_0_2827,plain,
    X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk2_2(X1,X1)),
    inference(rename_variables,[],[i_0_2212]) ).

cnf(i_0_2828,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_2252,i_0_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1821,i_0_2813,i_0_1472,i_0_2510,i_0_2112,i_0_2637,i_0_2117,i_0_2135,i_0_2212,i_0_2809,i_0_2825,i_0_2105,i_0_2107,i_0_2229,i_0_2666,i_0_2163,i_0_2745,i_0_2763,i_0_2185,i_0_2695,i_0_2715,i_0_2395,i_0_2331,i_0_2661,i_0_2738,i_0_2374,i_0_2508,i_0_2634,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2686,i_0_2195,i_0_2293,i_0_2218,i_0_2496,i_0_2499,i_0_2145,i_0_2206,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2175,i_0_2188,i_0_2592,i_0_2126,i_0_2403,i_0_2351,i_0_1329,i_0_2804,i_0_1161,i_0_2247,i_0_1879,i_0_1880,i_0_1837,i_0_1864,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433,i_0_1436,i_0_1527,i_0_1636,i_0_1738,i_0_1756,i_0_1842,i_0_1556,i_0_1560,i_0_1614,i_0_1737,i_0_1742,i_0_1744,i_0_1753,i_0_1802,i_0_1828,i_0_1692,i_0_1574,i_0_1633,i_0_1671,i_0_1606,i_0_1535,i_0_1546,i_0_1665,i_0_1576,i_0_1657,i_0_1884,i_0_1886,i_0_1887,i_0_1153,i_0_1264,i_0_1455,i_0_1778,i_0_1783,i_0_2021,i_0_1984,i_0_1985,i_0_1986,i_0_1987,i_0_1988,i_0_1950,i_0_1975,i_0_1345]) ).

cnf(i_0_2829,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_1345]) ).

cnf(i_0_2830,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_fun(X1,X2),tc_HOL_Obool)),c_FuncSet_OPi(X1,X2,X3,X4)),c_FuncSet_OPi(X1,X2,c_Set_Oinsert(X1,X5,X3),X4))),
    inference(scs_inference,[],[i_0_2252,i_0_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1821,i_0_2813,i_0_2039,i_0_1472,i_0_2510,i_0_2112,i_0_2637,i_0_2117,i_0_2135,i_0_2212,i_0_2809,i_0_2825,i_0_2105,i_0_2107,i_0_2229,i_0_2666,i_0_2163,i_0_2745,i_0_2763,i_0_2185,i_0_2695,i_0_2715,i_0_2395,i_0_2331,i_0_2661,i_0_2738,i_0_2374,i_0_2508,i_0_2634,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2686,i_0_2195,i_0_2293,i_0_2218,i_0_2496,i_0_2499,i_0_2145,i_0_2206,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2175,i_0_2188,i_0_2592,i_0_2126,i_0_2403,i_0_2351,i_0_1329,i_0_2804,i_0_1161,i_0_2247,i_0_1879,i_0_1880,i_0_1837,i_0_1864,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433,i_0_1436,i_0_1527,i_0_1636,i_0_1738,i_0_1756,i_0_1842,i_0_1556,i_0_1560,i_0_1614,i_0_1737,i_0_1742,i_0_1744,i_0_1753,i_0_1802,i_0_1828,i_0_1692,i_0_1574,i_0_1633,i_0_1671,i_0_1606,i_0_1535,i_0_1546,i_0_1665,i_0_1576,i_0_1657,i_0_1884,i_0_1886,i_0_1887,i_0_1153,i_0_1264,i_0_1455,i_0_1778,i_0_1783,i_0_2021,i_0_1984,i_0_1985,i_0_1986,i_0_1987,i_0_1988,i_0_1950,i_0_1975,i_0_1345,i_0_1378]) ).

cnf(i_0_2831,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X2)),
    inference(rename_variables,[],[i_0_2039]) ).

cnf(i_0_2832,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_1378]) ).

cnf(i_0_2833,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)),tc_Nat_Onat)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(scs_inference,[],[i_0_2252,i_0_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1821,i_0_2813,i_0_2039,i_0_1472,i_0_2510,i_0_2112,i_0_2637,i_0_2117,i_0_2135,i_0_2212,i_0_2809,i_0_2825,i_0_2105,i_0_2107,i_0_2229,i_0_2666,i_0_2163,i_0_2745,i_0_2763,i_0_2185,i_0_2695,i_0_2715,i_0_2395,i_0_2331,i_0_2661,i_0_2738,i_0_2374,i_0_2508,i_0_2634,i_0_2612,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2686,i_0_2195,i_0_2293,i_0_2218,i_0_2496,i_0_2499,i_0_2145,i_0_2206,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2175,i_0_2188,i_0_2592,i_0_2126,i_0_2403,i_0_2351,i_0_1329,i_0_2804,i_0_1161,i_0_1739,i_0_2247,i_0_1879,i_0_1880,i_0_1837,i_0_1864,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433,i_0_1436,i_0_1527,i_0_1636,i_0_1738,i_0_1756,i_0_1842,i_0_1556,i_0_1560,i_0_1614,i_0_1737,i_0_1742,i_0_1744,i_0_1753,i_0_1802,i_0_1828,i_0_1692,i_0_1574,i_0_1633,i_0_1671,i_0_1606,i_0_1535,i_0_1546,i_0_1665,i_0_1576,i_0_1657,i_0_1884,i_0_1886,i_0_1887,i_0_1153,i_0_1264,i_0_1455,i_0_1778,i_0_1783,i_0_2021,i_0_1984,i_0_1985,i_0_1986,i_0_1987,i_0_1988,i_0_1950,i_0_1975,i_0_1345,i_0_1378,i_0_1565]) ).

cnf(i_0_2834,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_1739]) ).

cnf(i_0_2835,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_1565]) ).

cnf(i_0_2836,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_2252,i_0_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1821,i_0_2813,i_0_2039,i_0_1472,i_0_2510,i_0_2112,i_0_2637,i_0_2117,i_0_2135,i_0_2212,i_0_2809,i_0_2825,i_0_2105,i_0_2107,i_0_2229,i_0_2666,i_0_2163,i_0_2745,i_0_2763,i_0_2185,i_0_2695,i_0_2715,i_0_2395,i_0_2331,i_0_2661,i_0_2738,i_0_2374,i_0_2508,i_0_2634,i_0_2612,i_0_2708,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2686,i_0_2195,i_0_2293,i_0_2218,i_0_2496,i_0_2499,i_0_2145,i_0_2206,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2175,i_0_2188,i_0_2592,i_0_2126,i_0_2403,i_0_2351,i_0_1329,i_0_2804,i_0_2817,i_0_1161,i_0_1739,i_0_2247,i_0_1879,i_0_1880,i_0_1837,i_0_1864,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433,i_0_1436,i_0_1527,i_0_1636,i_0_1738,i_0_1756,i_0_1842,i_0_1556,i_0_1560,i_0_1614,i_0_1737,i_0_1742,i_0_1744,i_0_1753,i_0_1802,i_0_1828,i_0_1692,i_0_1574,i_0_1633,i_0_1671,i_0_1606,i_0_1535,i_0_1546,i_0_1665,i_0_1576,i_0_1657,i_0_1884,i_0_1886,i_0_1887,i_0_1153,i_0_1264,i_0_1455,i_0_1778,i_0_1783,i_0_2021,i_0_1984,i_0_1985,i_0_1986,i_0_1987,i_0_1988,i_0_1950,i_0_1975,i_0_1345,i_0_1378,i_0_1565,i_0_1637]) ).

cnf(i_0_2837,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_1329]) ).

cnf(i_0_2838,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_2612]) ).

cnf(i_0_2839,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_1637]) ).

cnf(i_0_2840,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(esk32_2(hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(esk32_2(hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X3),X4)) = X4,
    inference(scs_inference,[],[i_0_2252,i_0_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1821,i_0_2813,i_0_2039,i_0_1472,i_0_2510,i_0_2112,i_0_2637,i_0_2768,i_0_2117,i_0_2135,i_0_2212,i_0_2809,i_0_2825,i_0_2105,i_0_2107,i_0_2229,i_0_2666,i_0_2163,i_0_2745,i_0_2763,i_0_2185,i_0_2695,i_0_2715,i_0_2395,i_0_2331,i_0_2661,i_0_2738,i_0_2374,i_0_2508,i_0_2634,i_0_2612,i_0_2708,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2686,i_0_2195,i_0_2293,i_0_2218,i_0_2496,i_0_2499,i_0_2145,i_0_2206,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2175,i_0_2188,i_0_2592,i_0_2126,i_0_2403,i_0_2351,i_0_1329,i_0_2804,i_0_2817,i_0_1161,i_0_1739,i_0_2452,i_0_2247,i_0_1879,i_0_1880,i_0_1837,i_0_1864,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433,i_0_1436,i_0_1527,i_0_1636,i_0_1738,i_0_1756,i_0_1842,i_0_1556,i_0_1560,i_0_1614,i_0_1737,i_0_1742,i_0_1744,i_0_1753,i_0_1802,i_0_1828,i_0_1692,i_0_1574,i_0_1633,i_0_1671,i_0_1606,i_0_1535,i_0_1546,i_0_1665,i_0_1576,i_0_1657,i_0_1884,i_0_1886,i_0_1887,i_0_1153,i_0_1264,i_0_1455,i_0_1778,i_0_1783,i_0_2021,i_0_1984,i_0_1985,i_0_1986,i_0_1987,i_0_1988,i_0_1950,i_0_1975,i_0_1345,i_0_1378,i_0_1565,i_0_1637,i_0_1725]) ).

cnf(i_0_2841,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_2112]) ).

cnf(i_0_2842,plain,
    ( 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)
    | X3 = X4 ),
    inference(rename_variables,[],[i_0_1725]) ).

cnf(i_0_2843,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_2252,i_0_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1821,i_0_2813,i_0_2039,i_0_1472,i_0_2510,i_0_2112,i_0_2637,i_0_2768,i_0_2117,i_0_2135,i_0_2212,i_0_2809,i_0_2825,i_0_2105,i_0_2107,i_0_2229,i_0_2666,i_0_2240,i_0_2163,i_0_2745,i_0_2763,i_0_2185,i_0_2695,i_0_2715,i_0_2395,i_0_2331,i_0_2661,i_0_2738,i_0_2374,i_0_2508,i_0_2634,i_0_2612,i_0_2708,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2686,i_0_2195,i_0_2293,i_0_2218,i_0_2496,i_0_2499,i_0_2145,i_0_2206,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2175,i_0_2188,i_0_2592,i_0_2126,i_0_2403,i_0_2351,i_0_1329,i_0_2804,i_0_2817,i_0_1161,i_0_1739,i_0_2452,i_0_2247,i_0_1840,i_0_1879,i_0_1880,i_0_1837,i_0_1864,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433,i_0_1436,i_0_1527,i_0_1636,i_0_1738,i_0_1756,i_0_1842,i_0_1556,i_0_1560,i_0_1614,i_0_1737,i_0_1742,i_0_1744,i_0_1753,i_0_1802,i_0_1828,i_0_1692,i_0_1574,i_0_1633,i_0_1671,i_0_1606,i_0_1535,i_0_1546,i_0_1665,i_0_1576,i_0_1657,i_0_1884,i_0_1886,i_0_1887,i_0_1153,i_0_1264,i_0_1455,i_0_1778,i_0_1783,i_0_2021,i_0_1984,i_0_1985,i_0_1986,i_0_1987,i_0_1988,i_0_1950,i_0_1975,i_0_1345,i_0_1378,i_0_1565,i_0_1637,i_0_1725,i_0_1763]) ).

cnf(i_0_2844,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_2240]) ).

cnf(i_0_2845,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
    inference(rename_variables,[],[i_0_1840]) ).

cnf(i_0_2846,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_1763]) ).

cnf(i_0_2847,plain,
    $false,
    inference(scs_inference,[],[i_0_2252,i_0_2091,i_0_2650,i_0_2259,i_0_2554,i_0_2262,i_0_1821,i_0_2813,i_0_2039,i_0_1472,i_0_2114,i_0_2510,i_0_2112,i_0_2637,i_0_2768,i_0_2117,i_0_2135,i_0_2212,i_0_2809,i_0_2825,i_0_2105,i_0_2107,i_0_2229,i_0_2666,i_0_2240,i_0_2163,i_0_2745,i_0_2763,i_0_2185,i_0_2695,i_0_2715,i_0_2395,i_0_2331,i_0_2661,i_0_2738,i_0_2374,i_0_2508,i_0_2634,i_0_2612,i_0_2708,i_0_2172,i_0_2609,i_0_2191,i_0_2154,i_0_2686,i_0_2195,i_0_2293,i_0_2218,i_0_2496,i_0_2499,i_0_2145,i_0_2206,i_0_2588,i_0_2169,i_0_2669,i_0_2672,i_0_2175,i_0_2188,i_0_2592,i_0_2126,i_0_2403,i_0_2351,i_0_2722,i_0_1329,i_0_2804,i_0_2817,i_0_1161,i_0_1739,i_0_2452,i_0_2247,i_0_1840,i_0_1879,i_0_1880,i_0_1837,i_0_1864,i_0_1137,i_0_1435,i_0_1752,i_0_1736,i_0_1192,i_0_1208,i_0_1232,i_0_1254,i_0_1272,i_0_1275,i_0_1278,i_0_1279,i_0_1296,i_0_1306,i_0_1310,i_0_1317,i_0_1318,i_0_1324,i_0_1331,i_0_1359,i_0_1365,i_0_1380,i_0_1381,i_0_1418,i_0_1457,i_0_1506,i_0_1514,i_0_1545,i_0_1548,i_0_1550,i_0_1552,i_0_1605,i_0_1663,i_0_1672,i_0_1700,i_0_1703,i_0_1745,i_0_2023,i_0_1239,i_0_1267,i_0_1309,i_0_1416,i_0_1432,i_0_1433,i_0_1436,i_0_1527,i_0_1636,i_0_1738,i_0_1756,i_0_1842,i_0_1556,i_0_1560,i_0_1614,i_0_1737,i_0_1742,i_0_1744,i_0_1753,i_0_1802,i_0_1828,i_0_1692,i_0_1574,i_0_1633,i_0_1671,i_0_1606,i_0_1535,i_0_1546,i_0_1665,i_0_1576,i_0_1657,i_0_1884,i_0_1886,i_0_1887,i_0_1153,i_0_1264,i_0_1455,i_0_1778,i_0_1783,i_0_2021,i_0_1984,i_0_1985,i_0_1986,i_0_1987,i_0_1988,i_0_1950,i_0_1975,i_0_1345,i_0_1378,i_0_1565,i_0_1637,i_0_1725,i_0_1763,i_0_1348]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SCT165+1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.12  % Command    : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33  % Computer : n019.cluster.edu
% 0.16/0.33  % Model    : x86_64 x86_64
% 0.16/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33  % Memory   : 8042.1875MB
% 0.16/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33  % CPULimit   : 300
% 0.16/0.33  % WCLimit    : 300
% 0.16/0.33  % DateTime   : Tue May  5 02:01:29 EDT 2026
% 0.16/0.33  % CPUTime    : 
% 0.16/0.34  % start to proof: theBenchmark
% 5.46/5.80  % Version  : CSE_E---1.7
% 5.46/5.80  % Problem  : theBenchmark.p
% 5.46/5.80  % SZS status Theorem for theBenchmark.p
% 5.46/5.80  % SZS output start CNFRefutation
% See solution above
% 15.27/15.63  % Total time : 5.458s
%------------------------------------------------------------------------------